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Content, Cognition, and Communication - Reflexivity, Reflections on Reflexivity, Demonstrating and Necessity

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Content, Cognition, and Communication


Abstract: This volume brings together Nathan Salmon's papers from the early 1980s to 2006 on closely connected topics central to analytic philosophy, on the theory of direct reference, names and descriptions, demonstratives, reflexivity, propositional attitudes, apriority, meaning and use, and more generally, the distinction between semantics and pragmatics.




Introduction to Volume II

The present volume and its companion encompass most of the papers I wrote during the two decades since I left ivy to return to sunnier shores. Together with my previous books, Reference and Essence (second edition, Prometheus Books, 1981, 2004) and Frege's Puzzle (second edition, Atascadero, Calif.: Ridgeview, 1986, 1991), these volumes represent my thought to date on a variety of topics philosophical. I am grateful to Ernest Sosa, who first suggested that I compile the collection. With his suggestion came the realization: ‘If not now, when?’

I have been deeply influenced by the writings of two dead, white, European males: Gottlob Frege and Bertrand Russell. I have also been deeply influenced by intellectual interactions with a number of remarkable American philosophers I have been privileged to know personally. Deserving of special mention are my former teachers, Tyler Burge, Keith Donnellan, Donald Kalish, and most especially, Alonzo Church, David Kaplan, and Saul Kripke. Standing on the shoulders of giants, the view has been breathtaking. For more than a quarter century I have strived—not always successfully—to strike a happy balance between independent thought and recognition of the fascinating and deeply significant insights of extraordinarily gifted minds. The pages that follow are a result of that endeavor.

In his second lecture on The Philosophy of Logical Atomism, Russell said, ‘the point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it’. Presumably, each of the transitions among the steps that lead from simple triviality to the paradoxically incredible must be like the starting point itself: so simple as not to seem worth stating. (Far too often in contemporary philosophy, this feature of the enterprise is undervalued, even ignored.) There is more to philosophy than the paradox of the heap, of course, and no one has demonstrated that better than Russell. Still, Russell's work often did conform to his succinct characterization of philosophy as the attempt to derive the incredible from the trivial. My own objective has often been similar to Russell's—more modest undoubtedly, but only somewhat. It has been to proceed by a sequence of obviously valid inferences (though not always uncontroversial) from clearly correct premisses (though not generally indubitable) to a significant but unpopular thesis (though not typically incredible), or at least a rather surprising one.

In short, I have sought to establish (and insofar as possible, to prove) the surprising. If I should be accused of valuing this philosophical style because it is what I do, rather than the other way around, I shall take it as a compliment. I have argued for theses that fly in the face of conventional wisdom not because those theses are unfashionable, but because they are in each case, to the best of my ability to make a determination, the unrecognized, unappreciated truth of the matter. How far I have succeeded is for the reader to decide.

end p.xi


Part I

The first part of the present volume is concerned with the theory of direct reference. Frege and Russell held that an ordinary proper name functions fundamentally like a definite description (in English, a singular noun phrase beginning with the definite article ‘the’, or instead with a possessive adjective, as with ‘Ryan's daughter’). For Frege this meant that a name expresses as its semantic content a Sinn (traditionally translated as sense)—a conceptual ‘mode of presentation’, or manner of specification, which determines the name's designatum to be whatever uniquely fits that manner of specification. Russell also held, though Frege did not, that besides ordinary proper names there are, or at least there could be, logically proper names, i.e. terms about which it is true that the semantic content is instead simply the object designated, nothing more and nothing less. The semantic content of a sentence employing a Russellian logically proper name is a singular proposition—a proposition that is about the name's designatum by virtue of including that very designatum, rather than a Fregean sense, as a constituent. The paradigm of a logically proper name is an individual variable, whose only semantic content, under an assignment of a value, is its assigned value. A variable must be a logically proper name; otherwise quantification into a context of propositional attitude would not express a de re attitude. Suppose, for example, that Jones believes of the planet Venus, de re, that it is a star, by virtue of believing that the Evening Star is a star. Then the sentence,

(0x002203x)[x is the second closest planet to the sun & Jones believes that x is a star],

should express something true. By standard quantificational semantics, this sentence is true if and only if its component open sentence,

Jones believes that x is a star

is true under the assignment of the second closest planet to the sun as value for the variable ‘x’, i.e., if and only if Venus satisfies the open sentence. And this is so, in turn, if and only if Jones believes the proposition expressed by the simpler open sentence ‘x is a star’ under the same assignment of Venus as the value of ‘x’. Although Venus is specified as the second closest planet to the sun in being assigned to ‘x’, the variable is not ipso facto assigned that manner of specification as its content. If it were, then the proposition expressed by ‘x is a star’ under the assignment would be that the second closest planet to the sun is a star—which Jones does not believe. Instead, the variable functions as a logically proper name of its value. Accordingly, the semantic content of an open sentence, like ‘x is ingenious but ingenuous’, under an assignment of a value to the free variable ‘x’, is the singular proposition about that assigned value that he or she (or it) is ingenious but ingenuous.

Saul Kripke and Keith Donnellan demonstrated, to my mind beyond a reasonable doubt, that ordinary proper names function very differently from definite descriptions—whether definite descriptions are taken to be singular terms, as with Frege, or

end p.xii


taken to be quantifiers, as with Russell. Kaplan demonstrated, again I think conclusively, that ordinary demonstratives are essentially Russellian logically proper names. A few philosophers, myself included, have argued for the doctrine of Millianism—that ordinary proper names too are Russellian logically proper names. One argument for this, provided in ‘A Millian Heir Rejects the Wages of Sinn’, comes directly from the analysis of de re attitudes. Analogously with quantification into an attribution of belief, in order for ‘Jones believes of the second closest planet to the sun that it is a star’ to be true, the sub-sentence ‘Jones believes that it is a star’ must be true under the anaphoric assignment of the second closest planet to the sun, i.e., Venus, to the pronoun ‘it’ as its designatum. The proposition expressed by ‘It is a star’ under this assignment must be the singular proposition about Venus that it is a star; otherwise the original sentence would be de dicto rather than de re. Hence the ‘it’ is a logically proper name. As goes the variable, so goes the pronoun, and so too the constant. For the only difference between a variable and a constant is that the latter is constant while the former is variable (and whatever differences follow from this). The constant is married, while the variable is playing the field. A variable is basically a constant wannabe. (Or is it the other way around?) If either is a logically proper name, so is the other. Just as the variable ‘x’ is a logically proper name of its assigned designatum—and similarly the anaphoric pronoun ‘it’—so too is the name ‘Venus’.

Several chapters of the present volume are concerned with Millianism. In ‘Reflexivity’ and ‘Reflections on Reflexivity’, I argue that Millianism should maintain a genuine distinction between the proposition that Cicero admires Tully and the proposition that Cicero is a self-admirer. ‘Are General Terms Rigid?’ answers the title question: As with singular terms, some general terms are rigid designators, some not.

‘Demonstrating and Necessity’ concerns the nature of both bare demonstratives, like ‘that’ used deictically, and complex demonstratives, i.e. demonstrative phrases of the form ‘that F’. Following Frege, Kaplan has argued that the demonstrative itself is essentially incomplete and that the demonstration that typically accompanies the use of a demonstrative is an essential component of the complete expression uttered, which is a demonstrative-cum-demonstration. I argue contrary to Frege and Kaplan that the demonstrative itself (whether bare or complex) is the complete expression, whereas the accompanying demonstration is an additional feature of the context of utterance. Some interesting consequences of this alternative to Kaplan's account are explored, focusing on a unified solution to Frege's Puzzle (How can the informative 0x00231c0x0003b1=0x0003b20x00231d, if true, differ at all in content from the uninformative 0x00231c0x0003b1=0x0003b10x00231d?), as it arises with demonstratives as well as proper names.

‘A Theory of Bondage’ presents a non-classical account of the semantics of expression-occurrences in accordance with Frege's admonition that the designation and semantic content of an expression must be relativized to that expression's position within a sentence. The theory is brought to bear on the binding of variables and on recent fallacious arguments concerning anaphoric pronouns and quantification into compound designators.

end p.xiii


Part II

‘How to Measure the Standard Metre’, ‘How Not to Become a Millian Heir’, ‘Relative and Absolute Apriority’, and ‘Analyticity and Apriority’ concern particular consequences of Millianism with respect to the semantic-epistemological status of certain special kinds of sentences. Kripke has forcefully argued that certain true identity sentences of the sort invoked in Frege's Puzzle—including ‘Hesperus is Phosphorus’ and ‘Cicero is Tully’—express necessary truths even though they are synthetic and a posteriori. His arguments appear to have persuaded the philosophical community. He has also forcefully argued that certain sentences made true through a special kind of terminological stipulation, including Wittgenstein's example, ‘The Metre Stick (assuming it exists) is exactly one metre long at time t 0 (which Wittgenstein evidently thought neither true nor false), express contingent truths that are knowable a priori. Kaplan has made a similar claim about certain indexical sentences whose truth is guaranteed by the indexical logic, e.g., ‘I am here now’.

I agree that these sentences (most of them, anyway) are of a rather special and peculiar sort. I argue that the identity sentences arising in Frege's Puzzle, while they do indeed express necessary truths, are in fact analytic, in the sense that they are true solely as a consequence of pure semantics, without invoking any non-semantic facts, and the necessary truths they express are in fact knowable a priori. (I believe this notion of sentential truth solely by virtue of pure semantics underlies the traditional conception of analyticity.) Turning Kaplan and Kripke on their heads, I also argue that while Wittgenstein's metre sentence and indexical-logically true sentences do indeed typically express contingent truths, those truths are not in general a priori. Instead many of them are a posteriori even though the sentences in question are analytic, contrary to Kripke's characterization. (Kaplan's example of ‘I am here now’ is not even analytic; it is synthetic a posteriori.) In ‘Demonstrating and Necessity’ I offer what I believe is a purer example of the same general phenomenon of the analytic-contingent-a posteriori: ‘That student (if existent) is a student.’


Part III

‘Illogical Belief’, ‘The Resilience of Illogical Belief’, ‘Being of Two Minds’, ‘Relational Belief’, and ‘Is De Re Belief Reducible to De Dicto?’ develop and continue a substantial project undertaken in Frege's Puzzle: the reconciliation of Millianism with a host of problems posed by locutions of propositional attitude, especially by attributions of belief. Chief among these problems is the apparent failure of substitution of co-referential names (or relevantly similar devices). Apparent substitution failures include substitutions within iterations (a problem originally introduced by Benson Mates), as in ‘Tyler disbelieves that Pierre believes that London is pretty.’ Also addressed at length is Quine's question in ‘Quantifiers and Propositional Attitudes’ concerning belief de re, and Kripke's question ‘A Puzzle about Belief’ concerning belief de dicto. Quine asks whether Ralph believes

end p.xiv


of Ortcutt, de re (‘relationally’), that he is a spy, when Ralph believes de dicto (‘notionally’) that the man in the brown hat is a spy but also that the man seen at the beach is not a spy, and when, unbeknownst to Ralph, both men are Ortcutt. Kripke asks whether Pierre believes de dicto that London is pretty when he evidently believes (also de dicto) that the city known to Frenchmen as ‘Londres’ is pretty whereas the city known to its own denizens as ‘London’ is not, and when, unbeknownst to Pierre, these cities are one.

The first step toward solving all of these problems is to recognize that insofar as one believes a singular proposition about a person, place, or thing that one fails to recognize, one likewise fails to recognize the very singular proposition one believes. As a result, one's failure to recognize some person, place, or thing nearly inevitably results in one harboring cognitively dissonant attitudes without realizing it toward one and the same proposition about that person, place, or thing—for example, believing the proposition while also disbelieving, doubting, or suspending judgment in taking it to be a distinct and independent proposition. It may be supposed that if someone has cognitive access to each of a pair of things, x and y (which may or may not be the same), and he or she takes them to be distinct, then there are distinct ways of taking something, or guises, g 1 and g 2 , such that he or she has cognitive access to x under g 1 and has cognitive access to y under g 2 . Belief of a proposition is a cognitive attitude toward that proposition, but whether one bears this attitude is relative to the guise under which one apprehends the proposition. Just as Ralph believes that Ortcutt is a spy under one of that proposition's guises while failing to believe it under another, so Pierre believes that London is pretty under one of that proposition's guises while failing to believe under another. An exactly similar situation can obtain with regard to the propositions that Cicero is Cicero, that Venus is Venus, that Superman is Superman.

To believe of something x, de re, that it is such-and-such is to believe the singular proposition about x that it is such-and-such. It is in this sense, but only in this sense, that de re belief is reducible to de dicto. To believe a proposition p is to believe it under some guise or other. To disbelieve p is to believe its denial under some guise or other. One suspends judgment about p if there is a proposition guise under which one fails either to believe or to disbelieve p. One doubts whether p if one either disbelieves p or suspends judgment about p under some guise. Though it is logically impossible to believe and fail to believe one and the same proposition, one can easily believe while also disbelieving or suspending judgment with regard to the same proposition, by believing it under one guise and doubting under another.

Specifically, Ralph believes of Ortcutt that he is a spy even while also doubting whether Ortcutt is a spy, and Pierre believes that London is pretty even while doubting whether London is pretty. Worse than that, contrary to Quine and contrary to Kripke, Ralph and Pierre believe straightforwardly contradictory propositions: that Ortcutt is a spy and Ortcutt is not a spy; and that London is pretty and London is not pretty. Ralph would not express his belief with the words ‘Ortcutt is a spy and Ortcutt is not a spy’, nor would Pierre express this belief with the words ‘London is pretty and London is not pretty.’ Indeed, both would dissent from such a formulation, precisely because both rightly disbelieve the relevant proposition taking it thus

end p.xv


presented, as an explicit contradiction. Instead, Ralph expresses his belief by uttering ‘He is a spy, but he isn't’, pointing with the first ‘he’ to the man in the brown hat, with the second to Ortcutt at the beach. Similarly, Pierre expresses his belief with the words ‘Londres is pretty but London is not’, not realizing that this sentence expresses a contradictory proposition. He is in no position to infer, for example, (and he does not, indeed could not, believe) the trivial consequence that London is both pretty and not pretty. In order to draw even the simplest inferences—in order to recognize the validity of the inference of that London is both F and G from that London is F and London is G, or the inference of that London is pretty from that it is not the case that London isn't pretty, or even the inference of that London is pretty from itself—one must recognize the relevant proposition as it occurs within and among premisses and conclusion. Absence such recognition, one is unable to reason in a way that would be second nature in the presence of such recognition. We justifiably criticize or censure someone for being illogical only when his or her failure to reason correctly is not a direct result of recognition failure.

From the present point of view, Kripke's puzzle is reducible to Quine's. Or is it the other way around? Either way, they are essentially the same. So are their solutions.


Part IV

The papers in this section are all about the distinction between meaning and use, or more generally, the distinction between semantics and pragmatics. The delineation of the exact relationship between meaning and use is extremely difficult, and (partly as a result) highly controversial. Blurring of the distinction is commonplace, even fashionable. Worse, respect for the distinction has been suppressed through professional authoritative abuse. It is my considered judgment that the most common source of error in the philosophy of language—and consequently the most important impediment to progress—has long been, and remains, the mistaking of pragmatic phenomena as properly semantic. Confusion between semantics and pragmatics is rampant. In these papers I defend the legitimacy of the distinction with special reference to a widely discussed distinction between two kinds of uses of descriptive phrases.

It is ironic that the theory of direct reference—most directly applicable to simple proper names, individual variables, pronouns, and indexical (context-sensitive) words—embarked from its least promising turf: the definite description. If there are any singular terms to which the direct-reference theory does not apply, and instead an essentially Fregean account directly applies, they are definite descriptions. (A version of the Fregean theory applies also to predicates and to whole sentences.) Nevertheless, the contemporary incarnation of direct-reference theory began in 1966 with the publication of Keith Donnellan's seminal ‘Reference and Definite Descriptions’. Donnellan pointed to a distinction between significantly distinct ways of using a definite description. On the referential use, the speaker has a particular individual object in mind, which is presumed to answer to the description, and the speaker's use is directed toward that object, as that to which the speaker is referring. An attributive use, by contrast, is not directed toward any object in particular. Instead,

end p.xvi


in using ‘the such-and-such’, the speaker intends primarily to make a general remark to the effect that (or to ask a general question whether, etc.) whoever or whatever is (uniquely) such-and-such is thus-and-so. An attributive use of a description yields the familiar Russellian truth conditions for the sentence uttered. Donnellan argued that a referential use, by contrast, results in the sentence expressing a singular proposition about the object the user has in mind, regardless of whether that object actually answers to the description used. Others, notably Kripke, objected that the referential-attributive distinction is entirely pragmatic, and has no bearing on such semantic issues as content or truth conditions for the sentence uttered.

In ‘Assertion and Incomplete Definite Descriptions’ and ‘The Pragmatic Fallacy’, I argue that whenever asserting that the such-and-such is thus-and-so, by uttering a sentence with exactly this content, the speaker typically also asserts a singular proposition about the such-and-such, to the effect that he, she, or it is thus-and-so. In ‘The Good, the Bad, and the Ugly’, some interesting consequences are investigated, while still other types of uses of definite descriptions are examined. One alleged consequence that it is fallacious to draw, however, is that the sentence uttered expresses the singular proposition with respect to the context of the speaker's utterance. The sentence does one thing, the speaker another. The distinction between what the sentence says (or designates) and what its user says highlights two competing conceptions of the enterprise known as semantics, explored in ‘Two Conceptions of Semantics’. On the speech-act centered conception (perhaps the dominant conception at the turn of the millennium), the designation of a term, the truth-value of a sentence, the semantic content of an expression—all of these fundamentally derive from what the speaker accomplishes in using the expression. On the expression-centered conception, inherited from Frege and Russell—and to which I remain fiercely loyal—an expression's semantics enjoys a kind of autonomy from the speaker, allowing for the possibility of divergence, even widespread and systematic deviation, between what the expression and its user mean.


Part I Direct Reference


1 A Millian Heir Rejects the Wages of Sinn (1990)*


Nathan Salmon


It is argued, in sharp contrast to established opinion, that the linguistic evidence arising out of propositional-attitude attributions strongly supports Millianism (the doctrine that the entire contribution to the proposition content of a sentence made by a proper name is simply the name's referent) without providing the slightest counter-evidence. This claim is supported through a semantic analysis of such de re attributions as ‘Jones believes of Venus that it is a star.’ The apparent failure of substitutivity of co-referential names in propositional-attitude attributions is shown to be evidentially irrelevant through consideration of analogous phenomena involving straightforward synonyms.

I

In Frege's Puzzle [27] I defended a Millian theory of the information contents of sentences involving proper names or other simple (noncompound) singular terms. The central thesis is that ordinary proper names, demonstratives, other single-word indexicals or pronouns (such as ‘he’), and other simple singular terms are, in a given possible context of use, Russellian ‘genuine names in the strict logical sense’.1 Put more fully, I maintain the following anti-Fregean doctrine: that the contribution made by an ordinary proper name or other simple singular term to securing the information content of, or the proposition expressed by, declarative sentences (with respect to a given possible context of use) in which the term occurs (outside of the scope of nonextensional operators, such as quotation marks) is just the referent of the term, or the bearer of the name (with respect to that context of use). In the terminology of Frege's Puzzle, I maintain that the information value of an ordinary proper name is just its referent.2

end p.3


Another thesis that I maintain in Frege's Puzzle—and which both Frege and Russell more or less accepted—is that the proposition that is the information content of a declarative sentence (with respect to a given context) is structured in a certain way, and that its structure and constituents mirror, and are in some way readable from, the structure and constituents of the sentence containing that proposition.3 By and large, a simple (noncompound) expression contributes a single entity, taken as a simple (noncomplex) unit, to the information content of a sentence in which the expression occurs, whereas the contribution of a compound expression (such as a phrase or sentential component) is a complex entity composed of the contributions of the simple components.4 Hence, the contents of beliefs formulatable using ordinary proper names, demonstratives, or other simple singular terms, are on my view so-called singular propositions (David Kaplan), i.e., structured propositions directly about some individual, which occur directly as a constituent of the proposition. This thesis (together with certain relatively uncontroversial assumptions) yields the consequence that de re belief (or belief of) is simply a special case of de dicto belief (belief that). To believe of an individual x, de re, that it (he, she) is F is to believe de dicto the singular proposition about (containing) x that it (he, she) is F, a proposition that can be expressed using an ordinary proper name for x. Similarly for the other propositional attitudes.

end p.4


Here I will elaborate and expand on certain aspects of my earlier defense of Millian theory, and present some new arguments favoring Millianism. It is commonly held that Millianism runs afoul of common-sense belief attributions, and other propositional-attitude attributions, in declaring intuitively false attributions true. Ironically, the main argument I shall propose here essentially relies on common-sense belief attributions and the semantics of the English phrase ‘believes that’. I shall argue, in sharp contrast to established opinion, that the seemingly decisive evidence against Millianism from the realm of propositional-attitude attributions is no evidence at all, and is in fact evidentially irrelevant and immaterial. If I am correct, common-sense propositional-attitude attributions, insofar as they provide any evidence at all, strongly support Millianism without providing even the slightest counter-evidence (in the way that is commonly supposed).

Historically, the most influential objection to the sort of theory I advocate derives from Frege's notorious ‘Hesperus’–‘Phosphorus’ puzzle. The sentence ‘Hesperus is Phosphorus’ is informative; its information content apparently extends knowledge. The sentence ‘Hesperus is Hesperus’ is uninformative; its information content is a ‘given’. According to my theory, the information content of ‘Hesperus is Hesperus’ consists of the planet Venus, taken twice, and the relation of identity (more accurately, the relation of identity-at-t, where t is the time of utterance). Yet the information content of ‘Hesperus is Phosphorus’, according to this theory, is made of precisely the same components, and apparently in precisely the same way.5 Assuming a plausible principle of compositionality for propositions, or pieces of information—according to which if p and q are propositions that involve the very same constituents arranged in the very same way, then p and q are the very same proposition—the theory ascribes precisely the same information content to both sentences. This seems to fly in the face of the fact that the two sentences differ dramatically in their informativeness.

This puzzle is easily transformed into an argument against Millian theory, by turning its implicit assumptions into explicit premisses. The major premiss, which I call Frege's Law, connects the concept of informativeness (or that, in Frege's words, of ‘containing a very valuable extension of our knowledge’) with that of cognitive information content (what Frege called ‘Erkenntniswerte’, or ‘cognitive value’):

If a declarative sentence S has the very same cognitive information content as a declarative sentence S′, then S is informative if and only if S′ is.

A second premiss is the compositionality principle for propositions. A third critical premiss consists in the simple observation that whereas ‘Hesperus is Phosphorus’ is informative, ‘Hesperus is Hesperus’ is not. Assuming that the information contents of ‘Hesperus is Phosphorus’ and ‘Hesperus is Hesperus’ do not differ at all in structure

or mode of composition, it follows that they differ in their constituents.6 This points to a difference in information value between the names ‘Hesperus’ and ‘Phosphorus’. Since these names are co-referential, it cannot be that the information value of each is simply its referent.

As I pointed out in Frege's Puzzle (pp. 73–76), there is a very general difficulty with this Fregean argument: an exactly similar argument can be mounted against any of a wide variety of theories of information value, including Frege's own theory that the information value of a term consists in an associated purely conceptual representation. It happens that I, like Hilary Putnam, do not have the slightest idea what characteristics differentiate beech trees from elm trees, other than the fact that the English term for beeches is ‘beech’ and the English term for elms is ‘elm’.7 The purely conceptual content that I attach to the term ‘beech’ is the same that I attach to the term ‘elm’, and it is a pretty meager one at that. My concept of elm wood is no different from my concept of beech wood. Nevertheless, an utterance of the sentence ‘Elm wood is beech wood’ would (under the right circumstances) be highly informative for me. In fact, I know that elm wood is not beech wood. At the same time, of course, I know that elm wood is elm wood. By an argument exactly analogous to the one constructed from Frege's puzzle about the informativeness of ‘Hesperus is Phosphorus’ we should conclude that the information value of ‘elm’ or ‘beech’ is not the conceptual content.8

This argument employs the same general strategy, and mostly the very same premisses (including Frege's Law and the compositionality principle for propositions), as the original Fregean argument in connection with ‘Hesperus’ and ‘Phosphorus’. This generalized Fregean strategy may be applied against virtually any minimally plausible and substantive theory of information value. In this particular application of the generalized strategy, the relevant informative identity statement is not even true, but that does not matter to the general strategy. The truth of an informative identity statement is required only in the application of the general argument against theories that locate information value, at least in part, in reference. In the general case, only informativeness is required. False identity statements are always informative—so informative, in fact, as to be misinformative. Thus, virtually any substantive theory of information value imaginable reintroduces a variant of Frege's puzzle (or else it is untenable on independent grounds, such as Kripke's modal arguments against orthodox Fregean theory).

The sheer scope of the generalized Fregean strategy—the fact that, if sound, it is applicable to virtually any substantive theory of information value—would seem to indicate that the strategy involves some error. That the generalized strategy does indeed involve some error can be demonstrated through an application of the generalized strategy to a situation involving straightforward (strict) synonyms for which it is uncontroversial that information value is exactly preserved. Suppose that foreign-born Sasha learns the words ‘ketchup’ and ‘catsup’ not by being taught that they are perfect synonyms, but by actually consuming the condiment and reading the labels on the bottles. Suppose further that, in Sasha's idiosyncratic experience, people typically have the condiment called ‘catsup’ with their eggs and hash browns at breakfast, whereas they routinely have the condiment called ‘ketchup’ with their hamburgers at lunch. This naturally leads Sasha to conclude, erroneously, that ketchup and catsup are different condiments that happen to share a similar taste, color, consistency, and name. He thinks to himself, ‘Ketchup is a sandwich condiment, but no one in his right mind would eat a sandwich condiment with eggs at breakfast; so catsup is not a sandwich condiment.’ Whereas the sentence ‘Ketchup is ketchup’ is uninformative for Sasha, the sentence ‘Catsup is ketchup’ is every bit as informative as ‘Hesperus is Phosphorus’. Applying the generalized Fregean strategy, we would conclude that the terms ‘catsup’ and ‘ketchup’ differ in information value for Sasha. But this is clearly wrong. The terms ‘ketchup’ and ‘catsup’ are perfect synonyms in English. Some would argue that they are merely two different spellings of the very same


English word.9 Most of us who have learned these words (or these spellings of the single word) probably learned one of them in an ostensive definition of some sort, and the other as a strict synonym (or as an alternative spelling) of the first. Some of us learned ‘ketchup’ first and ‘catsup’ second; for others the order was the reverse. Obviously, it does not matter which is learned first and which second. Either word (spelling) may be learned by ostensive definition. If either may be learned by ostensive definition, then both may be. Indeed, Sasha has learned both words (spellings) in much the same way that nearly everyone else has learned at least one of them: by means of a sort of ostensive definition. This manner of acquiring the two words (spellings) is unusual, but not impossible. Sasha's acquisition of these words (spellings) prevented him from learning at the outset that they are perfect synonyms, but the claim that he therefore has not learned both is highly implausible. Each word (spelling) was learned by Sasha in much the same way that some of us learned it. Even in Sasha's idiolect, then, the two words (spellings) are perfectly synonymous, and therefore share the same information value. Since this contradicts the finding generated by the generalized Fregean strategy, the generalized Fregean strategy must involve some error. This discredits the original Fregean argument.10

What is the error? It is tempting to place the blame on Frege's Law. In Sasha's case, the sentences ‘Catsup is ketchup’ and ‘Ketchup is ketchup’ have the very same information content, yet it seems that the first is informative and the second is not. This would be a mistake. A sentence is informative in the sense invoked in Frege's Law only insofar as its information content is a ‘valuable extension of our knowledge’, or is knowable only a posteriori, or is not already ‘given’, or is nontrivial, etc. There is some such property P of propositions such that a declarative sentence S is informative in the only sense relevant to Frege's Law if and only if its information content has P. Once the informativeness or uninformativeness of a sentence is properly seen as a derivative semantic property of the sentence, one that the sentence has only in virtue of encoding the information that it does, Frege's Law may be seen as a special instance of Leibniz's Law, the doctrine that things that are the same have the same properties: if the information content of S is the information content of S′, then the information content of S has the informative-making property P if and only if the information content of S′ does. Since Frege's Law is a logical truth, it is unassailable.

By the same token, the sentence ‘Catsup is ketchup’ is definitely not informative in this sense. The proposition it semantically contains is just the information that ketchup is ketchup, a proposition that clearly lacks the relevant informative-making property P. The sentence ‘Catsup is ketchup’, unlike the sentences ‘Ketchup is ketchup’ and ‘Catsup is catsup’, is ‘informative’ in various other senses. If uttered under the right circumstances, the former can convey to someone like Sasha that the sentence itself is true, and hence that the words (or spellings) ‘ketchup’ and ‘catsup’ are English synonyms, or at least co-referential. To someone who already understands ‘ketchup’ but not ‘catsup’, an utterance of the sentence can convey what ‘catsup’ means. These pieces of linguistic information about English do have the informative-making property P, but in order for a sentence to be informative in the relevant sense its very information content itself must have the informative-making property P. It is not sufficient that utterances of the sentence typically impart information that has P, if that imparted information is not included in the semantic information content of the sentence. The question of information value concerns semantically contained information, not pragmatically imparted information.

Exactly analogously, once the word ‘informative’ is taken in the relevant sense, thereby rendering Frege's Law a truth of logic, one of the other crucial premisses of the original Fregean argument against Millian theory is rendered moot. Specifically, with the word ‘informative’ so understood, and with a sharp distinction between semantically contained information and pragmatically imparted information kept in mind, the assumption that the sentence ‘Hesperus is Phosphorus’ is informative in the relevant sense requires special justification. To be sure, an utterance of the sentence typically imparts information that is more valuable than that typically imparted by an utterance of ‘Hesperus is Hesperus’. For example, it may impart the nontrivial linguistic information about the sentence ‘Hesperus is Phosphorus’ itself that it is true, and hence that the names ‘Hesperus’ and ‘Phosphorus’ are co-referential. But presumably this is not semantically contained information. The observation that ‘Hesperus is Phosphorus’ can be used to convey information that has the informative-making property P does nothing to show that the sentence's semantic content itself has the property P. It is by no means obvious that this sentence, stripped naked of its pragmatic impartations and with only its properly semantic information content left, is any more informative in the relevant sense than ‘Hesperus is Hesperus’. I claim that the information content of ‘Hesperus is Phosphorus’ is the trivial proposition about the planet Venus that it is it—a piece of information that clearly lacks the informative-making property P. It is by no means certain, as the original Fregean argument maintains, that the difference in ‘cognitive value’ we seem to hear between ‘Hesperus is Hesperus’ and ‘Hesperus is Phosphorus’ is not due entirely to a difference in pragmatically imparted information. Yet, until we can be certain of this, Frege's Law cannot be applied and the argument does not get off the ground. In effect, then, the original Fregean argument begs the question, by assuming that the typical impartations of ‘Hesperus is Phosphorus’ that have the informative-making property P are included in the very information content. Of course, if one fails to draw the distinction between semantically contained and pragmatically imparted information (as so many philosophers have), it is small wonder that information pragmatically imparted by ‘Hesperus is Phosphorus’ may be mistaken for semantically contained information. If the strategy of the original Fregean argument is ultimately to succeed, however, a further argument must be given to show that the information imparted by ‘Hesperus is Phosphorus’ that makes it seem informative is, in fact, semantically contained. In the meantime, Frege's ‘Hesperus’–‘Phosphorus’ puzzle is certainly not the conclusive refutation of Millian theory that it has been taken to be. For all that the Fregean strategy achieves, some version of Millianism may be the best and most plausible theory available concerning the information value of proper names.


What evidence is there in favor of the Millian theory? One extremely important consideration comes by way of the paradigms of nondescriptional singular terms: individual variables. A related consideration involves pronouns. Consider the following so-called de re (as opposed to de dicto), or relational (as opposed to notional), propositional-attitude attribution, expressed in the formal mode by way of quantification into the nonextensional context created by the nonextensional operator ‘that’:


(1)  

(0x002203x)[x = the planet Venus & Jones believes thatxis a star].


Such a de re locution might be expressed less formally in colloquial English as:

(1′)  

Jones believes of the planet Venus that it is a star.


What is characteristic of these de re locutions is that they do not specify how Jones conceives of the planet Venus in believing it to be a star. It is left open whether he is thinking of Venus as the first heavenly body visible at dusk, or as the last heavenly body visible at dawn, or instead as the heavenly body he sees at time t, or none of the above. The Fregean (or ‘neo-Fregean’) theorist contends that this lack of specificity is precisely a result of the fact that the (allegedly sense-bearing) name ‘Venus’ is positioned outside of the scope of the oblique context created by the nonextensional operator ‘believes that’, where it is open to substitution of co-referential singular terms and to existential generalization. What is more significant, however, is that another, non-sense-bearing singular term is positioned within the scope of the nonextensional context: the last bound occurrence of the variable ‘x’ in (1), the pronoun ‘it’ in (1′). Consider first the quasi-formal sentence (1). It follows by the principles of conventional formal semantics that (1) is true if and only if its component open sentence

(2)  

Jones believes that x is a star

is true under the assignment of the planet Venus as value for the variable ‘x’—or in the terminology of Tarski, if and only if Venus satisfies (2). The open sentence (2) is

end p.10


true under the assignment of Venus as value of ‘x’ if and only if Jones believes the proposition that is the information content of the complement open sentence

(3)  

x is a star



under the same assignment of Venus as the value of ‘x’.

A parallel derivation proceeds from the colloquial de re attribution (1′). Sentence (1′) is true if and only if its component sentence


(2′)  

Jones believes that it is a star

is true under the anaphoric assignment of Venus as referent for the pronoun ‘it’. As with the open sentence (2), sentence (2′) is true under the assignment of Venus as the referent of ‘it’ if and only if Jones believes the information content of

(3′)  

It is a star



under this same assignment.

Now, the fundamental semantic characteristic of a variable with an assigned value, or of a pronoun with a particular referent, is precisely that its information value is just its referent. The referent-assignment provides nothing else for the term to contribute to the information content of sentences like (3) or (3′) in which it figures. In fact, this is precisely the point of using a variable or a pronoun rather than a definite description (like ‘the first heavenly body visible at dusk’) within the scope of an attitude verb in a de re attribution. A variable with an assigned value, or a pronoun with a particular referent, does not have in addition to its referent a Fregean sense—a conceptual representation that it contributes to semantic content. If it had, (3) and (3′) would semantically contain specific general propositions, under the relevant referent-assignments, and (2) and (2′) would thus be notional rather than relational. If (2) and (2′), used with reference to Venus, are to be relational—if they are to fail to specify how Jones conceives of Venus—the contents of (3) and (3′) under the assignments of Venus to ‘x’ and ‘it’ can only be the singular proposition about Venus that it is a star, the sort of proposition postulated by the Millian theory. This means that the information value of the variable or the pronoun must be its referent.

What is good for the variable or the pronoun, under an assigned referent, is good for the individual constant. Indeed, the only difference between a variable and a constant is that the variable varies where the constant stands fast. The semantics for a given language fixes the reference of its individual constants. It happens that some particularly useful operators, included in the usual mathematical languages, operate simultaneously on a certain kind of simple singular term and a formula, by surveying the various truth values that the operand formula takes on when the operand singular term is assigned different referents (and the rest of the sentence remains fixed), and then assigning an appropriate extensional value to the whole formed from the operator and its two operands. (Technically, the extension of such an operator is a function from the extension of its operand formula with respect to its operand term to an appropriate extension for the compound formed by attaching the operator to an appropriate term and a formula—where the extension of a formula S v with respect to a term v is a function that assigns to any assignment of a referent to v the corresponding


truth value of S v under that referent-assignment.) If a given language includes operators of this sort, it is natural for it to include also special singular terms that are not coupled with a particular referent to which they remain faithful, and that are instead allowed to take on any value from a particular domain of discourse as temporary referent. These special singular terms are the individual variables, and the operators that induce their presence are the variable-binding operators. Individual variables are singular terms that would be individual constants but for their promiscuity. Conversely, then, individual constants are singular terms that would be variables but for their monogamy. The variability of a variable has nothing whatsoever to do with the separate feature that the variable's information value, under an assignment of a referent, is just the assigned referent. It is the simplicity of the variable that gives it the latter feature; the variability only guarantees that the information value also varies. Once the variable is assigned a particular value, the variable becomes, for all intents and purposes pertaining to that assignment, a constant. Hence, if the open sentence (3), under the assignment of Venus as the value of ‘x’, semantically contains the singular proposition about Venus that it is a star, then the closed sentence


a is a star,

where ‘a’ is an individual constant that refers to Venus, semantically contains this same proposition. Assuming that the individual constants of natural language are the proper names, single-word indexical singular terms, and other (closed) simple singular terms, the considerations raised here support the Millian theory.11

There is an alternative way of looking at the same result. All of us are accustomed to using special variables or pronouns that have a restricted domain over which they range. In ordinary English, the pronoun ‘he’ often ranges only over males, the pronoun ‘she’ only over females. Among special-purpose technical languages, some variables range only over numbers, some only over sets, some only over times. The domain over which a variable ranges (at least typically) must be non-empty, but it can be quite small in size. In standard extensional second-order logic, for example, the range of the second-order variables ‘p’, ‘q’, and ‘r’ is the pair set consisting of (representatives of) the two truth values. Could there be variables whose range is a unit set? Of course there could. Why not? Except that it would be odd to call such


terms ‘variables’. Their range is too restrictive to allow for genuine variation, in an ordinary sense; they are maximally restricted. Let us not call them ‘variables’, then. What should we call them? We could call them ‘invariable variables’. (This has the advantage that it emphasizes the exact analogy with the less restrictive variables.) Alternatively, we could call them ‘constants’. In fact, we do. The proper names and demonstratives of ordinary language might be seen as nothing other than the hypothesized ‘invariable variables’. Proper names and unrestricted variables are but the opposite limiting cases of a single phenomenon.12

This sort of consideration favoring the sort of account I advocate is complemented by a new application of a general form of argument that has been suggested, and usefully exploited, by Saul Kripke.13

What compelling evidence is there that the proper names of ordinary language are not simply the hypothesized invariable variables? We have seen that the original Fregean argument from the alleged informativeness of ‘Hesperus is Phosphorus’ is illegitimate, or at least seriously incomplete. What other evidence is there? An alternative argument against Millian theory derives from the apparent failures of substitutivity in propositional-attitude attributions. Consider the familiar story of Jones and his ignorance concerning the planet Venus. Jones sees a bright star in the dusk sky, before any other heavenly body is visible, and is told that its name is ‘Hesperus’. Subsequently he sees another bright star in the dawn sky, later than any other heavenly body is visible, and is told that its name is ‘Phosphorus’. What Jones is not told is that these are one and the very same heavenly body, the planet Venus. Although Jones believes the


proposition that Hesperus is Hesperus, he seems not to believe (and indeed to disbelieve) the proposition that Hesperus is Phosphorus. That is, upon substitution of ‘Phosphorus’ for the second occurrence of ‘Hesperus’ in the true sentence


(4)  

Jones believes that Hesperus is Hesperus



we obtain the evidently false sentence

(5)  

Jones believes that Hesperus is Phosphorus.

The apparent failure of substitutivity in propositional-attitude attributions is generally taken by philosophers to constitute a decisive refutation of the sort of account I advocate. But the very phenomena that appear to show that substitutivity fails would arise even if the Millian theory were absolutely correct (for standard English) and substitutivity of co-referential proper names in propositional-attitude attributions were uniformly valid. In particular, the same feeling of invalidity in connection with substitution in such attributions as (4) would arise even in a language for which it was stipulated—say, by an authoritative linguistic committee that legislates the grammar and semantics of the language, and to which all speakers of the language give their cooperation and consent—that the theory of Frege's Puzzle is correct. Suppose, for example, that such a committee decreed that there are to be two new individual constants, ‘Schmesperus’ and ‘Schmosphorus’. (I am deliberately following the genius as closely as possible.) It is decreed that these two words are to function exactly like the mathematician's variables ‘x’, ‘y’, and ‘z’ as regards information value, except that they are to remain constant (with whatever other differences this key difference requires)—the constant value of the first being the first heavenly body visible at dusk and the constant value of the second being the last heavenly body visible at dawn. Suppose further that some English speakers—for example, the astronomers—are aware that these two new constants are co-referential, and hence synonymous. Nevertheless, even if our character Jones were fully aware of the legislative decree in connection with ‘Schmesperus’ and ‘Schmosphorus’, he would remain ignorant of their co-reference. Jones would dissent from such queries as ‘Is Schmesperus the same heavenly body as Schmosphorus?’ Would those who are in the know—the astronomers—automatically regard the new constants as completely interchangeable, even in propositional-attitude attributions? Almost certainly not. English speakers who use ‘ketchup’ and ‘catsup’ as exact synonyms but who do not reflect philosophically on the matter—and even some who do reflect philosophically—may be inclined to assent to the sentence ‘Sasha believes that ketchup is a sandwich condiment, but he does not believe that catsup is.’14 On reflection, however, it emerges that this sentence expresses a logical impossibility, since the proposition that catsup is a sandwich condiment just is the proposition that ketchup is a sandwich condiment. Similarly, speakers who agree to abide by the legislative committee's decree about ‘Schmesperus’ and ‘Schmosphorus’ and who recognize that these two terms are co-referential—especially if these speakers

do not reflect philosophically on the implications of the decree in connection with such de re constructions as (1)—might for independent pragmatic reasons be led to utter or to assent to such sentences as ‘Jones believes that Schmesperus appears in the evening, but he does not believe that Schmosphorus does’ and ‘Jones believes that Schmesperus is Schmesperus, but he does not believe that Schmesperus is Schmosphorus.’ The astronomers may be led to utter the latter sentence, for example, in order to convey (without knowing it) the complex fact about Jones that he agrees to the proposition about Venus that it is it, taking it in the way he would were it presented to him by the sentence ‘Schmesperus is Schmesperus’ but not taking it in the way he would were it presented to him by the sentence ‘Schmesperus is Schmosphorus’. The astronomers would thus unknowingly speak in a way that conflicts with the usage to which they have agreed. This, in turn, would lead to their judging such belief attributions as ‘Jones believes that Schmesperus is Schmosphorus’ not only inappropriate but literally false, and to the unmistakable feeling that substitution of ‘Schmosphorus’ for (some occurrences of) ‘Schmesperus’ in such attributions as ‘Jones believes that Schmesperus is Schmesperus’ is logically invalid. Insofar as the same phenomena that give rise to Frege's puzzle about identity sentences and to the appearance of substitutivity failure would arise even in a language for which the theory advanced in Frege's Puzzle was true by fiat and unanimous consent (and do in fact arise with respect to such straightforward strict synonyms as ‘ketchup’ and ‘catsup’), these phenomena cannot be taken to refute the theory.

IV

The anti-Millian argument deriving from the apparent failure of substitutivity is closely related to the original Fregean argument about the informativeness of ‘Hesperus is Phosphorus’. The analogue of the questionable premiss that ‘Hesperus is Phosphorus’ is informative is the assertion that (5) is false (or that ‘Hesperus is Phosphorus’ does not correctly give the content of one of Jones's beliefs, etc.). This premiss too, I claim, is incorrect.15 However, this premiss, unlike its analogue in the original Fregean argument, does not simply beg the question. The intuition that (5) is false (according to the story) is strong and universal. We have seen that this intuition cannot be regarded as decisive—or even evidentially relevant—regarding the question of the actual truth value of (5), since (for some reason) the intuition of falsity would arise in any case. But there are forceful reasons for deeming (5) false, and the intuition of falsity must be addressed and explained. A full reply to the objection from the apparent failure of substitutivity involves greater complexities.16

In Frege's Puzzle, I propose the sketch of an analysis of the binary relation of belief between believers and propositions (sometimes Russellian singular propositions). I take the belief relation to be, in effect, the existential generalization of a ternary relation, BEL, among believers, propositions, and some third type of entity. To believe a proposition p is to adopt an appropriate favorable attitude toward p when taking p in some relevant way. It is to agree to p, or to assent mentally to p, or to approve of p, or some such thing, when taking p a certain way. This is the BEL relation. The third relata for the BEL relation are perhaps something like modes of acquaintance or familiarity with propositions, or ways in which a believer may take a given proposition. The important thing is that, by definition, they are such that if a fully rational believer adopts conflicting attitudes (such as belief and disbelief, or belief and suspension of judgment) toward propositions p and q, then the believer must take p and q in different ways, by means of different modes of acquaintance, in harboring the conflicting attitudes towards them—even if p and q are in fact the same proposition. More generally, if a fully rational agent construes objects x and y as distinct (or even merely withholds construing them as one and the very same—as might be evidenced, for example, by the agent's adopting conflicting beliefs or attitudes concerning x and y), then for some appropriate notion of a way of taking an object, the agent takes x and y in different ways, even if in fact x = y.17 Of course, to use a distinction of Kripke's, this formulation is far too vague to constitute a fully developed theory of ways-of-taking-objects and their role in belief formation, but it does provide a picture of belief that differs significantly from the sort of picture of propositional attitudes advanced by Frege or Russell, and enough can be said concerning the BEL relation to allow for at least the sketch of a solution to certain philosophical problems, puzzles, and paradoxes involving belief.18

In particular, the BEL relation satisfies the following three conditions:


(a)  

A believes p if and only if there is some x such that A is familiar with p by means of x and BEL(A, p, x);19

(b)  

A may believe p by standing in BEL to p and some x by means of which A is familiar with p without standing in BEL to p and all x by means of which A is familiar with p;

(c)  

In one sense of ‘withhold belief’, A withholds belief concerning p (either by disbelieving or by suspending judgment) if and only if there is some x by means of which A is familiar with p and not-BEL(A, p, x).


These conditions generate a philosophically important distinction between withholding belief and failure to believe (i.e., not believing). In particular, one may both withhold belief from and believe the very same proposition simultaneously. (Neither withholding belief nor failure to believe is to be identified with the related notions of disbelief and suspension of judgment—which are two different ways of withholding belief, in this sense, and which may occur simultaneously with belief of the very same proposition in a single believer.)

It happens in most cases (though not all) that when a believer believes some particular proposition p, the relevant third relatum for the BEL relation is a function of the believer and some particular sentence of the believer's language. There is, for example, the binary function f that assigns to any believer A and sentence S of A's language, the way A takes the proposition contained in S (in A's language with respect to A's context at some particular time t) were it presented to A (at t) through the very sentence S, if there is exactly one such way of taking the proposition in question. (In some cases, there are too many such ways of taking the proposition in question.)

According to this account, (5) is true in the story of Jones and the planet Venus, since Jones agrees to the proposition that Hesperus is Phosphorus when taking it in a certain way—for example, if one points to Venus at dusk and says (peculiarly enough) ‘That is that’, or when the proposition is presented to him by such sentences as ‘Hesperus is Hesperus’ or ‘Phosphorus is Phosphorus’. That is,

BEL[Jones, that Hesperus is Phosphorus, f (Jones, ‘Hesperus is Hesperus’)].

Jones also withholds belief concerning whether Hesperus is Hesperus. In fact, according to my account, he believes that Hesperus is not Hesperus! For he agrees to the proposition that Hesperus is not Hesperus, taking it in the way he would were it presented to him by the sentence ‘Hesperus is not Phosphorus’. That is,

BEL[Jones, that Hesperus is not Hesperus, f (Jones, ‘Hesperus is not Phosphorus’)],

and hence, assuming Jones is fully rational, it is not the case that

BEL[Jones, that Hesperus is Hesperus, f (Jones, ‘Hesperus is Phosphorus’)].

As noted above, these consequences of my account do not conform with the way we actually speak. Instead it is customary when discussing Jones's predicament to say such things as ‘Jones does not realize that Hesperus is Phosphorus; in fact, he believes that Hesperus is not Phosphorus.’ It is partly for this reason that the anti-Millian's premiss that (5) is false does not simply beg the question. Yet, according to my account, what we say when we deny such things as (5) is literally false. In fact, (5)’s literal truth conditions are, according to the view I advocate, conditions that are plainly fulfilled (in the context of the Jones story). Why, then, do we not say such things, and instead say just the opposite? Why is it that substitution of ‘Phosphorus’ for ‘Hesperus’—or even of ‘Schmosphorus’ for ‘Schmesperus’—feels invalid in propositional-attitude attributions? Some explanation of our speech patterns and intuitions of invalidity in these sorts of cases is called for. The explanation I offer in Frege's Puzzle is somewhat complex, consisting of three main parts. The first part of the explanation for the common disposition to deny or to dissent from (5) is that speakers may have a tendency to confuse the content of (5) with that of


(5′)  

Jones believes that ‘Hesperus is Phosphorus’ is true (in English).


Since sentence (5′) is obviously false, this confusion naturally leads to a similarly unfavorable disposition toward (5). This part of the explanation cannot be the whole story, however, since even speakers who know enough about semantics to know that the fact that Hesperus is Phosphorus is logically independent of the fact that the sentence ‘Hesperus is Phosphorus’ is true, and who are careful to distinguish the content of (5) from that of (5′), are nevertheless unfavorably disposed toward (5) itself—because of the fact that Jones demurs whenever the query ‘Is Hesperus the same heavenly body as Phosphorus?’ is put to him.

The second part of my explanation for (5)′s appearance of falsity is that its denial is the product of a plausible but mistaken inference from the fact that Jones sincerely dissents (or at least does not sincerely assent) when queried ‘Is Hesperus Phosphorus?’, while fully understanding the question and grasping its content, or (as Keith Donnellan has pointed out) even from his expressions of preference for the Evening Star over the Morning Star. More accurately, ordinary speakers (and even most nonordinary speakers) are disposed to regard the fact that Jones does not agree to the proposition that Hesperus is Phosphorus, when taking it in a certain way (the way it might be presented to him by the very sentence ‘Hesperus is Phosphorus’), as sufficient to warrant the denial of sentence (5). In the special sense explained in the preceding section, Jones withholds belief from the proposition that Hesperus is Phosphorus, actively failing to agree with it whenever it is put to him in so many words, and this fact misleads ordinary speakers, including Jones himself, into concluding that Jones harbors

no favorable attitude of agreement whatsoever toward the proposition in question, and hence does not believe it.

The third part of the explanation is that, where someone under discussion has conflicting attitudes toward a single proposition that he or she takes to be two independent propositions (i.e., in the troublesome ‘Hesperus’–‘Phosphorus’, ‘Superman’–‘Clark Kent’ type cases), there is an established practice of using belief attributions to convey not only the proposition agreed to (which is specified by the belief attribution) but also the way the subject of the attribution takes the proposition in agreeing to it (which is no part of the semantic content of the belief attribution). Specifically, there is an established practice of using such a sentence as (5), which contains the uninteresting proposition that Jones believes the singular proposition about Venus that it is it, to convey furthermore that Jones agrees to this proposition taking it in the way he would were it presented to him by the very sentence ‘Hesperus is Phosphorus’ (assuming he understands this sentence). That is, there is an established practice of using (5) to convey the false proposition that

BEL[Jones, that Hesperus is Phosphorus, f (Jones, ‘Hesperus is Phosphorus’)].

V

An unconventional objection has been raised by some self-proclaimed neo-Fregeans against versions of Millianism of the sort advanced in Frege's Puzzle. It is charged that such theories are, at bottom, versions of a neo-Fregean theory.20 Ironically, this unorthodox criticism is invariably coupled with the further, standard criticism that such versions of Millianism are problematic in some way or other that neo-Fregean theory is not (for example, in counting sentence (5) true). The fact that this more familiar criticism is directly contrary to the newer criticism is all but completely ignored. More importantly, this more recent criticism betrays a serious misunderstanding of the gulf that separates Frege's theory from that of Mill or Russell.

It should be said that the theory of Frege's Puzzle does indeed follow Frege's theoretical views in a number of significant respects. First and foremost, the theory sees the information value (contribution to proposition-content) of such compound expressions as definite descriptions as complexes whose constituents are contributed by the component expressions and whose structure parallels the syntactic structure of the compound itself. Although my theory has been called ‘neo-Russellian’, it departs radically from the theory of Russell in treating definite descriptions as genuine singular terms, and not as contextually defined ‘incomplete symbols’ or quantificational locutions. In addition to this, a semantic distinction is observed, following Frege's distinction of Bedeutung and Sinn, between a definite description's referent and the

description's information value. A similar distinction is maintained for predicates, sentential connectives, quantifiers, other operators, and even for whole sentences. The referent of a predicate is taken to be its semantic characteristic function from (sequences of) objects to truth values; the information value is taken to be something intensional, like an attribute or concept. Sentences are viewed entirely on the model of a definite description that refers (typically nonrigidly) to a truth value. The content (‘information value’) of a sentence is taken to be a proposition—the sort of thing that is asserted or denied, believed or disbelieved (or about which judgment is suspended), etc., something that is never-changing in truth value. The account of predicates, sentences and the rest as referring to their extensions is defended by means of the principle of extensionality (the principle that the referent of a compound expression is typically a function solely of the referents of the component expressions and their manner of composition). In all of these respects, the theory advanced in Frege's Puzzle self-consciously follows Frege.

There remains one crucial difference, however: the information value of a simple singular term is identified with its referent. This major plank makes the theory Millian (or ‘neo-Russellian’), and hence severely and deeply anti-Fregean.

Although a great deal of attention has been paid to the differences between Russell and Frege over the question of whether it is false that the present king of France is bald, their disagreement on this question is dwarfed in significance by their disagreement over the information values of simple proper names. This primary bone of contention emerged in correspondence in 1904, even before Russell came to herald his Theory of Descriptions, which later supplemented his Millianism.21 Russell answered Frege's protest that Mont Blanc with its snowfields cannot be a constituent of the ‘thought’, or information, that Mont Blanc is more than 4000 meters high, arguing that unless we admit that Mont Blanc is indeed a constituent of the content of the sentence ‘Mont Blanc is over 4000 meters high’ we obtain the absurd conclusion that we know nothing at all concerning Mont Blanc. Although Frege apparently made no attempt at a response (Russell did not seem to be fully apprehending Frege's remarks), one can be certain that he did not regard Russell's vision of the proposition that Mont Blanc is over 4000 meters high as merely a minor departure from his own sense-reference theory. There can be no real doubt that Frege would have vigorously denounced all versions of Millianism as completely inimical to his theoretical point of view.22

What, then, is the rationale for the charge that my version of Millianism is, at bottom, a neo-Fregean theory? My critics have not been absolutely clear on this point. The charge appears to stem from my acknowledgment of something like ways of taking objects, and my reliance on them to explain away the appearance of falsity in connection with such propositional-attitude attributions as (5). To this somewhat vague and general criticism, a specific and detailed response was offered in Frege's Puzzle.23 To begin with, my ways-of-taking-objects do not have all of the features that characterize Fregean senses. (See below.) Even if they had, however, they play a significantly different role in my theory. My analogy to the philosophy of perception (pp. 122–125) illustrates the anti-Fregean nature of my view (despite its acknowledgment of sense-like entities): Whereas my theory is analogous to the naive theory that we perceive external objects—apples, tables, chairs—Fregean theory is analogous to the sophisticated theory that the only objects of genuine perception are percepts, visual images, auditory images, and so on. The naive theorist of perception sees the ‘sees’ in ‘Jones sees the apple’ as expressing a relation between perceivers and external objects, and its


grammatical direct object ‘the apple’ as occurring in purely referential position and referring there to the apple. By contrast, the sophisticated theorist sees the ‘sees’ as expressing a relation between perceivers and mental objects, and ‘the apple’ as referring in that context to Jones's visual apple image. The two theories disagree fundamentally over what is perceived. The naive theorist need not deny that internal sensory images play a role in perception. He or she may even propose an analysis of perceptual relations (like seeing) that involves existential generalization over mental objects. Why not? Perception obviously does involve experience; there need be no quarrel over such trivial and extremely general matters. The fundamental disagreement over the objects of perception remains. This disagreement will manifest itself not only in differing interpretations of such sentences as ‘Jones sees the apple’, but often even in differing judgments concerning its truth value (for instance when Jones is hallucinating).

Likewise, I do not quarrel with Fregeans over the trivial question of whether belief and disbelief involve such things as conceptualizing. Our fundamental disagreement concerns the more substantial matter of what is believed—in particular, the question whether what is believed is actually made up entirely of such things as ‘ways of conceptualizing’. The ways of taking objects that I countenance are, according to my view, not even so much as mentioned in ordinary propositional-attitude attributions. In particular, on my view, a ‘that’-clause makes no reference whatsoever to any way of taking the proposition that is its referent, and a ‘that’-clause whose only singular terms are simple (such as the one occurring in (5)) makes no reference whatsoever to any way of taking (or conceiving of, etc.) the individuals referred to by those terms. Consequently, ways-of-taking-objects are not mentioned in (an appropriate specification of) the truth conditions of such an attribution. The only way they come into the picture at all is that in some cases, a certain sort of analysis of the propositional attribute designated by the relevant predicate (e.g., belief) involves existential generalization over them—and even this is not true in all cases. There are many propositional locutions that are not attitudinal as such, and that consequently do not involve ways-of-taking-objects in the way that belief does—for example, ‘The laboratory test indicates that Mary has contracted the disease’ or better still ‘It is necessary that Mary is human’ (perhaps even ‘Jones asserted that Venus is a star’). In short, my ways-of-taking-objects have nothing whatsoever to do with the semantic content of ordinary sentences, and consequently they have nothing whatsoever to do with the semantics of propositional attributions, even attributions of propositional attitude. Ways-of-taking-objects hail from philosophical psychology, not from philosophical semantics.

By contrast, for the Fregean, ways of conceptualizing objects are explicitly referred to in, and pivotal to the truth conditions of, all propositional attributions. I sharply disagree with the Fregean who claims that alethic modality—or even that laboratory tests—involve such things as conceptualizing in just the same way that belief does. (Consider the Fregean account of such valid inferences as ‘The physician believes whatever the laboratory test indicates, and the test indicates that Mary has contracted the disease; hence the physician believes that Mary has contracted the disease’, or ‘It


is necessary that Mary is human, and Jones believes that Mary is human; hence Jones believes at least one necessary truth.’)24 My fundamental disagreement with Fregeans over the objects of propositional attitude is manifested not only in our differing interpretations of propositional-attitude attributions, but often even in different judgments concerning their truth value. (Recall the conflict between the charge that my version of Millianism is neo-Fregean, and the more orthodox Fregean criticisms of Millianism.)

Fortunately, Graeme Forbes has provided a somewhat more detailed account of how my view is supposed to ‘dissolve’ into a neo-Fregean theory.25 It is especially instructive to examine his rationale for this criticism.

Forbes exploits the fact that the neo-Fregean is not shackled by the letter of Frege's specific views, and may preserve the general spirit of Frege's theoretical point of view while departing in various details. Forbes proposes two ways in which a neo-Fregean theory can converge, in certain respects, with my version of Millianism.26 One thing the neo-Fregean may do is to regard a belief attribution 0x00231cJones believes that S0x00231d, as uttered by a given speaker, as asserting not that Jones stands in the belief relation specifically to P, where P is the ‘thought’ (proposition) that is the sense of S in the speaker's idiolect, but instead that Jones stands in the belief relation to some thought or other that is relevantly similar to P. In this way, the neo-Fregean might find his or her way to delivering the same (somewhat liberal) verdicts as I do with respect to various controversial propositional-attitude attributions (presumably, such as (5)).

Forbes's second proposal suggests a particular way of fleshing out the similarity relation involved in the first proposal, one that is designed to ensure that the neo-Fregean's verdicts will always coincide exactly with mine. It is well-known that Fregean theory runs into difficulty with such de re constructions as (1) or (1′). Although Frege himself was largely tacit concerning constructions involving belief of, a number of neo-Fregeans have proposed various ways of accommodating them within the spirit of Fregean theory. The most famous (and I believe the most compelling) of these neo-Fregean proposals is still David Kaplan's from ‘Quantifying In’ [10].27 For present purposes, we shall modify Kaplan's proposal slightly. As can be gleaned from the previous section, the Fregean's difficulty with such constructions as (1) arises from a lack of genuine Fregean sense in connection with the open sentence (3), taken under an assignment of a value to x. Kaplan's analysis (as here modified) reconstrues (1) in such a way that (3) is no longer regarded as a proper (i.e., semantic) constituent. Specifically, the open sentence (2) is analyzed into the following:


(6)  

(0x0022030x0003b1)[0x0003b1 represents x to Jones 0x00231c0x0003b1is a star0x00231d],


where the special representation relation designated in the first conjunct is such as to entail that 0x0003b1is an individual concept (a sense appropriate to a singular term) that determines x as its referent, and where the quasi-quotation marks occurring in the second conjunct are sense-quoting marks that function in a manner analogous to standard quasi-quotation marks with respect to (i.e., without attempting to quote the sense of) the sense variable ‘0x0003b1’.28 (Think of this analysis as resulting from a contextual definition for open ‘that’-clauses, analogous to Russell's contextual definition for definite descriptions—complete with scope distinctions, the definiendum's lack of ‘meaning in isolation’, and all the rest.) It is a (fairly) straightforward matter to extend this analysis of such quasi-formal de re constructions as (1) to such informal constructions as (1′): The neo-Fregean analysis of (2′) is obtained from (6) by substituting the pronoun ‘it’ for the free variable ‘x’.29 Replacing the bound occurrence of (2) in (1) by its analysis (6) (or the scattered occurrence of (2′) in (1′) by a nonscattered occurrence of its analysis), we obtain something equivalent to


(7)  

(0x0022030x0003b1)[0x0003b1 represents Venus to Jones 0x00231c0x0003b1is a star0x00231d],

The neo-Fregean is struck by the fact that this analysis of (1) and (1′) is significantly similar to my proposed analysis of


(8)  

Jones believes that Venus is a star.


It is a small step to obtain (7) from (8). One need only extend Kaplan's analysis further, to cover all cases in which a simple singular term—whether a variable or pronoun, or even a proper name or demonstrative—occurs free in a propositional-attitude attribution. We thus obtain a special neo-Fregean theory, one according to which (8) asserts that Jones stands in the belief relation to some thought or other to the effect 0x00231c0x0003b1is a star0x00231d, where 0x0003b1is a sense that represents Venus to Jones. Thus (8) is counted true both by this theory and by my version of Millianism. Similarly, (5) is seen on this theory as asserting that Jones stands in the belief relation to some thought or other to the effect 0x00231c0x0003b1is 0x0003b20x00231d, where each of 0x0003b1and 0x0003b2is a sense that represents Venus to Jones. Thus (5) is also counted true, as with my Millianism. Therefore, Forbes argues, my version of Millianism dissolves, for all intents and purposes, into this special neo-Fregean theory—with my talk of ‘singular propositions’ and ‘ways of taking objects’ merely a notational variant of the neo-Fregean's talk of ‘representation’ and ‘individual concepts’.30

One significant difficulty with this neo-Fregean proposal is that it does not validate such apparently valid inferences as ‘Smith believes that Bush will win the presidency, and so does Jones; hence there is something (some proposition) that both Smith and

Jones believe.’31 This constitutes one fairly dramatic difference between the proposed theory and my version of Millianism. But there are more fundamental differences.

Does the proposed neo-Fregean theory even agree with my version of Millianism on every question of propositional-attitude attribution, without exception, as it is designed to do? On my theory, any propositional attribution involving a proper name within the scope of the ‘that’-operator is deemed equivalent to the corresponding de re construction in which the name is moved outside the scope of the ‘that’-operator. (For instance, (8) is true if and only if (1′) is.) Thus Forbes's proposed neo-Fregean theory succeeds in echoing the verdicts of my version of Millianism only insofar as neo-Fregean analyses along the lines of Kaplan's succeed in capturing the truth conditions of de re constructions. Several direct-reference theorists (including Kaplan) have mounted an impressive case that Kaplan-style neo-Fregean analyses fail in this attempt. Hilary Putnam's Twin-Earth argument suffices to demonstrate the point.32 Oscar believes his friend Wilbur to be stingy, while Oscar's exact doppelganger on Twin Earth, Oscar TE , likewise believes his friend Wilbur TE to be stingy. Duplicates in every detail, Oscar and Oscar TE believe the very same Fregean (nonsingular) thoughts. Neither Oscar nor Oscar TE is in possession of any Fregean individual concept (in which only senses occur as constituents) that differentiates between Wilbur and Wilbur TE , and consequently neither possesses a Fregean sense that determines the relevant friend as referent independently of context. Assuming that the objects of belief (whether Fregean thoughts or Russellian singular propositions) and their constituents determine their objects (truth values, individuals, etc.) independently of context,33 each believes something de re that the other does not. Oscar's belief concerning Wilbur is therefore irreducible to his beliefs of Fregean (nonsingular) thoughts. The sentence ‘Oscar believes that Wilbur is stingy’, which is true on my theory, is deemed false by the proposed neo-Fregean theory. The theories are thus diametrically opposed on a key issue.

The Twin-Earth thought experiment illustrates a further, and more central, divergence between my theory and Fregean theory. The way in which Oscar takes Wilbur is presumably exactly the same as the way in which Oscar TE takes Wilbur TE —despite the fact that Oscar's thought of Wilbur that he is stingy and Oscar TE 's thought of Wilbur TE that he is stingy concern different individuals. By contrast, for the Fregean, each individual concept determines a unique object, or nothing at all. Oscar's thought that Wilbur is stingy and Oscar TE 's thought that Wilbur TE is stingy, if they were to have such thoughts concerning different individuals, would have to contain different individual concepts; the sense that Oscar attaches to the name ‘Wilbur’ would have to be different from the sense that Oscar TE attaches to the same name. This is made impossible by the fact that Oscar and Oscar TE are exact duplicates.34 This sort of consideration points up a crucial difference—in many respects the crucial difference—between my ways-of-taking-objects (which are not precluded from determining their objects only contextually) and Fregean senses (which, since they are information values, cannot do so). (See note 18 above.)

The neo-Fregean might attempt to remedy this serious difficulty with his or her attempt to accommodate de re constructions, by tinkering with the Kaplan-style analysis (for example, by relaxing the determination requirement on representation). I remain doubtful that this can be successfully accomplished in a plausible manner without resorting to singular propositions, or the like. But suppose I am wrong and the neo-Fregean can find Fregeanistically acceptable necessary-and-sufficient conditions for de re belief and other de re propositional attributes, including alethic necessity. (Committed neo-Fregeans might suppose that this must be possible.) Would this show that my version of Millianism is simply a notational variant of a suitably designed neo-Fregean theory? Certainly not. Even if (1′) is true with respect to a possible circumstance if and only if Jones believes some Fregean thought or other of such-and-such a sort in that possible circumstance—so that, on my view, (8) is also true exactly on the same Fregean condition—still (8), according to my account, does not say that this Fregean condition is fulfilled. On my view, (8) asserts a certain relationship—the belief relationship—between Jones and the singular proposition about Venus that it is a star. It does not merely characterize Jones's belief as being of some Fregean thought or other of such-and-such a special sort; it specifies a particular belief and attributes it to Jones. In short, even if the neo-Fregean's promise can be kept by adjusting the Kaplan-style analysis (a very big ‘if’), the suitably designed neo-Fregean theory ascribes to (8) a very different semantic content from that ascribed by my version of Millianism. The neo-Fregean's semantic truth conditions for (8) are, at best, a priori and metaphysically necessarily equivalent to my own. They are not identical.

Finally, we must consider whether the suitably designed theory would be neo-Fregean. It is true, of course, that a neo-Fregean need not follow the master in every detail. (I do not know of any follower of Frege, for instance, who has not shied away from Frege's views concerning the concept horse.) But there must be some limit as to how much departure still qualifies as neo-Fregean. Certainly the theory of Russell, for example, differs too extensively from that of Frege on central issues to qualify as neo-Fregean. (It is worth noting in this connection that Russell too recognized certain nonsemantic elements from philosophical psychology in his correspondence with Frege over the proposition that Mont Blanc is over 4000 meters high. It is highly doubtful that Frege saw this as simply another way of saying what he himself was saying.) The sort of theory that Forbes envisions (on this reconstruction of his criticism) is a theory that denies that the ‘that’-operator occurring in (8) is functioning there merely as a device for sense-quotation, in the same way that it functions in ‘Jones believes that the first heavenly body visible at dusk is a star’; specifically, it denies that (8) asserts a relationship between Jones and the sense of the sentence ‘Venus is a star’. Furthermore, the theory denies that (8) specifies a particular belief and attributes it to Jones, claiming instead that (8) merely characterizes Jones's belief as being one or another of a particular sort. Most significantly, the theory construes any occurrence of a simple singular term (even of a proper name) within the scope of the ‘that’-operator in a propositional attribution (even in an attribution of propositional attitude) as completely open to substitution by any co-referential simple singular term. The theory is specifically designed to have the consequence that Jones believes that Hesperus is Hesperus if and only if he also believes that Hesperus is Phosphorus. It draws no significant distinction at all, in fact, between the ostensibly de dicto (8) and the patently de re (1′). Otherwise it would be very different from my version of Millianism—obviously so—and hence unsuited to support Forbes's charge of mere notational variance. I submit that there is not enough of Frege's overall theoretical point of view left here for this (would-be) theory to warrant the epithet ‘neo-Fregean’.35 The same would be true of any of its notational variants.

Nor is the envisioned theory a version of Millianism exactly. It is more a curious admixture, a strange brew made up of elements of both Fregeanism and Millianism. I do not claim that one (perhaps even an erstwhile Fregean) could not find reason to adopt this strange theory; I claim only that doing so would involve abandoning too much of the spirit of orthodox Fregean theory for the proponent to qualify as a neo-Fregean. Indeed, if (much to my surprise) genuinely Fregean necessary-and-sufficient conditions are eventually found for the de re, I would urge any committed anti-Millian to give the envisioned blend of Fregeanism and Millianism serious consideration as a superior alternative to neo-Fregeanism. Given greater flexibility, however, I would strongly advise against its adoption. Some version of genuine Millianism is much to be preferred. (This was the moral of Sections II and III above.)


References


[1] Burge, T. (1978). ‘Belief and Synonymy’, Journal of Philosophy, 75: 119–138.  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them

[2] Church, A. (1954). ‘Intensional Isomorphism and Identity of Belief’, Philosophical Studies, 5(5): 65–73 The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them. Also in N. Salmon and S. Soames (eds), Propositions and Attitudes (Oxford: Oxford University Press, 1988).

[3] Evans, G. (1981). ‘Understanding Demonstratives’, in H. Parret and J. Bouveresse (eds), Meaning and Understanding (Berlin and New York: De Gruyter).

[4] Evans, G. (1982). The Varieties of Reference (Oxford: Oxford University Press).

[5] Forbes, G. (1987). ‘Review of Nathan Salmon's Frege's Puzzle’, The Philosophical Review, 96(3): 455–458.

[6] Frege, G. (1918). ‘Thoughts’, in N. Salmon and S. Soames (eds), Propositions and Attitudes (Oxford: Oxford University Press, 1988). Originally appeared in English in Mind 65 (1956): 289–311. Clicking this link will take you to related content from Oxford University Press.  Please note that this site may require additional subscription or purchase rights to view protected content

[7] Frege, G. (1979). Posthumous Writings. H. Hermes, F. Kambartel, and F. Kaulbach (eds), P. Long and R. White (trans.) (Chicago: University of Chicago).

[8] Frege, G. (1980). Philosophical and Mathematical Correspondence. G. Gabriel, H. Hermes, F. Kambartel, C. Thiel, and A. Veraart (eds) (Chicago: University of Chicago Press).

[9] Frege, G. (1984). Collected Papers on Mathematics, Logic, and Philosophy. Brian McGuinness (ed.) (Oxford: Basil Blackwell).

[10] Kaplan, D. (1969). ‘Quantifying In’, in D. Davidson and G. Harman (eds), Words and Objections: Essays on the Work of W. V. Quine (Dordrecht: Reidel). Also in L. Linsky (ed.), Reference and Modality (Oxford: Oxford University Press, 1971).

[11] Kaplan, D. (1986). ‘Opacity’, in L. E. Hahn and P. A. Schilpp (eds), The Philosophy of W. V. Quine (La Salle: Open Court).

[12] Kripke, S. (1972). Naming and Necessity (Cambridge, Mass.: Harvard University Press).

[13] Kripke, S. (1979). ‘A Puzzle about Belief’, in A. Margalit (ed.), Meaning and Use (Dordrecht: Reidel). Also in N. Salmon and S. Soames (eds), Propositions and Attitudes (Oxford: Oxford University Press, 1988).

[14] Kripke, S. (1979). ‘Speaker's Reference and Semantic Reference’, in P. French, T. Vehling, and H. Wettstein (eds), Contemporary Perspectives in the Philosophy of Language (Minneapolis: University of Minnesota Press.

[15] McDowell, J. (1981). ‘Engaging with the Essential’, Times Literary Supplement, (January 16, 1981): 61–62.

[16] McDowell, J. (1984). ‘De Re Senses’, in C. Wright (ed.), Frege: Tradition and Influence (Oxford: Basil Blackwell).

[17] Putnam, H. (1954). ‘Synonymity and the Analysis of Belief Sentences’, Analysis, 14: 114–122. The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of themAlso in N. Salmon and S. Soames (eds), Propositions and Attitudes (Oxford: Oxford University Press, 1988).

[18] Putnam, H. (1973). ‘Meaning and Reference’, Journal of Philosophy, 70: 699–711.  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them

[19] Putnam, H. (1979). ‘Comments’, in A. Margalit (ed.), Meaning and Use (Dordrecht: Reidel).

[20] Richard, M. (1986). ‘Attitude Ascriptions, Semantic Theory, and Pragmatic Evidence’, Proceedings of the Aristotelian Society, 87: 243–262.

[21] Richard, M. (1988). ‘Taking the Fregean Seriously’, in D. Austin (ed.), Philosophical Analysis: A Defense by Example (Dordrecht: Reidel).

[22] Russell, B. (1911). ‘Knowledge by Acquaintance and Knowledge by Description’, Chapter X of Mysticism and Logic and Other Essays (London: Longmans, Green and Company). Also in N. Salmon and S. Soames (eds), Propositions and Attitudes (Oxford: Oxford University Press, 1988).

[23] Russell, B. (1918). ‘The Philosophy of Logical Atomism’, in R. C. Marsh (ed.), Logic and Knowledge (London: George Allen and Unwin, 1956). Also in D. Pears (ed.), The Philosophy of Logical Atomism (La Salle: Open Court, 1985).

[24] Salmon, N. (1979). ‘Review of Leonard Linsky's Names and Descriptions’, Journal of Philosophy, 76(8): 436–452.

[25] Salmon, N. (1981). Reference and Essence (Princeton: Princeton University Press, and Oxford: Basil Blackwell).

[26] Salmon, N. (1986). ‘Reflexivity’, Notre Dame Journal of Formal Logic, 27(3): 401–429. The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of themAlso in N. Salmon and S. Soames (Oxford: Oxford University Press, 1988).

[27] Salmon, N. (1986). Frege's Puzzle (Cambridge, Mass.: MIT Press).

[28] Salmon, N. (1989). ‘Illogical Belief’, in J. Tomberlin (ed.), Philosophical Perspectives 3: Philosophy of Mind and Action Theory (Atascadero, Calif.: Ridgeview).

[29] Salmon, N. (1989). ‘Tense and Singular Propositions’, in J. Almog, J. Perry, and H. Wettstein (eds), Themes from Kaplan (Oxford: Oxford University Press).

[30] Salmon, N. and Soames, S. (eds) (1988). Propositions and Attitudes (Oxford: Oxford University Press).

[31] Scheffler, I. (1955). ‘On Synonymy and Indirect Discourse’, Philosophy of Science, 22(1): 39–44.  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them

[32] Smith, A. D. (1988). ‘Review of Nathan Salmon's Frege's Puzzle’, Mind, 97(385): 136–137.

[33] Soames, S. (1987). ‘Substitutivity’, in J. J. Thomson (ed.), On Being and Saying: Essays for Richard Castwright (Cambridge, Mass.: MIT Press).

[34] Wagner, S. (1986). ‘California Semantics Meets the Great Fact’, Notre Dame Journal of Formal Logic, 27(3): 430–455.


2 Reflexivity (1986)*



Nathan Salmon


In 1983 Mark Richard formulated a new and interesting problem for theories of direct reference with regard to propositional-attitude attributions.1 The problem was later discovered independently by Scott Soames, who recently advanced it2 as a powerful objection to the theory put forward by Jon Barwise and John Perry in Situations and Attitudes.3 Interestingly, although both Richard and Soames advocate the fundamental assumption on which their philosophical problem arises, they disagree concerning the correct solution to the problem. In this paper I discuss the Richard–Soames problem, as I shall call it, as well as certain related problems and puzzles involving reflexive constructions in propositional-attitude attributions. I will treat these problems by applying ideas I invoked in Frege's Puzzle4 defending a semantic theory that shares certain features with, but differs significantly from, that of Barwise and Perry. Unlike the theory of Situations and Attitudes, the theory of Frege's Puzzle has the resources without modification to solve the Richard–Soames problem and related problems.

I

In setting out the Richard–Soames problem, we make some important assumptions. First, we make the relatively uncontroversial assumption that a monadic predicate 0x00231cbelieves that S0x00231d, where S is a declarative sentence, is simply the result of filling the second argument place of the dyadic, fully extensional predicate ‘believes’ with the term 0x00231cthat S0x00231d. Furthermore, it is assumed that the contribution made by the dyadic predicate ‘believes’ to securing the information content (with respect to a time t) of, or the proposition expressed (with respect to t) by, a declarative sentence in which the

predicate occurs (outside of the scope of any nonextensional devices, such as quotation marks) is a certain binary relation between believers and propositions, the relation of believing-at-t,5 and that a term of the form 0x00231cthat S0x00231d refers (with respect to a possible context of use c) to the information content (with respect to c) of the sentence S itself. More accurately, the following is assumed:

(B) A monadic predicate of the form 0x00231cbelieves that S0x00231d, where S is an (open or closed) sentence, correctly applies (with respect to a possible context of use and an assignment of values to individual variables) to all and only those individuals who stand in the binary belief relation (at the time of the context in the possible world of the context) to the information content of, or the proposition expressed by, S (with respect to that context and assignment).

On this assumption, a sentence of the form 0x00231ca believes that S0x00231d, where a is any singular term, is true if and only if the referent of a stands in the belief relation to the information content of S. Thesis (B) is generally agreed upon by Fregeans and Russellians alike, and is more or less a commonplace in the literature of the theory of meaning, and of the philosophy of semantics generally.

In addition to thesis (B), we assume that ordinary proper names, demonstratives, other single-word indexicals (such as ‘he’), and other simple (noncompound) singular terms are, in a given possible context of use, Russellian ‘genuine names in the strict logical sense’.6 Put more fully, we assume the following anti-Fregean thesis as a hypothesis:

(R) The contribution made by an ordinary proper name, demonstrative, or other simple singular term to securing the information content of, or the proposition expressed by, declarative sentences (with respect to a given possible context of use) in which the term occurs (outside of the scope of nonextensional operators, such as quotation marks) is just the referent of the term, or the bearer of the name (with respect to that context of use).

In various alternative terminologies, it is assumed that the interpretation (Barwise and Perry), or the Erkenntniswerte (Frege), or the content (David Kaplan), or the meaning (Russell), or the semantic value (Soames), or the information value (myself) of a proper name, demonstrative, or other simple singular term, with respect to a given context, is just its referent.

It is well-known that the thesis that ordinary proper names are Russellian, in this sense, in conjunction with thesis (B), gives rise to problems in propositional-attitude attributions, and is consequently relatively unpopular. (Even Russell rejected it.) Thus, thesis (R) is hardly the sort of thesis that can legitimately be taken for granted as accepted by the reader. However, I defend thesis (R) at some length and in some detail

in Frege's Puzzle. Moreover, the thesis has gained some long overdue respectability recently, and it cannot be summarily dismissed as obviously misguided. It is (more or less) accepted by Barwise–Perry, Kaplan, Richard, Soames, and others. One standard argument against the thesis—the argument from apparent failure of substitutivity in propositional-attitude contexts—has been shown by Kripke7 to be inconclusive at best, and the major rival approaches to the semantics of proper names and other simple singular terms have been essentially refuted by Keith Donnellan, Kripke, Perry, and others.8 The Richard–Soames problem is a problem that arises only on the assumption of thesis (R), and it is a problem for this thesis. It is not a problem for alternative approaches, such as those of Frege or Russell, which have much more serious problems of their own. Thesis (R) is to be taken as a hypothesis of the present paper, its defence given elsewhere. The conclusions and results reached in the present paper on the assumption of thesis (R) may be regarded as having the form ‘If thesis (R) is true, then thus-and-so.’ The present paper, in combination with Frege's Puzzle, allows for the all-important modus ponens step.

One version of the Richard–Soames problem can be demonstrated by the following sort of example, derived from Richard's. Suppose that Lois Lane, who is on holiday somewhere in the wilderness, happens to overhear an elaborate plot by some villainous misanthrope to expose Superman to Kryptonite (the only known substance that can harm Superman) at the Metropolis Centennial Parade tomorrow. She quickly rushes for the nearest telephone to warn Superman, but suddenly remembers that the nearest telephone is one day's journey away. As luck would have it, she happens to be standing in front of an overnight mail delivery service outlet. She quickly scribbles a note warning of the plot to harm Superman—a note that absolutely, positively has to get there overnight. She has no address for Superman (or so she believes), but she does have Clark Kent's address, and she (thinks she) knows that Clark planned to spend all day tomorrow at his apartment. Now the following sentence is true:


(1a)  

Lois believes that she will directly inform Clark Kent of Superman's danger with her note.


By the assumption of theses (B) and (R), it would seem that the following sentence contains the very same information as (1a), and hence must be true as well:

(1b)  

Lois believes that she will directly inform Superman of Superman's danger with her note.


Richard argues, however, that although (1a) is true in this example, (1b) cannot be true. For if (1b) were true, then the following sentence would also be true:


(1c)  

Lois believes that there is someone x such that she will directly inform x of x's danger with her note.


That is, if (1b) were true, then Lois would also believe that someone or other is such that she will inform him of his own danger with her note, since this follows trivially by existential generalization from what she believes according to (1b). Yet Lois believes no such thing. (Recall that Lois believes that she has no address for Superman.) Of course, Lois hopes that Clark will relay the warning to Superman before it is too late, but she has not formed the opinion that she herself will directly inform someone of his own danger with her note. To put it another way, it is simply false that Lois believes that there is someone with the special property that he will be directly informed by her of his own danger with her note. On the contrary, what she believes is that she will inform someone of someone else's danger with her note. Thus (1a) is true, though (1b) would seem to be false. This poses a serious problem for any theory—such as the theory formed from thesis (R) coupled with thesis (B) and some other natural assumptions—that claims that (1a) and (1b) have exactly the same information content, or even merely that they have the same truth value.

Using a similar example, Soames provides a powerful argument against semantic theories of a type that identify the information contents of declarative sentences with sets of circumstances (of some sort or other) with respect to which those sentences are either true or untrue (or equivalently, with characteristic functions from circumstances to truth values)—such as the possible-world theories of information content (David Lewis, Robert Stalnaker, and many others) or the ‘situation’ theory of Situations and Attitudes. The argument is this: the following sentence concerning a particular ancient astronomer is assumed to be true (where reference to a language, such as ‘English’, is suppressed):


(2a)  

The astronomer believes: that ‘Hesperus’ refers to Hesperus and ‘Phosphorus’ refers to Phosphorus.


Hence according to thesis (R) in conjunction with thesis (B) and some natural assumptions, the following sentence, which allegedly contains the very same information as (2a), must also be true:


(2b)  

The astronomer believes: that ‘Hesperus’ refers to Hesperus and ‘Phosphorus’ refers to Hesperus.


But if (2b) is true, and thesis (B) is also true, then on certain assumptions that are either trivial or fundamental to a set-of-circumstances theory of information content, the following is also true:

(2c)  

The astronomer believes: that something or other is such that ‘Hesperus’ refers to it and ‘Phosphorus’ refers to it.


Assuming thesis (B), the additional assumptions needed to validate the move from (2b) to (2c) on any set-of-circumstances theory of information content are: (i) that

a believer's beliefs are closed under simplification inferences from a conjunction to either of its conjuncts, i.e. if x believes p and q, then x believes q; and (ii) that the conjunction of an ordinary sentence S (excluding nonreferring singular terms and nonextensional devices such as the predicate ‘does not exist’) and any existential generalization of S is true with respect to exactly the same circumstances as S itself.

Now (2c) is tantamount to the claim that the astronomer believes that ‘Hesperus’ and ‘Phosphorus’ are co-referential. Yet certainly (2c) is no consequence of (2a). Indeed, we may take it as an additional hypothesis that (2c) is false of the ancient astronomer in question. Since (2a) is true and (2c) is false, it is either false that if (2a) then (2b)—contrary to the conjunction of theses (B) and (R)—or else it is false that if (2b) then (2c)—contrary to the conjunction of (B) and any set-of-circumstances theory of information content. Now (B) and (R) are true. Therefore, Soames argues, any set-of-circumstances theory of information content is incorrect. As Soames points out, the problem points to a fundamental error in the theory of Situations and Attitudes, which accepts both (B) and (R) as fundamental, thereby ensuring the validity of the move from (2a) to (2b), as well as the assumptions that validate the move from (2b) to (2c).

In the general case, we may have the first of the following three sentences true and the third false, where a and b are co-referential proper names, demonstratives, other simple singular terms, or any combination thereof, and R is a dyadic predicate:


(3a)  

c believes that aRb

(3b)  

c believes that aRa

(3c)  

c believes that (0x002203x)xRx.


The Richard–Soames problem is that (3b) appears to follow from (3a), and (3c) appears to follow from (3b). Since (3a) is true and (3c) false, something has got to give.

II

Now (3b) is either true or false. Hence it is either false that if (3a) then (3b), or else it is false that if (3b) then (3c). Both Richard and Soames accept thesis (R). Insisting that if (3b) then (3c), Richard maintains that it is false that if (3a) then (3b), thereby impugning thesis (B).9 Accepting thesis (B) as well as (R), Soames argues instead that ‘there is a principled means of blocking’ the move from (3b) to (3c) while preserving (B).

There is a certain intuitive picture of belief advanced by Barwise and Perry (Situations and Attitudes, chapter 10) and which is independently plausible in its own right. This is a picture of belief as a cognitive state arising from internal mental states that derive information content in part from causal relations to external objects. Soames points out that on this picture of belief, the following is indeed true if (3b) is:

(3d)  

(0x002203x) c believes that xRx.


Soames adds:10

However, [on this picture of belief] there is no reason to think that [the referent of c] believes the proposition that something bears R to itself. Since none of the agent's mental states has this as its information content, he does not believe it.

Quine distinguishes two readings of any sentence of the form 0x00231cc believes something is 0x0003d50x00231d—what he calls the notional and the relational readings. The notional reading may be spelled out as 0x00231cc believes: that something or other is 0x0003d50x00231d. It is the Russellian secondary occurrence or small-scope reading. The relational reading may be spelled out as 0x00231cc believes something in particular to be 0x0003d50x00231d, or more perspicuously as 0x00231cSomething is such that c believes: that it is 0x0003d50x00231d. It is the Russellian primary occurrence or large-scope reading. In Quine's terminology, Soames claims that the notional reading of 0x00231cc believes something bears R to it0x00231d does not follow from the relational. Quine demonstrated some time ago that the relational reading of 0x00231cc believes something is 0x0003d50x00231ddoes not in general follow from the notional reading, with his clever example of ‘Ralph believes someone is a spy’. Soames may be seen as arguing that, on a certain plausible picture of belief, there are cases in which the reverse inference also fails. Since the appearance of Quine's influential writings on the subject, it is no longer surprising that the notional reading does not imply the relational. It is at least somewhat surprising, however, that there could be converse cases in which the relational reading is true yet the notional reading false. This is what Soames is arguing.

My own view of the Richard–Soames problem favors Soames's account over Richard's. Thesis (B) is supported by strong linguistic evidence. It provides the simplest and most plausible explanation, for example, of the validity of such inferences as:

John believes the proposition to which our nation is dedicated.

Our nation is dedicated to the proposition that all men are created equal.

Therefore, John believes that all men are created equal.

Furthermore, although a number of philosophers have proposed a variety of truth-condition assignments for belief attributions contrary to thesis (B), these alternative truth-condition assignments often falter with respect to belief attributions that involve open sentences as their complement ‘that’-clause, and that are true under some particular assignment of values to individual variables or to pronouns—for example, ‘the astronomer believes that x is a planet’ in ‘There is something x such that x=Venus and the astronomer believes that x is a planet’ or ‘the astronomer believes that it is a planet’ in ‘As regards Venus, the astronomer believes that it is a planet’.11 Thesis (B) should be maintained to the extent that the facts allow, and should not be abandoned if Soames is correct that there is a principled means of solving the Richard–Soames problem while maintaining (B).

By contrast, Soames's proposals for solving the problem invoke essentially some of the same ideas advanced and defended in Frege's Puzzle. There I develop and defend

thesis (R) (and, to a lesser extent, thesis (B)), as well as the view (which Russell himself came to reject) that the contents of beliefs formulatable using ordinary proper names, demonstratives, or other simple singular terms, are so-called singular propositions (Kaplan), i.e. structured propositions directly about some individual which occurs directly as a constituent of the proposition. I take propositions to be structured in such a way that the structure and constituents of a proposition are directly readable from the structure and constituents of a declarative sentence containing the proposition as its information content. By and large, a simple (noncompound) expression contributes a single entity, taken as a simple (noncomplex) unit, to the information content of a sentence in which the expression occurs, whereas the contribution of a compound expression (such as a phrase or sentential component) is a complex entity composed of the contributions of the simple components.12 One consequence of this sort of theory is that, contrary to set-of-circumstances theories of information content, there is a difference, and therefore a distinction, between the information content of the conjunction of an ordinary sentence S and any of its existential generalizations and that of S itself. This disables the argument that applied in the case of a set-of-circumstances theory to establish the (alleged) validity of the move from (3b) to (3c).

Unfortunately, this difference between the two sorts of theories of information content does not make the problem disappear altogether. There is an interesting philosophical puzzle concerning the logic and semantics of propositional-attitude attributions that is generated by the Richard–Soames problem, a puzzle that arises even on the structured-singular-proposition sort of view sketched above.

Soames slightly misstates the case when he says that (on the intuitive picture of belief as deriving from certain mental states having information content), ‘there is no reason to think that (3c) is true’. For in fact, even though (1c) and (2c) are false in the above examples, there are very good reasons to think that they are true. One excellent reason to think that (1c) is true is the fact that (1b) is true, and one excellent reason to think that (2c) is true is the fact that (2b) is true. In general, it is to be expected that if a sentence of the form 0x00231cc believes that 0x0003d5a 0x00231dis true, then so is 0x00231cc believes that (0x002203x)0x0003d5 x 0x00231d, where a is a singular term that refers to something, 0x0003d5is an ordinary extensional context (excluding such predicates as ‘does not exist’), and 0x0003d5a is the result of substituting (free) occurrences of a for free occurrences of ‘x’ uniformly throughout 0x0003d5x . There is a general psychological law to the effect that subjects typically tend to believe the existential generalizations of their beliefs. Herein the puzzle arises. Even if the conjunctive proposition ‘Hesperus’ and ‘Phosphorus’ refer to Hesperus and there is something that ‘Hesperus’ and ‘Phosphorus’ refer to is not the same proposition as the simpler proposition ‘Hesperus’ and ‘Phosphorus’ refer to Hesperus, if the astronomer believes that ‘Hesperus’ and ‘Phosphorus’ refer to Hesperus, then it seems he ought to believe that there is something that ‘Hesperus’ and ‘Phosphorus’ refer to. And if Lois believes that she will inform Superman of his danger with her note, then it seems she ought to believe that there is someone whom she will inform of his danger with her note. It is precisely for this reason that Richard rejects (1b), even though he does not endorse a set-of-circumstances theory of information content and favors the structured-singular-proposition account.

Perhaps if a subject is insane or otherwise severely mentally defective, he or she may fail to believe the (validly derivable) existential generalizations of his or her beliefs, but we may suppose that neither Lois Lane nor the astronomer suffer from any mental defects. We may even suppose that they are master logicians, or worse yet, that they have a perverse penchant for drawing existential generalization (EG) inferences as often as possible. They go around saying things like ‘I'm tired now; hence, sometimes someone or other is tired’ and ‘Fred shaves Fred; hence someone shaves Fred, Fred shaves someone, and someone shaves himself.’ In this way, it can be built into the example that the truth of (1b) is an excellent reason to believe in the truth of (1c), and the truth of (2b) is an excellent reason to believe in the truth of (2c). For such EG-maniacs, one might expect that it is something of a general law that every instance of the following schema is true:


(L 1 )  

If c believes that 0x0003d5a , then c believes that something is such that 0x0003d5it ,


where c refers to the subject, a is any referring singular term of English, 0x0003d5it is any English sentence in which the pronoun ‘it’ occurs (free and not in the scope of quotation marks, an existence predicate, or other such operators) and which may also contain occurrences of a, and 0x0003d5a is the result of substituting (free) occurrences of a for (free) occurrences of ‘it’ throughout 0x0003d5it . In fact, one might expect that it is something of a general law that every instance of (L 1 ) is true where c refers to any normal speaker of English, even if he or she is not an EG-maniac.

I maintain with Soames that the sentences 0x00231cIf (1b) then (1c)0x00231d and 0x00231cIf (2b) then (2c)0x00231d constitute genuine counterexamples to this alleged general law. But even if the principle that every instance of (L 1 ), as formulated, is true is thereby refuted, surely something very much like it, some weakened version of it, must be true—even where the referent of c does not have a perverse penchant for existential generalization. For the most part, in the typical kind of case, it would be highly irrational for someone to fail to believe the existential generalizations of one of his or her beliefs. Neither Lois Lane nor the astronomer is irrational in this way. The conditionals 0x00231cIf (1b) then (1c)0x00231d and 0x00231cIf (2b) then (2c)0x00231d are not typical instances of schema (L 1 ), but it is not enough simply to point out how they are atypical and to leave the matter at that. It is incumbent on the philosopher who claims that these instances of (L 1 ) fail, to offer some alternative principle that is not falsified in these cases and thereby accounts for the defeasible reliability, and the prima facie plausibility, of the alleged general law.

This is not a problem special to set-of-circumstances theories of information content. It is equally a puzzle for the structured-singular-proposition sort of theory that


I advocate and that Soames proposes in his discussion of the Richard–Soames problem. It is a puzzle for the conjunction of theses (B) and (R), irrespective of how these theses are supplemented with a theory of information content.

III

There is a second, and surprisingly strong, reason to suppose that (1c) and (2c) are true. The general puzzle posed by the Richard–Soames problem can be significantly strengthened if we exploit a simple reflexive device already present to a certain degree in standard English.

Given any simple dyadic predicate 0x0003a0, we may form a monadic predicate 0x00231cself-0x0003a00x00231d defined by



(0x0003bbx)x0x0003a0x,

in such a way that 0x00231cself-0x0003a00x00231d is to be regarded as a simple (noncompound) expression, a single word. In English, this might be accomplished by converting a present tensed transitive verb V into a corresponding adjective and prefixing ‘self-’ to obtain a reflexive adjective; e.g. from ‘cleans’ we obtain ‘self-cleaning’, from ‘indulges’, ‘self-indulgent’, from ‘explains’, ‘self-explanatory’, and so on. The contribution made by a term of the form 0x00231cself-0x0003a00x00231d to the information content, with respect to a time t, of a typical sentence in which it occurs is simply the reflexive property of bearing R to oneself at t, where R is the binary relation semantically associated with 0x0003a0.13 Assuming thesis (R), if a is a proper name or other simple singular term and R is the binary relation semantically associated with 0x0003a0, then the information content, with respect to t, of the sentence 0x00231cself-0x0003a0(a)0x00231d is the singular proposition made up of the referent of a together with the property of bearing R to oneself at t.

Consider again the move from (3a) to (3b), where a and b are co-referential proper names, R is a simple dyadic predicate, and (3a) is true:


(3a)  

c believes that aRb.

(3b)  

c believes that aRa.


As Soames points out, (on a plausible picture of belief) the following relational, or de re, attribution follows from (3b):


(3d)  

(0x002203x) c believes that xRx.


In fact, a somewhat stronger de re attribution also follows from (3b), by exportation:14



(0x002203x)[x=a & c believes that xRx],

or less formally:


(3b′)  

c believes of a that it R it.


Now from this it would seem to follow that:


(3e′)  

c believes of a that it R itself.


From this (perhaps together with some general psychological law) it would seem to follow further that:


(3f′)  

c believes of a that self-R(it),


with the predicate 0x00231cself-R0x00231d understood as explained above. Finally by importation, we may infer:


(3f)  

c believes that self-R(a).


For example, suppose that, owing to certain miscalculations, the astronomer comes to believe that Hesperus weighs at least one thousand tons more than Phosphorus. Now every step in the following derivation follows by an inference pattern that is either at least apparently intuitively valid or else sanctioned by the conjunction of theses (B) and (R), or both:


(4a)  

The astronomer believes that Hesperus outweighs Phosphorus.

(4b)  

The astronomer believes that Hesperus outweighs Hesperus.

(4b′)  

The astronomer believes of Hesperus that it outweighs it.

(4e′)  

The astronomer believes of Hesperus that it outweighs itself.

(4f′)  

The astronomer believes of Hesperus that it is self-outweighing.

(4f)  

The astronomer believes that Hesperus is self-outweighing.


One could continue the sequence of inferences from (4f) all the way to:


(4c)  

The astronomer believes that there is something such that it outweighs it,


by invoking some corrected, weakened version of the law mentioned above (the alleged law that every appropriate instance of (L 1 ) is true), to pass from (4f) to:


(4g)  

The astronomer believes that there is something such that it is self-outweighing,


from which (4c) appears to follow directly. But there is no need to extend the derivation this far. A problem arises at least as soon as (4f). For unless the astronomer is insane, or otherwise severely mentally defective, (4f) is obviously false. The astronomer would not ascribe to Venus the reflexive property, which nothing could possibly have, of weighing more than oneself. Hence, in moving from a sentence to its immediate successor, somewhere in the derivation of (4f) we move from a truth to a falsehood. Where? The moves from (4a) to (4b′) and from (4f′) to (4f) are validated by the conjunction of theses (B) and (R), and both of the remaining transitions commencing with (4b′) are based on inference patterns that (assuming ordinary folk psychology and that the astronomer is normal) seem intuitively valid.

One may harbour some residual doubts about the exportation move from (4b) to (4b′) and/or the importation move from (4f′) to (4f). The theory formed from the conjunction of theses (B) and (R) requires the validity of both of these inferences, so that if either is invalid the theory is false. In fact, however, these inferences are not essential to the present puzzle. The exportation inference takes us on a detour that some may find helpful, though one may bypass the de re ‘believes of’ construction altogether. Instead, we may construct the following alternative derivation from (4b):


(4b)  

The astronomer believes that Hesperus outweighs Hesperus.

(4e)  

The astronomer believes that Hesperus outweighs itself.

(4f)  

The astronomer believes that Hesperus is self-outweighing.


If the inference from (4b′) to (4e′) is valid, then by parity of reasoning so is the inference from (4b) to (4e). And if the inference from (4e′) to (4f′) is valid, then by parity of reasoning so is the inference from (4e) to (4f). Hence, if the derivation of (4f′) from (4b′) via (4e′) is legitimate, then so is the derivation of (4f) from (4b) via (4e). But (4f) is false. Therefore, it would seem, so is (4b). Sentence (4a), on the other hand, is true. This raises anew doubts about the independently suspicious move from (4a) to (4b), or more generally, the move from (3a) to (3b), thereby impugning once again the conjunction of theses (R) and (B).

The new puzzle, then, is this: according to the conjunction of theses (B) and (R), (4b) follows from (4a) together with the fact that ‘Hesperus’ and ‘Phosphorus’ are co-referential proper names. Now in the sequence <(4b),(4e),(4f)>, each sentence appears to follow logically from its immediate predecessor. Alternatively in the sequence <(4b′),(4e′),(4f′)>, each sentence appears to follow logically from its immediate predecessor, and furthermore, according to the conjunction of (B) and (R), (4b) entails (4b′), and (4f′) entails (4f). One way or another, we seem to be able to derive (4f) from (4a), together with the fact that ‘Hesperus’ and ‘Phosphorus’ are co-referential proper names. Yet in the example, (4a) is plainly true and (4f) plainly false. Where does the derivation go wrong?

I call this the puzzle of reflexives in propositional attitudes. Here again, the problem posed by the puzzle is especially pressing for any set-of-circumstances theory of information content. In fact, the problem is even more pressing than the Richard–Soames problem for such theories, if that is possible. One difference between the Richard–Soames problem and the puzzle of reflexives in propositional attitudes is that what is said to be believed at the final step of the derivation, in this case step (3f), is not merely a consequence of, but is equivalent to, what is said to be believed in (3b). In fact, any circumstance in which an individual x bears R to x is a circumstance in which x has the reflexive property of bearing R to oneself, and vice versa. There is no need here to make the additional assumption that belief is closed under simplification inferences. Any set-of-circumstances theory of information content, in conjunction with thesis (B), automatically validates the derivation of (3f) from (3b). The problem thus also points to a fundamental error in the theory of Situations and Attitudes which includes both theses (B) and (R) as fundamental, thereby validating the full derivation of (3f) from (3a) without any further assumptions concerning belief. The puzzle of reflexives in propositional attitudes, however, is not peculiar to set-of-circumstances theories, and arises on any theory of information content that incorporates the conjunction of theses (B) and (R), including the structured-singular-proposition theory that I advocate. The difference is that the structured-singular-proposition view (in conjunction with (B) and (R)), unlike the theory of Situations and Attitudes, is not committed by its very nature to the validity of the derivation of (4f) from (4b). It is just that each step in the derivation of (4f) from (4b) is independently plausible.

IV

The puzzle of reflexives in propositional attitudes is related to a paradox that concerns quantification into belief contexts and that was discovered some time ago by Alonzo Church.15 Unlike the former puzzle, however, Church's paradox presents a serious problem in particular for the theory of structured singular propositions.

As a matter of historical fact, as of some appropriate date, King George IV was acquainted with Sir Walter Scott, but was doubtful whether Scott was the author of Waverley. We may even suppose that George IV believed at that time that Scott did not write Waverley. Yet, Church notes, if quantification into belief contexts is taken as meaningful in combination with the usual laws of the logic of quantification and identity, then the following is provable as a logical theorem using classical Indiscernibility of Identicals (Leibniz's Law):


(5)  

For every x and every y, if George IV does not believe that xx, if George IV believes that xy, then xy.


Mimicking the standard proof in quantified modal logic of the necessity of identity, Church remarks that although it is not certain, it was very likely true as of the same date that:


(6)  

For every x, George IV does not believe that xx,


since it is very likely that George IV did not believe anything to be distinct from itself. Taking (6) as premiss, we may derive:


(7)  

For every x and every y, if George IV believes that xy, then xy.


We are thus apparently led to ascribe to King George's beliefs the strange ‘power to control the actual facts about x and y’. Since Scott is in fact the author of Waverley, this derivation of (7) from (6) seems to preclude King George's believing, as of the same date, that Scott did not write Waverley. The derivation thus constitutes an unacceptable paradox, not unlike Russell's paradox of naïve set theory (set theory with unrestricted comprehension). Church concludes that this provides a compelling reason to reject the meaningfulness of quantification into belief contexts.16

As quantification into belief contexts goes, so goes the theory of structured singular propositions as potential objects of belief. Church's paradox thus poses a serious difficulty for the theory that I advocate. But it also poses a serious difficulty for any theory, including any set-of-circumstances theory, that purports to make sense of de re constructions or quantification into belief contexts. Furthermore, the paradox is quite independent of the conjunction of theses (B) and (R). Whether these are true or false, the paradox arises as long as quantification into belief contexts is regarded as meaningful.

V

It is precisely to treat philosophical puzzles and problems of the sort presented here that I proposed the sketch of an analysis of the binary belief relation between believers and propositions (sometimes Russellian singular propositions) in Frege's Puzzle. I take the belief relation to be, in effect, the existential generalization of a ternary relation,


BEL, among believers, propositions, and some third type of entity. To believe a proposition p is to adopt an appropriate favorable attitude toward p when taking p in some relevant way. It is to agree to p, or to assent mentally to p, or to approve of p, or some such thing, when taking p a certain way. This is the BEL relation. The third relata for the BEL relation are something like proposition guises, or modes of acquaintance with propositions, or ways in which a believer may be familiar with a given proposition. Of course, to use a distinction of Kripke's, this formulation is far too vague to constitute a fully developed theory of belief, but it does provide a picture of belief that differs significantly from the sort of picture of propositional attitudes advanced by Frege or Russell, and enough can be said concerning the BEL relation to allow for at least the sketch of a solution to certain philosophical puzzles, including the original puzzle generated by the Richard–Soames problem.

In particular, the BEL relation satisfies the following three conditions:


(i)  

A believes p if and only if there is some x such that A is familiar with p by means of x and BEL(A, p, x).

(ii)  

A may believe p by standing in BEL to p and some x by means of which A is familiar with p without standing in BEL to p and all x by means of which A is familiar with p.

(iii)  

In one sense of ‘withhold belief’, A withholds belief concerning p (either by disbelieving or by suspending judgment) if and only if there is some x by means of which A is familiar with p and not-BEL(A, p, x).


These conditions generate a philosophically important distinction between withholding belief and failure to believe (i.e. not believing). In particular, one may both withhold belief from and believe the very same proposition simultaneously. (Neither withholding belief nor failure to believe is to be identified with the related notions of disbelief and suspension of judgment—which are two different ways of withholding belief, in this sense, and which may occur simultaneously with belief of the very same proposition in a single believer.)

It happens in most cases (but not all) that when a believer believes some particular proposition p, the relevant third relatum for the BEL relation is a function of the believer and some particular sentence of the believer's language. Consider for example the binary function f that assigns to any believer A and sentence S of A's language, the way A takes the proposition contained in S (in A's language with respect to A's context at some particular time t) were it presented to A (at t) through the very sentence S. Then (assuming t is the time in question) Lois believes the proposition that she will inform Clark Kent of Superman's danger with her note by virtue of standing in the BEL relation to this proposition together with the result of applying the function f to Lois and the particular sentence ‘I will inform Clark Kent of Superman's danger with my note.’ That is, in the example the following is true:

BEL(Lois, that she will inform Clark Kent of Superman's danger with her note, f[Lois, ‘I will inform Clark Kent of Superman's danger with my note’]).

On the other hand, the following is false:

BEL(Lois, that she will inform Superman of his danger with her note, f[Lois, ‘I will inform Superman of his danger with my note’]).

Similarly, assuming the astronomer in Soames's example spoke English:

BEL(the astronomer, that ‘Hesperus’ refers to Hesperus and ‘Phosphorus’ refers to Phosphorus, f[the astronomer, ‘ “Hesperus” refers to Hesperus whereas “Phosphorus” refers to Phosphorus’]),

but not:

BEL(the astronomer, that ‘Hesperus’ refers to Hesperus and ‘Phosphorus’ refers to Hesperus, f [the astronomer, ‘ “Hesperus” and “Phosphorus” both refer to Hesperus’]).

In Frege's Puzzle the BEL relation and the function f are invoked in various ways to explain and to solve some of the standard (and some nonstandard) problems that arise on the sort of theory I advocate. This device is also useful with regard to the original puzzle that arises from the Richard–Soames problem and the puzzle of reflexives in propositional attitudes.

In the first example, (1c) is false, since Lois does not adopt an appropriate favorable attitude toward the proposition that there is someone whom she will inform of his own danger with her note, no matter how this proposition might be presented to her. That is, there is no x such that Lois stands in BEL to the proposition that she will inform someone or other of his own danger with her note and x. Similarly, in Soames's example. (2c) if false, since the astronomer does not adopt the appropriate favorable attitude toward the proposition that ‘Hesperus’ and ‘Phosphorus’ are co-referential, no matter how this proposition might be presented to him. He does not stand in BEL to this proposition and any x.

What about (1b) and (2b)? These are indeed true in the examples. Consider the first example. Sentence (1a) is true by hypothesis. Now notice that if Superman were somehow made aware of the truth of (1a), then he could truthfully utter the following sentence:


(1bI)  

Lois believes that she will directly inform me of my danger with her note.


In fact, (1bI) yields the only natural way for Superman to express (to himself) the very information that is contained in (1a). But if (1bI) is true with respect to Superman's context, then (1b) is true with respect to ours. Both (1bI), taken with respect to Superman's context, and (1b), taken with respect to ours, are true precisely because Lois adopts the appropriate favorable attitude toward the proposition about Superman, i.e. Clark Kent, that she will inform him of his danger with her note. Lois assents to this information when she takes it the way she would if it were presented to her through the sentence ‘I will inform Clark Kent of Superman's danger with my note.’ Hence, she believes it. Similarly, the astronomer inwardly assents to the proposition about Hesperus, i.e. Venus, that ‘Hesperus’ refers to it and ‘Phosphorus’ refers to it, when it is presented to him through the sentence ‘ “Hesperus” refers to Hesperus whereas “Phosphorus” refers to Phosphorus’. Hence (2b) is true.

In fact, in the examples Lois also believes that she will not inform Superman of his danger with her note, and the astronomer that ‘Hesperus’ and ‘Phosphorus’ do not both refer to Hesperus, since:

BEL(Lois, that she will not inform Superman of his danger with her note, f[Lois, ‘I will not inform Superman of his danger with my note’])

and:

BEL(the astronomer, that ‘Hesperus’ and ‘Phosphorus’ do not both refer to Hesperus, f[the astronomer, ‘ “Hesperus” and “Phosphorus” do not both refer to Hesperus’]).

Both Lois and the astronomer thus (unknowingly) believe some proposition together with its denial.17

One reason so many instances of schema (L 1 ) are true, although it fails in these special cases, is that the schema approximates the following weaker schema, all (or at least very nearly all) of whose instances are true, and which is not falsified in these special cases:

(L 2 ) If (0x002203p)BEL(c, p, f[c, ‘0x0003d5 a ’]), then (0x002203q)BEL(c, q, f[c, ‘Something is such that 0x0003d5it ’]),

where c refers to a normal speaker of English, a is any referring singular term of English, 0x0003d5it is any English sentence in which the pronoun ‘it’ occurs (free and not in the scope of quotation marks, an existence predicate, or other such operators) and which may also contain occurrences of a, and 0x0003d5a is the result of substituting (free) occurrences of a for (free) occurrences of ‘it’ throughout 0x0003d5it . I submit that the similarity of the former schema (L 1 ) to something like schema (L 2 ) is a major source of the plausibility of the alleged general law concerning the former. Schema (L 2 ) is not falsified in these special cases, even if Lois and the astronomer are normal speakers of English, since Lois does not agree to the proposition that she will inform Superman of his danger with her note when she takes it in the way she would if it were presented to her through the sentence ‘I will inform Superman of his danger with my note’, and the astronomer does not agree to the proposition that ‘Hesperus’ and ‘Phosphorus’ refer to Venus when it is presented to him through the sentence ‘ “Hesperus” and “Phosphorus” refer to Hesperus.’18

end p.47


VI

Even if this resolves the original puzzle generated by the Richard–Soames problem for the structured-singular-proposition account of information content, it does not yet lay to rest the puzzle of reflexives in propositional attitudes, not to mention Church's ingenious paradox concerning quantification into belief contexts.

Richard's proposal to solve the original puzzle by blocking the initial inference from (3a) (together with the fact that a and b are co-referential proper names or other simple singular terms) to (3b) would equally block the puzzle of reflexives in propositional attitudes. This proposal involves relinquishing thesis (B), and is motivated by the threat of the alleged derivability of falsehoods such as (1c) from (1b). But I argued above that thesis (B) is supported by strong linguistic evidence, and should be maintained insofar as the facts allow. We have seen that the account of belief in terms of the BEL relation effectively blocks the move from (1b) to (1c), while retaining thesis (B) and while also affording an explanation (or at least the sketch of an explanation) for the prima facie plausiblity of the move. If there is a solution to the problem of reflexives in propositional attitudes, it does not lie in the rejection of thesis (B).

Ruth Barcan Marcus has argued that, in at least one ordinary sense of ‘believe’, it is impossible to believe what is impossible.19 Marcus would thus claim that (4a) is false to begin with, since the astronomer cannot ‘enter into the belief relation’ to the information, which is necessarily misinformation, that Hesperus outweighs

Phosphorus. However, one of Marcus's arguments for this, perhaps her main argument, appears to be that where a and b are co-referential names, if (3a) is true so is (3c), and in a great many cases where one is inclined to hold an instance of (3a) true even though 0x00231caRb0x00231d encodes necessarily false information ((4a) for example), (3c) is patently false, because 0x00231c(0x002203x)xRx0x00231d (e.g. ‘Something outweighs itself’) encodes information that is not only impossible but patently unbelievable.20

Marcus's view that one cannot believe what cannot be true is highly implausible, and I believe, idiosyncratic. It often happens in mathematics and logic that owing to some fallacious argument, one comes to embrace a fully grasped proposition that is in fact provably false. Sometimes this happens even in philosophy, more often than we care to admit. In our example, we may suppose that, for some particular number n, the astronomer comes to believe the proposition that Hesperus weighs at least n tons, and also the proposition that Phosphorus weighs no more than (n − 1,000) tons. He embraces these two propositions. It is very implausible to suppose that the fact that their conjunction is such that it could not be true somehow prevents the astronomer from embracing that conjunction, along with its component conjuncts, or that the astronomer is somehow prevented from forming beliefs on the basis of inference from his two beliefs, as in (4a).

More important for our present purpose is that Marcus's argument for the falsehood of (4a), at least as the argument is interpreted here, has to be mistaken. Otherwise, one could also show that (1a) and (2a) are false in the original examples. For although the proposition that Lois will inform someone of his own danger with her note is not unbelievable, it is plain in the example that it is not believed by Lois, i.e. (1c) is plainly false. If Marcus's argument for the impossibility of believing the impossible were sound, then by parity of reasoning it would follow that (1a) is false. Similarly, although the proposition that ‘Hesperus’ and ‘Phosphorus’ are co-referential is believable, in fact true, it is a hypothesis of the example that the astronomer does not believe it, i.e. (2c) is stipulated to be false. If Marcus's claim that (3c) is true if (3a) is true were itself true, it would follow that (2a) is false. But (1a) and (2a) are plainly true in these examples. There must be something wrong, therefore, with Marcus's argument, at least as I have interpreted it here.

What is wrong is precisely the claim that (3c) is true if (3a) is. Since it is incorrect, this claim cannot give us a way out of the present problem. In fact by shifting from (4a)–(4f) to another example, we can remove the feature that what is said to be believed at step (a) is such that it could not be true. Thus from ‘Lois believes that

Clark Kent disparages Superman while Superman indulges Clark Kent’ we may construct a parallel and equally fallacious derivation of ‘Lois believes that Superman is self-disparaging and self-indulgent.’ Marcus's unusual contention that it is impossible to believe the impossible, whether correct or incorrect, is simply irrelevant to this example.

What, then, is the solution to the puzzle of reflexives in propositional attitudes for the theory of structured singular propositions?

In the example, (4b) and (4b′) are true, whereas (4f) and (4f′) are false. Any temptation to infer (4f) from (4b), or (4f′)(4b′), can be explained using the BEL relation and the function f in a manner similar to the explanation given above in connection with the prima facie plausibility of inferring (3c) from (3b). In any case, either the inference from (4b) to (4e) (and therewith the inference from (4b′) to (4e′)) is fallacious, or the inference from (4e) to (4f) (and therewith the inference from (4e′) to (4f′)) is. Which is it?

Answering this question involves taking sides in a current controversy concerning the identity or distinctness of propositions of the form x bears R to x and x bears R to itself. If the propositions that Hesperus outweighs Hesperus and that Hesperus outweighs itself are the very same, then the inference from (4b) to (4e) is valid by classical Indiscernibility of Identicals (or Leibniz's Law) together with thesis (B), and the inference from (4e) to (4f) must then be rejected. If, on the other hand, these propositions are not the same and instead the proposition that Hesperus outweighs itself is the same (or very nearly the same) as the proposition that Hesperus is self-outweighing, then the inference from (4e) to (4f) is unobjectionable and the inference from (4b) to (4e) must be rejected.

As noted in Section III above, the advocate of a set-of-circumstances theory of information content is committed to the claim that propositions of the form x bears R to x and x bears R to itself are exactly the same, since any circumstance in which x bears R to x is one in which x bears R to itself, and vice versa. Thus, M. J. Cresswell, a set-of-possible-worlds theorist, has recently claimed that:21

on any reasonable account of propositions, the proposition that Ortcutt loves himself ought to be the same as the proposition that Ortcutt loves Ortcutt.

This, however, is far from the truth. In fact, there are compelling reasons to distinguish a proposition of the form x bears R to x from the proposition x bears R to itself. One sort of consideration is the following: we must distinguish between the reflexive property of exceeding oneself in weight and the simple relational property of exceeding the planet Venus in weight. The former is an impossible property; it is quite impossible for anything to possess it. The latter property, on the other hand, is fairly widespread; a great many massive objects (e.g. the stars) possess it—although, of course, it is quite impossible for Venus to possess it. Now the sentence ‘Hesperus outweighs itself’ seems to ascribe to Hesperus, i.e. Venus, the impossible property of weighing more than oneself, rather than the simple relational property of weighing more than Venus. It seems to say about Venus what ‘Mars outweighs itself’ says about

Mars—that it has the reflexive property of exceeding oneself in weight—and not what ‘Mars outweighs Venus’ says about Mars. If one wants to ascribe to Venus the simple relational property of weighing more than Venus, rather than the impossible property of weighing more than oneself, one may use the sentence ‘Hesperus outweighs Hesperus’ (among others). It says about Venus what ‘Mars outweighs Venus’ says about Mars—that it weighs more than Venus—instead of what ‘Mars outweighs itself’ seems to say about Mars. If one prefers, it ascribes the relation of exceeding-in-weight to the ordered pair of Venus and itself. In either case, the proposition contained in ‘Hesperus outweighs Hesperus’ is not the same as what seems to be the proposition contained in ‘Hesperus outweighs itself’.22 Contrary to any set-of-circumstances account of propositions, the proposition about Venus, that it weighs more than it, is a different proposition from the proposition about Venus that it is self-outweighing, although they are, in some sense, logically equivalent to one another.23

end p.51


The astronomer in the example believes the former and not the latter. Neither the sentence ‘Hesperus outweighs Hesperus’ nor the sentence ‘Hesperus outweighs itself’ can be regarded as somehow containing both of these propositions simultaneously (as might be said, for example, of the conjunction ‘Venus has the simple relational property of weighing more than Venus and also the reflexive property of weighing more than oneself’). Each sentence contains precisely one piece of information, not two. Neither is ambiguous; neither is a conjunction of two sentences with different (albeit equivalent) information contents.24 Similar remarks may be made in connection with Cresswell's example of ‘Ortcutt loves Ortcutt’ and ‘Ortcutt loves himself’.

This conception of reflexive propositions of the form x bears R to itself involves rejecting the otherwise plausible view that the reflexive pronoun ‘itself’ in ‘Hesperus outweighs itself’ refers anaphorically to the planet Venus. Instead, the pronoun might be regarded as a predicate-operator, one that attaches to a dyadic predicate to form a compound monadic predicate. Formally, this operator may be defined by the following expression:25



(0x0003bbR)(0x0003bbx)xRx.


The alternative conception of propositions of the form x bears R to itself involves treating reflexive pronouns instead as anaphorically referring singular terms. On this view, in order to ascribe to Venus the reflexive impossible property of weighing more than oneself, it is not sufficient to use the sentence ‘Hesperus outweighs itself’. Instead, one must resort to some device such as the predicate ‘is self-outweighing’.

There can be no serious question about the possibility of an operator such as the one defined above. The displayed expression definitely captures a possible operator on dyadic predicates. There is no reason why English (and other natural languages) could not contain such an operator, and there is no a priori argument that standard English does not have this operator. The question is whether the reflexive pronouns

of standard English (‘itself’, ‘himself’, ‘myself’, ‘oneself’, etc.) are expressions for this operator, rather than anaphorically referring singular terms.

This is not a metaphysical question about the essential natures of propositions, but an empirical question about the accidents of standard English semantics. It is a question, moreover, for which decisive linguistic evidence is difficult to produce, since on either hypothesis the information content of ‘Hesperus outweighs itself’ is logically equivalent to the content yielded by the rival hypothesis (although writers on both sides of this dispute have advanced what they take to be compelling evidence for their view).

Assuming that the semantic analysis presented above of sentences such as ‘Hesperus outweighs Hesperus’ is at least roughly correct, the claim that propositions of the form x bears R to x and x bears R to itself are the same is tantamount to the empirical claim that the reflexive pronouns of standard English are singular terms and not expressions for the predicate-operator defined above, whereas the claim that the proposition x bears R to itself is not the same as x bears R to x but instead goes with x is self-R is tantamount to the empirical claim that the reflexive pronouns are expressions for the predicate-operator and not singular terms. This issue cannot be settled by a priori philosophical theorizing about the nature of propositions. A complete solution to the puzzle of reflexives in propositional attitudes thus turns on answering a difficult empirical question concerning the meanings of reflexive pronouns in standard English.

VII

The time has come to face the music. How can the theory of structured singular propositions solve Church's paradox concerning quantification into belief contexts?

Fortunately, some of the ideas discussed in the preceding sections bear directly on Church's paradox. Notice first that (7), taken literally, does not ascribe any power to King George or his beliefs per se. Nor does it ascribe to George an infallibility concerning the distinctness of distinct individuals x and y. It merely states a generalization concerning every pair of individuals x and y believed distinct by King George. In Humean terminology, it merely states a constant conjunction between any pair of individuals being believed distinct by King George and their actually being distinct. As Hume noted, there is no idea of power contained in that of constant conjunction. Analogously, the sentence ‘All crows are black’ merely states a generalization, or constant conjunction, concerning all crows. The idea that something's being a crow somehow makes it black arises only when this sentence is regarded as having the status of biological law, rather than that of a purely accidental generalization.

Likewise, the conclusion (7) can be regarded as ascribing a power or nomological regularity to King George's beliefs only if (7) is regarded as having the status of a law ascribing some special law-governed feature to George IV and his beliefs, rather than as an accidental constant conjunction. Now in deriving (7), we took (6) as our only premiss. Thus (7) may be regarded as stating some sort of law only if (6) may be.

Church remarks that, even though (6) is not certain, it is very likely. This observation may support a plausible view of (6) as some sort of psychological law concerning George IV and his beliefs. In this way, (7) would emerge as a law ascribing a nomological feature to King George's beliefs. Since no such law in fact obtains, and may even be falsified by the very case of Sir Walter Scott and the author of Waverley, the meaningfulness of quantification into belief contexts, and therewith the theory of structured singular propositions, would be thereby discredited.

On the theory that I advocate, however, (6) is not only not very likely, as of some particular date during King George's acquaintance with Scott, it is very likely false.

It may seem as if denying (6) is tantamount to saying that George IV believed of some x that it is distinct from itself, and this seems a serious charge indeed. If an interest in the law of identity can hardly be attributed to the first gentleman of Europe, it is nothing short of blasphemy to attribute to him an interest in denying that law. In claiming that (6) is very likely false, as of some appropriate date, I mean no disrespect. Sentence (6) can easily be false even though King George is, of course, entirely rational—in fact, even if he were (what is beneath his dignity) a master of classical logic. If there was some time when George IV was acquainted with Scott and nevertheless believed after reading a Waverley novel that Scott was not the author, then (6) is false with respect to that time. If this be disputed, imagine instead that George IV confronted Scott at a book-signing ceremony, at which Scott truthfully proclaimed his authorship of Waverley but disguised himself in order to conceal his identity as Sir Walter Scott. Suppose the disguise succeeded in fooling even King George.26 Let George IV say with conviction, pointing to the disguised author, ‘He is not Sir Walter Scott’. In this case, (6) is decisively false. George IV is in the same unfortunate position as that of the ancient astronomer who believed of Venus that it is distinct from it.

Why, then, does Church claim that (6) is very likely? My conjecture is that Church confuses (6) with:

(6′) For every x, George IV does not believe that (0x0003bbx′)[x′≠x′] (x)

or with:


(6″)  

For every x, George IV does not believe that x is self-distinct,


where the term ‘self-distinct’ is understood in accordance with the definition of the ‘self’-prefix given in Section III above. Both of these are indeed extremely likely—nay (I hasten to add), virtually certain. On the theory that I advocate, the pair of open sentences



xx

and


(0x0003bbx′)[x′ ≠ x′] (x)


(or ‘x is distinct from x’ and ‘x is self-distinct’), although logically equivalent, must be sharply distinguished as regards the propositions expressed under any particular assignment of a value to the variable ‘x’. Under the assignment of Scott to ‘x’, the singular proposition contained in the first open sentence is believed by George IV in the book-signing example, the second is not. The extreme likelihood of (6′) and (6″) does not extend to (6).

Whereas sentences (6′) and (6″) are similar to, and easily confused with sentence (6), the former sentences do not concern King George's doxastic attitudes toward the propositions involved in sentence (6). They concern propositions of the form x is self-distinct (which ascribe the plainly impossible property of self-distinctness to particular individuals x) rather than propositions of the form x is distinct from x (which ascribe the relation of distinctness to reflexive pairs of individuals <x,x>). Sentences (6′) and (6″) provide adequate explanation why George IV is disinclined to answer affirmatively when queried ‘Is Sir Walter self-distinct?’, but the substitution of these sentences for Church's (6) does not show sufficient appreciation for the fact that King George is similarly disinclined when queried ‘Is Sir Walter distinct from Sir Walter?’, or when any other similarly worded question is posed. These considerations give rise to a second potential confusion that could also lead one to conclude erroneously that (6) is true or at least very likely. By invoking the ternary BEL relation, something even closer to (6) may be assumed as at least very likely:

(6″′) For every x, if there is a y such that George IV is familiar with the proposition that xx by means of y, then there is a y′ such that George IV is familiar with the proposition that xx by means of y′ and not-BEL(George IV, that xx,y′).

That is, either George IV is not familiar at all with the proposition that xx (in which case he does not believe it) or he withholds belief concerning whether xx, either by disbelieving or by suspending judgment. (See the third condition on the BEL relation in Section V above.) Although (6″′) is not certain, it is very likely true as of the date in question, and this yields an explanation for King George's failure to assent to ‘Sir Walter is distinct from Sir Walter’. But (by the first and second conditions on BEL) it does not follow that (6) itself is true or even likely.

It is entirely an empirical question whether (6) itself is true. There is no reason in advance of an actual investigation to suppose that (6) is even probably true.27 By the same token, however, even if (6) is in fact very unlikely, it might well have been true throughout King George's lifetime. In some perfectly plausible alternative history of the world, it is true. If (6) were true, (7) would be as well. What then? Are we only contingently rescued from paradox in the actual world by the contingent falsity of (6)?

Even if (7) were true, it would not state a law ascribing some strange property to King George's beliefs. It would state a purely contingent constant conjunction concerning every pair of individuals x and y, an accidenal generalization that happens to

be true not by virtue of some nomological feature of King George IV and his beliefs, but because—fortunately for King George—(6) happens to be true. No power to control the actual facts about x and y would be ascribed to King George's beliefs. If (6) were true (and Scott still had written Waverley), it would have to be true as well that King George does not believe that Scott is not the author of Waverley, and that George IV is not otherwise mistaken about the distinctness of any other pairs of identical objects of his acquaintance. The derivation of (7) from (6) would be sound, but it would no more constitute an unacceptable paradox than the so-called ‘paradoxes of material implication’ constitute unacceptable paradoxes concerning ‘if . . ., then’. In fact, since (7) employs the material ‘if . . ., then’, Church's paradox concerning quantification into belief contexts is a version of one of the ‘paradoxes of material implication’.

VIII

What is the nature of the connection among the Richard–Soames problem, the puzzle of reflexives in propositional attitudes, and Church's ‘paradox’ concerning quantification into belief attributions?

It is important to notice that, unlike the original puzzle generated by the Richard–Soames problem, neither the puzzle of reflexives in propositional attitudes nor Church's paradox makes essential use of existentially general beliefs, such as those ascribed in (1c), (2c), or (4c), or that denied in:



George IV does not believe that for some x, xx.


Instead, the puzzle of reflexives in propositional attitudes and Church's paradox essentially employ beliefs whose formulation involves reflexive devices, such as the reflexive pronoun ‘itself’ and the ‘self’-prefix defined above. Conversely, the original puzzle, as constructed by means of sentences such as (1b), (2b), and (4b), makes no explicit use of beliefs whose formulations involve reflexive pronouns or other such devices. In lieu of such beliefs, the original puzzle employs beliefs whose formulations involve repeated occurrences of the same, or otherwise anaphorically related, bound variables or pronouns: the occurrences of ‘x’ in (3c), the occurrences of ‘it’ in (2c) and (4c), the ‘whom’ and ‘his’ in (1c). In each case, these recurrences, or similarly related occurrences, are bound together from within the belief context. If I am correct, Church's ‘paradox’ results, in part, from a confusion of a belief involving recurrences of the same variable bound together from outside the belief context with a belief involving a reflexive device. Nothing with the force of any of these puzzles is generated if we confine ourselves to beliefs involving recurrences of the same proper name, as in (1b), (2b), and (4b), or beliefs involving recurrences of the same variable or pronoun bound together from without, as ascribed in (3d) and (4b′) and denied in (6), and keep them sharply separated from beliefs involving reflexive devices or variables or pronouns bound together from within. On the theory formed from the conjunction of theses (B) and (R), sentences (1b), (2b), (4b), and (4b′) are all straightforwardly true. It appears likely, therefore, that the general phenomenon that gives rise to all three of these puzzles centers on some important element that is common to beliefs whose formulations involve reflexive devices and beliefs whose formulations involve recurrences of variables or pronouns bound together (from within any belief attribution), but absent from beliefs whose formulations involve recurrences of proper names or of free variables or pronouns (bound together from without the belief attribution).

Wherein is this common element of reflexivity? The question is significantly vague, and therefore difficult to answer. Some of the apparatus of Frege's Puzzle, however, points the way to a possible response.

In Frege's Puzzle the binding of a variable is regarded as involving the abstraction of a compound monadic predicate from an open sentence. Thus ‘(0x002203x)(“Hesperus” refers to x and “Phosphorus” refers to x)’ is seen on the model of ‘Something is such that “Hesperus” refers to it and “Phosphorus” refers to it’, and ‘(0x002203x)(x outweighs x)’ is seen on the model of ‘Something is such that it outweighs it’, where in each case the initial word ‘something’ is a second order predicate and the remainder of the sentence is the abstracted compound monadic predicate to which ‘something’ is attached. In fact, the abstracting of a predicate from an open sentence of formal logic using Church's ‘0x0003bb’-operator might be understood on the model of transforming an ‘open’ sentence such as ‘I love it and it loves me’ (with both occurrences of ‘it’ functioning as ‘freely’ as a free variable of formal logic) into the corresponding closed monadic predicate ‘is such that I love it and it loves me’.

Compound monadic predicates formed by variable-binding (or pronoun-binding) abstraction from open sentences are treated in Frege's Puzzle as yielding an exception to the general rule that the contribution to information content made by (i.e. the ‘information value’ of) a compound expression is a complex entity made up of the contributions of the components. Instead such compound predicates are taken as contributing a semantically associated temporally indexed property, taken as a unit. (See note 5.) Thus, the (closed) abstracted predicate ‘is an object x such that “Hesperus” refers to x and “Phosphorus” refers to x’ is regarded as contributing, with respect to a time t, simply the property of being referred to at t by both ‘Hesperus’ and ‘Phosphorus’, and the (closed) abstracted predicate ‘is an object x such that x outweighs x’ is regarded as contributing, with respect to t, the property of outweighing oneself at t. The proposition contained, with respect to t, by ‘Something is such that it outweighs it’ (or ‘Something is an object x such that x outweighs x’) is taken as being composed of this latter property together with the contribution made by ‘something’ (to wit, the property of being a nonempty class at t).

The properties of being referred to at t by ‘Hesperus’ and also by ‘Phosphorus’ and of outweighing oneself at t contain the element of reflexivity that also arises when using the ‘self-’prefix, defined in Section III above by means of the binding of a recurring variable. The dyadic-predicate-operator defined in Section VI above in connection with the question of the meanings of reflexive pronouns also involves the binding of a recurring variable, and thereby also involves this element of reflexivity. Some such aspect of the binding of recurring variables and pronouns seems to provide the link among the Richard–Soames problem, the puzzle of reflexives in propositional attitudes, and Church's paradox concerning quantification into belief contexts.


3 Reflections on Reflexivity (1992)*


Nathan Salmon


Although two or more are often lumped together as if they were the same, or virtually the same, at least five different theories should be sharply distinguished concerning the contributions to propositional content made by the pronouns occurring in sentences like the following:


(1)  

John loves himself

(2)  

John loves his wife.


Linguists will note that in both sentences the pronoun—either ‘himself’ or ‘his’—is c-commanded by ‘John’.1

In ‘Reflexivity’ I cited M. J. Cresswell as one theorist (among many) who claims that (1) expresses the same proposition as ‘John loves John’. On the Simple Anaphor Theory the pronoun occurrence in (1) or (2) is simply another singular term, one that takes on the same semantic content as its antecedent, referring anaphorically to John. The Simple Anaphor Theory treats (1) as expressing the proposition that John loves John, and (2) as expressing the proposition that John loves John's wife. We may represent these propositions as:


<C(‘John’), C(‘John’), C(‘loves’)>


<C(‘John’), C(‘the wife of’), C(‘John’), C(‘loves’)>,

where C is the semantic content function for English.2 Fancier representations are possible, but this will suffice for the present purpose. By adopting this form of representation I follow the Frege–Russell tradition in assuming that the semantic content of a sentence is not, for example, the set of possible worlds with respect to which the sentence is true, but rather a structured, composite entity whose constituents are

As a facilitating expedient we may further assume that ‘John’ is a Millian term that directly refers to John. We may then represent the two propositions as:




wife-of,John, loving>.3

Nothing that I shall argue here depends on the Millian assumption that the name ‘John’ contributes its referent to the propositions contained by sentences in which the name occurs; my central points are compatible with the Fregean thesis that ‘John’ instead contributes a Sinn that is thoroughly descriptional, or purely conceptual, in nature.

Contrary to the interpretation of several readers, ‘Reflexivity’ does not reject the Simple Anaphor Theory. The misunderstanding may have arisen because I gave reasons there for rejecting this analysis and presented a rival analysis. I cannot overemphasize that I do not know of any decisive refutation of the Simple Anaphor Theory. My own view is that sentences like (1) and (2) may be ambiguous, that the Simple Anaphor Theory may well capture one anaphoric reading (even if not the only, or even the most natural, reading), and that it is even possible, contrary to popular belief, that the Simple Anaphor Theory correctly gives the only legitimate reading of these sentences (aside from the indexical or deictic reading of (2)).

Whereas it remains a genuine possibility that the Simple Anaphor Theory correctly captures one reading for sentences like (1) and (2), I am inclined to believe that it does not give the whole story. My general dissatisfaction with the Simple Anaphor Theory stems from the fact that it leaves out the element I call reflexivity that seems present in (1) and (2), at least on one reading. The other four theories that I shall distinguish attempt to accommodate the reflexivity evidently intrinsic to these sentences.

On the Linked Anaphor Theory, as on the Simple Anaphor Theory, the pronouns occurring in (the alleged reflexive readings of) (1) and (2) are anaphoric singular terms that derive their content and reference from their antecedents, but their anaphoric character is also alleged to be something that itself shows up in the propositions expressed by (the relevant readings of) (1) and (2). The propositions are held to contain some further element indicating the ‘linkage’—or identification—between John's occurrences therein (or, if one prefers, between the occurrences of the Fregean sense of ‘John’ therein). This further propositional element might be represented through something like lines-of-connection, as follows:4

Figure acprof-9780199284726-graphic-2

The second proposition, for example, might be thought of as having something like the following import, where ‘0x0003b1’ and ‘0x0003b2’ are two distinct names having the same semantic content as ‘John’: 0x0003b1loves 0x0003b2's wife, and furthermore, that wife-lover is the same as that one whose wife is loved. Something like this theory was proffered in the mid-1950s by Hilary Putnam, and more recently by David Kaplan and William Taschek—for sentences like ‘John loves John’ and ‘John loves John's wife’ in which a singular term recurs (perhaps in addition to sentences like (1) and (2)).5

I know of no decisive evidence against the Linked Anaphor Theory, though there is one sort of consideration that inclines me against it. The relational proposition that is represented as may be said to attribute the property of loving Mary to John (or to ascribe the property to John, or to predicate the property of John, etc.). It might also be said to attribute the property of being loved by John to Mary. It does not do either of these things, however, in the same direct way that the proposition does the first, since the attributed property and the individual to whom the property is attributed occur as the sole elements of the latter proposition. Let us say that the second proposition directly attributes the property of loving Mary to John.6 Whereas the proposition may be regarded as directly attributing the binary loving relation to the ordered pair , and as thereby indirectly attributing the property (singularly attribute) of loving Mary to John, it does not directly attribute any property to any individual. Then the Linked Anaphor theory apparently does not capture the intuition that (1) directly attributes to John the same property that ‘James loves himself’ directly attributes to James, to wit, the Narcissistic property of loving oneself. Similarly, (2) seems directly to attribute to John the property of loving one's own wife. On the Linked Anaphor Theory, these reflexive properties make no appearance in the semantically contained propositions; they evidently must be inferred, as logical consequences, from the information actually present in those propositions.7

A closely related problem, or potential problem, with the Linked Anaphor Theory is that, on the view that the Simple Anaphor Theory is incorrect because (1) and


(2) have reflexive readings, the predicates ‘loves himself’ and ‘loves his wife’ (on the alleged reflexive readings) would seem to be closed predicates, complete and fully determinate in themselves as regards both content and extension, without an attached grammatical subject to serve as antecedent. Both the Simple Anaphor Theory and the Linked Anaphor Theory fail to achieve this result. On those theories, the pronouns in (1) and (2) derive their content and reference from their antecedents (the relevant occurrence of ‘John’).8

On the Polyadic-Predicate Operator Theory, the pronouns occurring in (1) and (2) are not singular terms at all—anaphoric or otherwise. They designate a higher-order entity. In the simplest kind of case, they designate the function that maps any binary relation R between individuals to (the characteristic function of) the class of individuals that reflexively bear R to themselves, (0x0003bbR)(0x0003bbx)[xRx]. On this theory, the ‘himself’ in (1) and the ‘him’ implicit in (2), on the alleged reflexive readings of these sentences, are expressions for this higher-order function, and they designate it non-anaphorically.

A special case of the Polyadic-Predicate Operator Theory, the Dyadic-Predicate Operator Theory for certain reflexive pronoun occurrences, is the rival theory (rival to the Simple Anaphor Theory) presented in Salmon (1986b). Some readers have erroneously thought that I endorse the theory there. Salmon (1986b) takes no sides on the question of whether the Polyadic-Predicate Operator Theory is correct, for reflexive pronouns or for other pronouns. In fact, however, the Polyadic-Predicate Operator Theory has difficulties which make it almost certainly false.

First, it makes pronouns generally—including reflexive pronouns—radically ambiguous, between pronominal singular terms on the one hand (at least for their indexical use and for occurrences not c-commanded by antecedents), and polyadic-predicate-operator expressions on the other. In fact, the Polyadic-Predicate Operator Theory regards the several (explicit or implicit) occurrences of ‘he’ and ‘him’ in a complex sentence like the following as somehow forming a single, albeit scattered, polyadic-predicate operator:

S:  

John, with his wife's help, fooled his sister into thinking that he was ill.

In this case, the scattered predicate operator would operate on the extension of a complex four-place predicate—even though the needed predicate does not seem to occur as a separate, unified component of the original surface sentence S. All of this is implausible purely as a matter of English syntax.9

Moreover, the Polyadic-Predicate Operator Theory fails to achieve the desired results as regards content. The motivation for the Polyadic-Predicate Operator Theory is the intuition—more or less shared by Peter Geach,10 David Wiggins,11 Tanya Reinhart,12 and many others—that (1) and (2) express the same propositions as those expressed by:

(1′)  

(0x0003bbx)[x loves x](John)

(2′)  

(0x0003bbx)[x loves x's wife](John).

These propositions are represented here as:

P1:  


P2:  


Instead of these desired propositions, the Polyadic-Predicate Operator Theory delivers the (respectively logically equivalent) propositions expressed by:


(0x0003bbR)(0x0003bbx)[xRx](loves)(John)


(0x0003bbR)(0x0003bbx)[xRx]((0x0003bbyz)[y loves z's wife])(John).

These propositions (which might be expressed in English by ‘John has the reflexivization of loving’ and ‘John has the reflexivization of loving the wife of’) would be represented here as:


O, the binary loving relation>


O, the binary relation of loving the wife of>,


where O is the content of the predicate-operator expression ‘(0x0003bbR)(0x0003bbx)[xRx]’ (perhaps something like the operation of assigning to any binary relation R between individuals the characteristic function of the class of individuals that reflexively bear R to themselves). Here again, the propositions delivered by the theory do not directly attribute reflexive properties; the desired properties make no appearance in the relevant propositions, and must be inferred on the basis of the information actually present in those propositions.

It would appear that the Polyadic-Predicate Operator Theory, extended to cover pronouns c-commanded by singular-term antecedents generally, is advocated by Scott Soames. He proposes extending the Dyadic-Predicate Theory presented in Salmon (1986b) into a theory according to which

anaphoric pronouns with c-commanding singular term antecedents are not themselves singular terms, but rather are abstraction operators which combine with predicates of the sort illustrated by [‘—— loves ——'s mother’] to produce predicates . . . represented by [‘(0x0003bbx)[x loves x's mother]’]. In the simplest cases the effect of the anaphoric pronoun is to map a two-place relation R onto the corresponding one-place property of being an object o to which R applies reflexively—i.e. of being an object o such that R applies to the pair <o,o>.13

Evidently the term ‘antecedent’ must be given a nonstandard sense here, since the pronouns are alleged on this theory not to be anaphoric terms.

Soames's characterization of the proposed theory as an extension of the Dyadic-Predicate Operator Theory of Salmon (1986b) and his characterization of the pronoun in (2) as having the effect of mapping a binary relation onto the corresponding reflexive property, strongly support an interpretation on which he is defending a version of the Polyadic-Predicate Operator Theory. On the other hand, Soames's use of the phrase ‘abstraction operator’ instead of ‘predicate operator’, and his subsequent discussion, suggest that he may have in mind a variant of the Polyadic-Predicate Operator Theory. According to the fourth theory considered here, the pronoun ‘him’ in (2) is a genuine predicate-abstraction operator, which forms a monadic predicate for loving one's own wife when attached to the gappy expression ‘—— loves ——'s wife’. Although Soames calls this gappy expression a ‘predicate’, it would in fact play the role of an open formula, like ‘x loves x's wife’, with gaps serving as separate occurrences of a single free variable.

This Abstraction Operator Theory duplicates the syntactic implausibility of the Polyadic-Predicate Operator Theory by treating gappy expression's like ‘—— with ——'s wife's help, fooled ——'s sister into thinking that —— was ill’ as unified, semantically
significant constituents of sentences like S above.14 The Abstraction Operator Theory compounds the syntactic implausibility by treating this gappy expression not as a closed predicate but as an open formula with its gaps serving as bindable free-variable occurrences. The Abstraction Operator Theory also apparently shares with the Linked Anaphor Theory the undesirable feature that English predicates like ‘loves himself’ and ‘loves his wife’, on their alleged reflexive readings, are not complete and determinate in themselves as regards content and extension without an attached antecedent. Unlike the situation on the Linked Anaphor Theory, in which the incompleteness of these predicates arises from lack of a content and referent provided by an antecedent, here the incompleteness arises from lack of the antecedent's syntactic position—an additional gap, which needs to be bound by the alleged pronominal abstraction operator. On the Abstraction Operator Theory, the ‘himself’ in (1) functions like the abstraction phrase ‘(0x0003bbx)’ in ‘(0x0003bbx)[x loves x]’, forming a monadic predicate from an open formula. It cannot abstract the monadic predicate from the dyadic predicate ‘loves’, nor from the ‘open’ expression ‘loves ——’;15 it requires an open formula ‘—— loves ——’ with two gaps (the analogue of ‘x loves x’).

The final theory discussed here, the Bound Variable Theory, succeeds where the previous theories fail. On the Bound Variable Theory, (1) has precisely the same content as (1′), (2) precisely the same as (2′), and the pronouns in (1) and (2) function as variables bound by a ‘0x0003bb’-abstraction operator—like the final occurrences of ‘x’ in (1′) and (2′). The Bound Variable Theory simultaneously achieves the following results: (i) a complex sentence like S above is not regarded as somehow containing a scattered polyadic-predicate operator or predicate-abstraction operator and a complex, polyadic predicate or gappy open formula to serve as the operator's operand; (ii) predicates like ‘loves himself’ and ‘loves his wife’ are closed expressions, determinate in content and extension without an attached antecedent; (iii) the pronouns in (1) and (2) are singular terms; (iv) the pronouns in (1) and (2) may be regarded as anaphors; and (v) (1) expresses P1 and (2) expresses P2, thereby directly attributing reflexive properties. Although the pronouns in (1) and (2) may be seen as anaphors on the Bound Variable Theory, the theory has an additional feature stressed by Geach: (vi) it is a mistake to ask for the referent or designation of the pronoun occurrences in (1) and (2) — just as it is a mistake to ask for the referent of ‘x’ in (1′) or (2′) (even under an assignment of values to variables).16

Something similar to the Bound Variable Theory has been advocated by Geach, Reinhart, and others. If (1) and (2) indeed have reflexive readings that the Simple Anaphor Theory fails to capture (as I am inclined to believe), then the Bound Variable Theory would appear to be the most likely of the theories discussed here to yield the correct analysis of those readings. The only problem with the theory that I can see (aside from the fact that it posits a potentially controversial reading—the alleged reflexive reading—for (1) and (2)) derives from the fact that it carries the burden of positing an invisible abstraction operator in the predicates of (1) and (2), on their alleged reflexive (closed) readings.17 One might explain the invisible abstraction operator in the predicates of (1) and (2) by positing a reflexive–nonreflexive ambiguity in (1) and (2), incorporating the Simple Anaphor Theory for the nonreflexive reading, and declaring that the reflexive reading is shorthand for something involving an abstractor phrase like ‘is someone who’ or ‘is something that’. If (1) and (2) have reflexive readings (and I am inclined to think they do), it is not immediately objectionable to regard the sentences, on those readings, as shortened versions of


John is someone who loves himself


John is someone who loves his wife.

Here the pronouns ‘himself’ and ‘his’ are to be construed in conformity with the Simple Anaphor Theory. They are anaphoric here not on ‘John’, but on the bound variable ‘who’ (or on its trace, in Chomsky's sense).

The Bound Variable Theory does not require Geach's view that all pronoun occurrences other than pronouns of laziness (even so-called E-type or donkey occurrences) are bound variables. There are always the indexical or deictic occurrences. Still, a similar hypothesis might even accommodate a reflexive reading for sentences in which an anaphoric pronoun occurrence is not c-commanded by its antecedent, as in:


If John married Joan, then John loves her


Anyone who marries Joan loves her.


The former sentence, for example, on its alleged reflexive reading, is supposed to express something like that Joan is loved-by-John-if-married-by-John. The alleged reflexive reading of these sentences, however, seems strained. It is questionable whether the Bound Variable Theory should be extended this far.18

References

Geach, P. T. 1962, Reference and Generality, Cornell University Press, Ithaca.

—— 1965, ‘Logical Procedures and the Identity of Expressions’, Ratio 7; reprinted in Geach's Logic Matters, University of California Press, pp. 108–115.

Kaplan, David. 1990, ‘Words’, Proceedings of the Aristotelian Society, pp. 93–119.

McKay, Thomas. 1991, ‘Representing De Re Beliefs’, Linguistics and Philosophy 14, 711–739.  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them

Putnam, Hilary. 1954, ‘Synonymity, and the Analysis of Belief Sentences’, Analysis 14, pp. 114–122, reprinted in Salmon and Soames (1988), pp. 149–158.  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them

Reinhart, Tanya. 1983, Anaphora and Semantic Interpretation, University of Chicago Press, Chicago.

Salmon, Nathan. 1981, Reference and Essence, Princeton University Press, Princeton, New Jersey and Basil Blackwell, Oxford.

—— 1986a, Frege's Puzzle, Ridgeview, Atascadero, California.

—— 1986b, ‘Reflexivity’, Notre Dame Journal of Formal Logic, 27, 401–429; reprinted in Salmon and Soames (1988), pp. 240–274.  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them

Salmon, Nathan and Soames, Scott (eds). 1988, Propositions and Attitudes, Oxford Readings in Philosophy, Oxford.

Soames, Scott. 1989/90, ‘Pronouns and Propositional Attitudes’, Proceedings of the Aristotelian Society, 90, Part 3, pp. 191–212.

—— 1987, ‘Substitutivity’, in J. J. Thomson (ed.), On Being and Saying: Essays for Richard Cartwright, MIT Press, pp. 99–132.

Taschek, William. 1991, ‘Belief, Substitution, and Logical Structure’, unpublished.

Wiggins, David. 1976a, ‘Frege's Problem of the Morning Star and the Evening Star’, in M. Schirn (ed.), Studies on Frege II: Logic and the Philosophy of Language, Bad Canstatt, Stuttgart, pp. 221–255.

—— 1976b, ‘Identity, Necessity and Physicalism’, in S. Korner (ed.), Philosophy of Logic, University of California Press, Berkeley, California, pp. 96–132, 159–182.

4 Demonstrating and Necessity (2002)*

My title is meant to suggest a continuation of the sort of philosophical investigation into the nature of language and modality undertaken in Rudolf Carnap's Meaning and Necessity (University of Chicago, 1947, 1956) and Saul Kripke's Naming and Necessity (Harvard University Press, 1972, 1980). My topic belongs in a class with meaning and naming. It is demonstratives, i.e., expressions like ‘that darn cat’ or the pronoun ‘he’ used deictically (in contrast to its use either as a bound variable or as a ‘pronoun of laziness’). A few philosophers deserve particular credit for advancing our understanding of demonstratives and other indexical (i.e., context-dependent) words. Though Naming and Necessity is concerned with proper names, not demonstratives, it opened wide a window that had remained mostly shut in Meaning and Necessity but which, thanks largely to Kripke, shall forevermore remain unbarred. Understanding of demonstrative semantics grew by a quantum leap in David Kaplan's remarkable work, especially in his masterpiece ‘Demonstratives’ together with its companion ‘Afterthoughts’.1 In contrast to the direct-reference propensities of these two contemporary figures, Gottlob Frege, with his uncompromisingly thoroughgoing intensionalism, shed important light on the workings of demonstratives in ‘Der Gedanke’—more specifically, in a few brief but insightful remarks from a single paragraph concerning tense and temporal indexicality.

Frege and Kaplan are especially concerned with Frege's Puzzle. As it applies to demonstratives, the Puzzle may be posed thus: How can ‘This is that’, if true, differ at all in content from an utterance of ‘That is that’ while pointing with two hands straight ahead to the same thing? Kaplan lifts much of his theory of demonstratives from Frege's remarks, yet disagrees with Frege concerning the Puzzle's solution. This results in a fundamental tension in Kaplan's observations concerning demonstratives.

Kaplan distinguishes among three semantic values for a single expression: extension, content, and character. Extension is essentially Frege's notion of Bedeutung. The extension of a singular term is its designatum, i.e., the designated object for which the term stands; the extension of a sentence is either truth or falsity. Content corresponds closely to Frege's notion of Sinn or sense, and coincides with Russell's notion of what he called ‘meaning’. It also corresponds to Strawson's notion of the statement made in using a sentence. The content of a declarative sentence is the proposition expressed, the content of a singular term is its contribution to the content of sentences in which it occurs. The content of an expression determines its extension with respect to discourse about various scenarios, and in particular, with respect to any possible ‘circumstance of evaluation’, i.e., any possible world at a particular time. Indexicals reveal a need for a third layer of semantic value. An indexical sentence like ‘I'm busy now’ expresses different propositions on different uses. Some of these propositions may be true and others false. Likewise, when the sentence ‘It is rainy today’ is uttered one day and again the following day, the propositions asserted are different. Even if the extensions (in this case, the truth-values) happen to be the same, the propositions asserted still might have differed in truth-value—there are possible scenarios in which the same propositions determine different truth-values—and even a merely possible divergence in truth-value is sufficient to establish distinctness of the propositions expressed. Yet the sentence uttered is not ambiguous in regard to linguistic meaning; it is univocal. The meaning, which remains constant among different utterances, generates a distinct proposition for each distinct day on which the sentence is uttered, to wit, the proposition about that day to the effect that it is rainy. The character of an expression determines what content is expressed with respect to any particular context.2

A competent speaker need not know the extension of an expression (e.g., the truth-value of a sentence) in order to understand the expression properly. But neither must a competent speaker always know the content. The detective who stumbles upon an unsigned note containing the words ‘The loot will be deposited in a Swiss account the

day after tomorrow’ understands the sentence but cannot know which proposition it was used to express without knowing the extension of ‘tomorrow’. What a competent speaker must know to understand the sentence (as opposed to understanding the speaker's speech act) is the character, and it is the character which is best identified with the meaning. An expression is indexical if its character determines different contents depending on the context.3

Among indexicals, Kaplan distinguishes between demonstratives, which require an accompanying demonstration (e.g., a fingerpointing or hand gesture), and ‘pure indexicals’, which do not (like ‘I’ or ‘tomorrow’).4 Moreover, according to Kaplan, demonstrations function rather like context-dependent definite descriptions: when performed (‘mounted’) in a particular context, a demonstration takes on a representational content that determines an object with respect to a possible circumstance. Which content is taken on depends on the context; which object is determined depends on the circumstance. Kaplan calls the demonstrated object the demonstratum of the demonstration (in the relevant circumstance), e.g., the person, place, or thing pointed to in an act of ostension.

II

As mentioned, Frege made insightful observations concerning tense and indexicality. He wrote:

[in some cases] the mere wording, which can be made permanent by writing or the gramophone, does not suffice for the expression of the thought. . . . If a time indication is made in present tense, one must know when the sentence was uttered to grasp the thought correctly. Thus the time of utterance is part of the expression of the thought. If someone wants to say today what he expressed yesterday using the word ‘today’, he will replace this word with ‘yesterday’. Although the thought is the same, the verbal expression must be different to compensate for the change of sense which would otherwise be brought about by the different time of utterance. The case is the same with words like ‘here’ and ‘there’. In all such cases, the mere wording, as it can be written down, is not the complete expression of the thought; one further needs for its correct apprehension the knowledge of certain conditions accompanying the utterance, which are used as means of expressing the thought. Pointing the finger, gestures, and glances may belong here too. The same utterance containing the word ‘I’ will express different thoughts in the mouths of different people, of which some may be true and others false.5

Tyler Burge argues that this passage strongly supports an interpretation on which there is a very nearly explicit distinction in Frege's thought about language very much

like Kaplan's—not merely the celebrated dichotomy of sense and designatum, but a distinction among those two and, thirdly, conventional linguistic meaning.6 Here again, the distinction among these three is said to be revealed by indexicals. Indexical words like ‘yesterday’, ‘there’, and the demonstratives express different senses with respect to different contexts of use. The linguistic meaning of an indexical remains constant among different uses, and determines what sense the expression takes on with respect to a possible use, whereas the sense determines what the expression designates. Since the sense shifts with context while the linguistic meaning remains the same, the sense is different from the meaning.

Burge's interpretation is evidently based on a misreading of the quoted passage. Frege explicitly denies that an indexical by itself expresses a sense that determines the relevantly designated object, let alone a different such sense in different contexts. Rather, it is supposed to be the indexical supplemented by the associated contextual element that expresses the relevant sense. In an utterance of a sentence involving an indexical, Frege observes, what expresses a proposition (a ‘thought’) is not the sentence itself—the ‘mere wording’ which might be written down or recorded onto an audiocassette—but the wording taken together with certain accompanying elements, like the time of utterance or an ostension, things that cannot be ‘made permanent’ by writing them down or by recording the spoken word. In such cases, the mere wording itself is, in an important sense, essentially incomplete. What expresses the proposition is neither the uttered words nor the conditions accompanying the utterance, but the words and the conditions working in tandem. Indeed, Frege says that the conditions form part of the expression of the proposition, as if what really plays the role of a sentence—what actually expresses the proposition—is a hybrid entity made up of syntactic material (words) together with such supplementary contextual material as a time of utterance or a gesture of the hand. According to Frege, the union of sentence and context accomplishes what neither can do without the other. Frege makes his position even clearer in ‘Logic in Mathematics’ (1914):

I can use the words ‘this man’ to designate now this man, not that man. . . . The sentences of our everyday language leave a good deal to guesswork. It is the surrounding circumstances that enable us to make the right guess. The sentence I utter does not always contain everything that is necessary; a great deal has to be supplied by the context, by the gestures I make and the direction of my eyes. A concept-word combined with the demonstrative pronoun or definite article often has in this way the logical status of a proper name in that it serves to designate a single determinate object. But then it is not the concept-word alone, but the whole consisting of

the concept-word together with the demonstrative pronoun and accompanying circumstances which has to be understood as a proper name.7

Let us call these hybrid expressions-cum-contextual-elements supplemented expressions—e.g., supplemented words, supplemented sentences, etc. And let us call the expression that requires supplementation by a contextual element a mere expression (a mere word, etc.). Where there is no danger of confusion, we may call the latter entity simply an expression—although doing so evidently conflicts to some extent with the spirit of Frege's account, on which it is not the mere indexical sentence but the non-syntactically supplemented sentence that serves as ‘the expression’ of a proposition. Let us call Frege's claim that it is not the mere words themselves but the union of the mere indexical sentence with non-syntactic material that expresses the proposition, the syntactic incompleteness thesis.

The syntactic incompleteness thesis precludes Burge's interpretation. If a mere indexical does not express a sense that determines the relevantly designated object, and instead only the supplemented indexical does, then neither does the mere indexical have a linguistic meaning that assigns it such senses with respect to contexts of use. It is very much in keeping with the spirit of Fregean semantic theory to ascribe linguistic meaning to supplemented expressions. But the same indexical differently supplemented yields different supplemented expressions, evidently with different linguistic meanings. The supplemented indexical ‘tomorrow’0x002322today (the word supplemented by this very day), insofar as it functions as a meaningful expression itself, evidently means something very different from ‘tomorrow’0x002322tomorrow. As ‘tomorrow’ is uttered on different days, and the sense that determines the designated day shifts, so the time that supplements the word also shifts; hence so does the supplemented word and its meaning. Conversely, the meaning of ‘tomorrow’0x002322t is held fixed only by holding the supplementing time t fixed, hence also the sense that determines the designated day (the one after that of t). This blurs the line between the linguistic meaning and the sense of a supplemented expression, effectively eliminating any pressure to distinguish between them. If there remains any such distinction here, it threatens to be a distinction without a difference.

If the mere indexical or the mere present-tensed verb does not express a sense that determines the relevantly designated object, it does not follow that the mere expression does not express any sense at all. Does the mere indexical have a sense on Frege's view? If it does not, then its role is completely syncategorematic, i.e., it is then a contextually defined ‘incomplete symbol’ having no content itself yet affecting the content of the larger expressions of which it is a part (the supplemented word and the supplement sentence in which it occurs)—like a right parenthesis or a crucially placed comma. But as a matter of general philosophical policy, Frege eschews syncategorematicity wherever it is not excessively implausible to do so. Instead Frege very likely viewed mere indexicals as designating functions—those ‘unsaturated’ entities in Frege's ontology that stand in need of supplementation—and he regarded the  supplementing contextual element, the time of utterance or a hand gesture, as a name of the argument to the designated function.8 A demonstration functions as a name of its demonstratum, whereas the time of an utterance might serve in the utterance as a name of itself. The mere word ‘yesterday’ could be taken to designate a function from a time t (which supplements the mere word, designating itself) to the day before t. Correspondingly, the word ‘now’ would designate the identity function restricted to times, just as a mere demonstrative like ‘that’ or ‘he’ would designate the identity function on demonstrata. Accordingly, the sense of the mere demonstrative would be the identity function on the senses of demonstrations.9 A mere demonstrative would thus express a sense (albeit not a concept, in Alonzo Church's sense, of the object designated by the supplemented demonstrative), and its sense would remain constant among various utterances, determining the designata for those utterances, precisely as the linguistic meaning intuitively does. This interpretation—which is both a plausible reading of the passage and true to the general spirit of a Fregean philosophy of semantics—does not merely fail to support Burge's attribution to Frege of a three-way distinction like Kaplan's. It strongly suggests that Frege rejected the postulation a level of semantic value distinct from sense which yields a sense for various contexts. By regarding the mere indexical as an expression for an identity function, and any contextual elements as separate designating parts of the completed expression, one eliminates the need to postulate an additional semantic value beyond sense and designatum. The task that Kaplan's character was designed to perform is held to be accomplished instead by the context-independent sense of the mere indexical.10

III

Although Kaplan's account of indexicals owes much to Frege, it differs from Frege's in important respects. First and foremost, the content of an indexical word is taken to be the designatum itself, rather than a concept of the designatum (in Church's sense). Furthermore, a mere indexical word like ‘yesterday’ is said by Kaplan to designate the relevant object—in this case, the day before the time of utterance—not a function from times to days. The word takes on, relative to a context of use, a content that determines the designated object with respect to the context. The time of the context serves to determine the content. Though Frege assigns a different designatum to the mere word, he also allows that the supplemented word designates the relevant day. One may wonder whether there is any non-arbitrary way to choose between saying with Frege that the word ‘yesterday’ supplemented by the time of utterance designates the day before the supplementing time, and saying instead with Kaplan that ‘yesterday’ designates with respect to a context the day before the context. Can it make any difference whether we say that a word plus a context designates a given object, or instead that the word designates the object ‘relative to’ or ‘with respect to’ the context?

From a purely formal perspective the different ways of speaking amount to the same thing. Either way we assert a ternary relation between a word, a context, and an object. But from a broader philosophical perspective, Kaplan's manner of speaking better captures the underlying facts. There are linguistic intuitions governing the situation, and on that basis it must be said that the word ‘yesterday’ (the mere word) designates a particular day—which day depending on the context of utterance—not a function from times to days. The intuition is unshaken even among sophisticates who, through proper training, have acquired the intuition that, for example, the

exponentiation in the numerical term ‘72’ (and likewise the word ‘squared’ in ‘seven squared’) designates a particular mathematical function.11

It is preferable, both theoretically and conceptually, to see the ternary relation between word, context, and object as the relativization to context of the binary relation of designation between word and object, rather than as assigning a semantic value to a cross-bred mereological union of word and context. One unwelcome consequence of Frege's syntactic incompleteness thesis is the damage it inflicts on the syntax of an indexical language. The material that supplements the mere word to form the supplemented expression does not itself have a genuine syntax as such. It is not that such entities as times and gestures could not have their own syntax. In Über Sinn und Bedeutung Frege observes that ‘it is not forbidden to take any arbitrarily produced event or object as a sign for anything’. A highly systematic mode of composition of such signs, and with it a generative grammar, could be cleverly devised, or might even evolve through usage. Although the expressions that make up a sign language, for example, cannot be ‘made permanent’ by writing them down or by audio recording, still sign language itself has its own definite syntax. But as a matter of sociological linguistics, such aids to communication as times of utterance and fingerpointings do not have an obvious and recognizable syntax. On Frege's account, a language with indexicals recruits elements from beyond conventional syntax in order to express propositions. What manages to express a proposition in such a language is not something that can be recorded by writing or the gramophone, at least not in its entirety. It is partly syntactic and partly contextual. Natural-language syntax becomes a fine theoretical mess.

In sharp contrast, one welcome consequence of relativizing the semantic relations of designation, and of expressing a content, to context is the recognition of a third kind of semantic value—Kaplan's character—that at least approximates the intuitive notion of meaning. Frege's account avoids the claim that utterances on different days of the word ‘yesterday’ are of a single univocal expression with different designata, but only at a serious cost: the cost of misinterpretation. Frege imputes univocality by interpreting the word in such a manner that it allegedly designates the same thing on each occasion of use—that designated thing being a function and not an ‘object’, in Frege's sense. Though the word's meaning intuitively remains constant from one use to the next, that same word (not some other expression) also does in fact have different designata, and therefore also different contents, on different occasions of use.

There is a closely related reason why Kaplan contends that an indexical is monogamous in meaning while promiscuous in designation, a reason pertaining to Frege's Puzzle in connection with indexicals. Frege recognizes that ‘Today is Smith's birthday’, uttered one day, expresses the same proposition as ‘Yesterday was Smith's

birthday’ uttered the next. Yet, as Kaplan notes, Frege apparently overlooks that the two sentences can differ in informativeness or ‘cognitive value’ (Erkenntniswerte). Contrary to Frege's assertion, the information conveyed in an utterance at 11:59:59 pm of the former sentence is different from that conveyed in an utterance of the latter only seconds later. An auditor who does not keep a close eye on an accurate clock is apt to find the two assertions incompatible. But how can the two utterances differ in cognitive value when the very same proposition is asserted in each?

Kaplan's explanation proceeds in terms of the characters of the two sentences. There is an important yet generally overlooked aspect of character, one that I believe Kaplan invokes in his solution to Frege's Puzzle in connection with indexicals, even if only implicitly. (He does not articulate it in precisely the way I shall here.) It is that the character has a contextual perspective on content. More elaborately, the character specifies the content with respect to a given context of use in a particular manner, describing it in terms of its special relation to the context. To illustrate, the particular English sentence ‘I had a fever yesterday’ is governed by the following content rule:

(CR1) With respect to any context c the (English) content of ‘I had a fever yesterday’ is the proposition composed of the (English) contents of ‘I’, ‘had a fever’, and ‘yesterday’ with respect to c.

This rule fixes content for any context. Taking this together with such further English semantic facts as that the content of ‘yesterday’ with respect to a context is the day before the context, then ‘multiplying through’, one derives a content rule of a rather special form, one that fixes the character:

(CR2) With respect to any context c the (English) content of ‘I had a fever yesterday’ is the singular proposition about the agent of c, and about the day before c, that the former had a fever on the latter.

I call this rule ‘character-building’. Unlike the content rule (CR1), (CR2) specifies the content of the sentence with respect to any context as a particular appropriately non-linguistic function of the context, instead of merely fixing the content by reference to the semantics of component expressions. It thereby gives the character.12 Every utterance has a speaker and typically at least one auditor or reader, whom I shall call a ‘speakee’. When a speaker utters ‘I had a fever yesterday’ in a context c, the speakee who understands the sentence (and thus knows its character-building content

rule (CR2)) is thereby presented a particular proposition. The proposition in this case is singular, directly concerning a particular agent (the speaker) and a particular day (the preceding). But the sentence itself, via its character, presents the proposition to the speakee ‘by description’ (in Russell's sense), in terms of its relation to the very context c—specifically (and roughly), as the singular proposition about the agent of this very context, and about the day before this very context, that he/she had a fever that day. The speakee who has been paying even minimal attention, by knowing which day and agent are in question, easily determines which singular proposition was expressed. The speakee therewith apprehends that proposition. The speakee is acquainted with the proposition, yet that acquaintance is obtained through identification of the objects given in a context-specific description. The meaning of the sentence describes a singular proposition in terms of the context, and two separate things occur as a result: the utterance issues in the speaker's assertion of that very proposition; and the attentive speakee thereby makes the acquaintance of the presented proposition.13

Return now to the utterances of ‘Today is Smith's birthday’ one day and ‘Yesterday was Smith's birthday’ the next. The same content is presented differently by the different characters. It is presented in the first context c as the singular proposition about the day of the time of this very context c that it is Smith's birthday, whereas it—the very same proposition—is presented in the second context c′ as the singular proposition about the day before this very context cthat it is Smith's birthday. The two different descriptions of the same proposition in terms of its relations to two different contexts reflect the different characters' separate contextual perspectives. Kaplan proposes identifying the ‘cognitive value’ (‘Erkenntniswerte’) of an expression with its
character—the way the content is presented as a function of context—rather than with the content.14

IV

As mentioned, Kaplan's attention to Frege's Puzzle also motivates his distinction between demonstratives and the so-called pure indexicals. Since different syntactic occurrences of the same demonstrative can converge on the same designatum (hence the same content) yet differ in cognitive value, Kaplan reasons, the characters of those different occurrences must be different. But how can the characters differ when the two occurrences are of the very same univocal vocable?

Kaplan's solution: It is the same vocable, but different expressions. Kaplan's account of demonstratives, as contrasted with ‘pure’ indexicals, can be summed up in a pair of succinct theses:

KT1: Although incorrect about pure indexicals, Frege's syntactic incompleteness thesis is correct with respect to demonstratives; but

KT2: As with all indexical words, the propositions expressed by sentences invoking supplemented demonstratives are singular rather than general.15

The attribution of KT1 is based on numerous passages in ‘Demonstratives’ and in its forerunner, ‘Dthat’.16 In both of these works, sentences invoking demonstratives are uniformly given with a bracketed specification immediately following the demonstrative of a demonstration. The demonstration that completes the mere demonstrative is typically (not always) performed by the agent of the context, and this demonstration is supposed to serve as a component of the sentence that it accompanies. As Kaplan observes (‘Demonstratives’, pp. 490–491), demonstratives are unlike other indexicals in this respect. A demonstration of oneself is completely superfluous in an utterance of ‘I’ or ‘me’, and a demonstration of anything else is completely infelicitous. By contrast, a typical demonstrative is essentially incomplete without an accompanying demonstration. Not vacuous; incomplete. A demonstrative can be used vacuously, by performing a demonstration with no unique demonstratum. What designates, or fails to designate, is not the demonstrative itself but a supplemented demonstrative, a demonstrative-cum-demonstration. An unsupplemented demonstrative—the mere word—is not even a candidate for designating. In effect, it is grammatically incomplete. As Kaplan puts it:

Demonstratives are incomplete expressions which must be completed by a demonstration (type). A complete sentence (type) will include an associated demonstration (type) for each of its demonstratives. (ibid., p. 527)

Kaplan tentatively accepts a ‘Fregean theory of demonstrations’, on which demonstrations have a character, and express an individual concept as content with respect to a context, and on which the demonstration's content determines a demonstratum with respect to a circumstance (i.e., with respect to a world at a time). Demonstrations are, in these respects, exactly like indexical definite descriptions. The demonstration fixes the designatum of the supplemented demonstrative, hence also its content. With this in mind, Kaplan proposes a sanitized demonstration-free model of how the natural-language demonstrative works: a mere indexical, ‘dthat’, which is supplemented not by a demonstration but by a singular term to form a complete singular term. Kaplan's ‘dthat’ is intended to represent our natural-language demonstrative ‘that’, except that it accepts accompanying supplemental specifications of anything whatsoever as demonstratum—even of something that cannot be strictly demonstrated (because, for example, it is nowhere to be found in the context)—as long as the supplemental specification is strictly verbalized:

Dthat [the suspicious-looking guy I saw yesterday wearing a brown hat] is a spy.

The content of this sentence is to be the singular proposition about the suspicious-looking guy the agent saw the day before wearing the relevant brown hat—Bernard J. Ortcutt, to give him a name—that he is a spy.17 Kaplan writes:

Dthat’ is simply the demonstrative ‘that’ with the following singular term functioning as its demonstration.(ibid., pp. 521–522)

I regard my ‘dthat’ operator as representing the general case of a demonstrative. . . . I regard the treatment of the ‘dthat’ operator in the formal logic . . . as accounting for the general case.(ibid., p. 527)

Though the content of the complete singular term is the designatum (Ortcutt himself), the actual meaning should be given by a character-building content rule. Kaplan suggests the needed content rule by saying that ‘dthat’ is ‘a special demonstrative which requires completion by a description and which is treated as a directly referential term whose referent is the denotation of the associated description’ (ibid., p. 521). He then liberalizes by allowing the supplemental expression to be any singular term, definite description or otherwise. Earlier in ‘Dthat’, he wrote: ‘I would like to count my verbal demonstration . . . as part of the sentence type’ (p. 237). The content rule suggested by these remarks can be stated thus:

(D) With respect to any context c the content of the singular term 0x00231cdthat[0x0003b1]0x00231d is the designatum with respect to c, if there is one, of the component operand singular term 0x0003b1(i.e., the designatum, if any, of 0x0003b1with respect to c and the particular circumstance c W -at-c T of c). Otherwise 0x00231cdthat[0x0003b1]0x00231d has no content.18

In effect, (D) constitutes a contextual definition of ‘dthat’. Taking (D) together with such further semantic facts as that ‘yesterday’ designates the day before the context and ‘multiplying through’, the character-building content rule for the particular term ‘dthat [the suspicious-looking guy I saw yesterday wearing a brown hat]’ is obtained:

(CR3) With respect to any context c the Kaplish content of ‘dthat [the suspicious-looking guy I saw yesterday wearing a brown hat]’ is, if anything, the suspicious-looking guy whom the agent of c saw in the possible world of c wearing a brown hat on the day before c.19

The semantic rule (D) also yields the following corollaries (Cf. ‘Demonstratives’, pp. 520–522):


(D1) The singular term 0x00231cdthat[0x0003b1]0x00231d is indexical—i.e., its content depends on and varies with the context.

(D2) With respect to any context 0x00231cdthat[0x0003b1]0x00231d is directly referential—i.e., its content with respect to a context, if any, is simply its designatum with respect to that context.

(D3) With respect to any context 0x00231cdthat[0x0003b1]0x00231d rigidly designates the designatum, if any, of 0x0003b1with respect to that context, and is otherwise a rigid non-designator.

Corollary (D3) demonstrates that ‘dthat’ is, inter alia, an intensional operator. The content and designatum of 0x00231cdthat[the 0x0003d5]0x00231d with respect to a given context c and a given circumstance w-at-t is the designatum of 0x00231cthe0x0003d50x00231d with respect to the circumstance of c, never mind the given circumstance w-at-t. The ‘dthat’-operator is thus a rigidifier. With respect to any context, ‘dthat [the suspicious-looking guy I saw yesterday wearing a brown hat]’ rigidly designates whoever in that context is the suspicious-looking guy the agent saw wearing a brown hat on the day before the context. The operator is in this respect analogous to the modal operator ‘actually’: ‘Actually, the suspicious-looking guy I saw yesterday wearing a brown hat is a spy’ is true with respect to a context c and a possible world w if and only if the suspicious-looking guy that the agent of c saw wearing the relevant brown hat on the day before c is (at the time of c) a spy in the possible world of c, even if he is not a spy in w.20

As mentioned, Kaplan intends his ‘dthat’-operator as a kind of idealized, thoroughly syntactic model of natural-language demonstratives, which require supplementation by actual demonstrations rather than by singular terms. Kaplan sees in a single deictic utterance of ‘that’ a pair of component ‘expressions’: the mere word and the supplemental demonstration. Although the demonstration has a content, that content forms no part of the content of the supplemented sentences in which it figures. The content rule governing supplemented demonstratives is modeled after (D):

(T K ) With respect to any context c the (English) content of the supplemented English demonstrative ‘that’0x0023220x0003b4 (where 0x0003b4is a demonstration) is the demonstratum with respect to c, if there is one, of 0x0003b4, and nothing otherwise.21

Demonstratives on Kaplan's theory are thus content operators, in that the designation of a supplemented demonstrative with respect to a circumstance w-at-t depends not merely on the demonstratum of the supplementing demonstration with respect to

w-at-t but on the content. (It is the demonstratum determined by that content with respect to a different circumstance, viz., the circumstance c W -at-c T of the context of utterance.) But demonstratives are counter-examples to a strong compositionality principle, on which the content of a compound expression is formed from the contents of the component expressions. This feature of Kaplan's account is brought into focus by (D). The content of ‘dthat [the suspicious-looking guy I saw yesterday wearing a brown hat]’ is not formed from the content of its component operand—contrary to what one might have expected on the basis of the general behavior of English compound expressions. The content is the guy himself.

V

By distinguishing supplemented demonstratives in virtue of their demonstrations, Kaplan provides a solution to Frege's Puzzle (as it applies to demonstratives) that builds on the idea that the cognitive value of an indexical is its character rather than its content. A supplemented demonstrative ‘that’0x0023220x0003b4 presents its content/designatum in a context c, roughly, as the such-and-such in this very context, where the content of the accompanying demonstration 0x0003b4is: the such-and-such. Supplemented demonstratives whose supplementary demonstrations differ in content differ themselves in character, in the way their content/designatum is presented as a function of context. The different completions of the sentence ‘That is that’, even though they share the same content, differ in informativeness because of a difference in meaning. The same proposition is presented two different ways, by means of different supplemented sentences with different characters: one time as the singular proposition about the such-and-such in this very context and about the so-and-so in this very context, that they are one and the very same; and a second time (pointing to the same object simultaneously with two hands) as the singular proposition about the such-and-such in this very context that it is itself. The same proposition is given by distinct descriptions of it in terms of different relations that it bears to the same context, descriptions invoking the contents of the distinct accompanying demonstrations.

Kaplan briefly considers an alternative account that does away with Frege's syntactic incompleteness thesis even for demonstratives, treating all indexical words on a par (pp. 528–529). Kaplan calls this alternative the Indexical theory of demonstratives. I shall call it the Bare Bones Theory. On this theory, a context of use is regarded as including alongside an agent (to provide content for ‘I’), a time (‘now’), a place (‘here’), and any other such features, a demonstratum—or better yet, a sequence consisting of first demonstratum, second demonstratum, and so on, in case a single demonstrative is repeated in a single context with different designata, as in ‘That 1 [pointing to a carton] is heavier than that 2 [a different carton]’. Demonstratives on the Bare Bones Theory function according to a very simple character-building content rule:

(T n )  

With respect to any context c the content of the nth occurrence in a sentence of ‘that’ is the nth demonstratum (if any) of c.

This semantic rule imputes different characters to the demonstrative occurrences in ‘That is that’, since there are contexts in which the first demonstratum is one thing, the second demonstratum another. According to the Bare Bones Theory, the meaning (character) of a sentence like ‘That is heavier than that’ presents its content with respect to a context as the singular proposition about the first and second demonstrata, respectively, of this very context, that the former is heavier than the latter. This contrasts sharply with Kaplan's theory, on which the content is presented instead by means of the contents of the supplemental demonstration, as the singular proposition about the such-and-such in this context and about the so-and-so in this context, that the former is heavier than the latter. The Bare Bones Theory makes no place in semantics for the demonstration that accompanies the use of a demonstrative, and consequently misses the epistemologically significant content-demonstratum distinction. Kaplan favors this distinction as providing a more satisfying solution to Frege's Puzzle with regard to demonstratives, How can an utterance ofThat 1 is that 2, if true, differ at all in content from an utterance ofThat 1 is that 1? He says:

The Fregean theory of demonstrations may be extravagant, but compared with its riches, [the Bare Bones Theory] is a mean thing . . . the Fregean idea that the very demonstration might have picked out a different demonstratum seems to me to capture more of the epistemological situation than the [Bare Bones] Indexicalist's idea that in some contexts the first and second demonstrata differ. (ibid., pp. 528–529)

VI

We looked at some grounds for favoring an account of indexicals on which contextual features are regarded as indices to which the semantic relations of designation and content are relativized over Frege's idea that such features instead form part of the expression. All of these grounds extend straightforwardly to demonstratives. There is first the damage inflicted upon English syntax. This is the main reason, or at least one very important reason, for the retreat from ‘that’ to ‘dthat’, with the resulting well-behaved syntax of a sort that we students of language have come to treasure. But foremost, there is this: linguistic intuition demands that a demonstrative has a single context-sensitive meaning that assigns different designata, and hence also different contents, on different occasions of use. On Kaplan's theory, in sharp contrast, each utterance of ‘that’ with a different designatum is an utterance of a different term with a different character or meaning. In fact, as with Frege, each utterance of ‘that’ accompanied by a different demonstration with a different content is an utterance of a different term with a different meaning—even if the demonstrata in that context are exactly the same. (The character is represented by the function that assigns to any context the demonstratum in that context of the particular accompanying demonstration; cf. (D) above.) One might say that the demonstrative ‘that’ is highly ambiguous on Kaplan's account, its precise meaning depending on the content of the accompanying demonstration. This is not merely somewhat counter-intuitive; it is obviously incorrect. As with all indexicals, the designatum of ‘that’, and therefore also the content, depends on the context, but the English meaning is the same on each occasion of use.22

It is not quite correct, however, to say that a demonstrative is ambiguous on Kaplan's account. More accurately, precisely the opposite is true: the mere demonstrative—the word itself—is utterly meaningless in isolation. One feature of Kaplan's operator ‘dthat’ that is easy to overlook but that makes it a highly implausible model for natural-language demonstratives like ‘that’ is that the former is, by stipulation, a syncategorematic ‘incomplete symbol’. The content and designatum of the compound term 0x00231cdthat[0x0003b1]0x00231d is a function of the content of its operand 0x0003b1(viz., the designatum thereby determined), but the ‘dthat’-operator itself has no character or content (no ‘meaning in isolation’). Natural-language demonstratives, in sharp contrast, have a meaning that remains fixed for each use and determines its content in that use.

This is one respect in which Kaplan's account is inferior to Frege's. As we have seen, Frege easily accommodates the fact that a demonstrative has a fixed yet context-sensitive meaning by taking the mere demonstrative to designate a function from features of context to appropriate designata. By contrast, semantically ‘dthat’ is not (as its syntax would have us expect) a functor. It might appear that Kaplan could improve his account significantly by following Frege's lead and taking ‘dthat’ to be a functor for the identity function, and by analogy, taking ‘that’ to designate the identity function on demonstrata. For numerous reasons such a modification is not open to Kaplan. One immediate problem—in fact, an immediate reductio of Frege's account—is that in the typical case a supplemented demonstrative is, according to that account, a non-rigid designator. Its designatum is simply the demonstratum of the supplementing demonstration, and thus varies from one possible world to the next. This conflicts with Kaplan's thesis KT2 and his semantic corollary (D3).

It might be thought that although Kaplan cannot follow Frege in taking a demonstrative to designate the identity function on demonstrata, this only goes to show that he must seek a different sort of function. As noted above, ‘dthat’ is, inter alia, an intensional operator. An appropriate designatum for ‘dthat’, therefore, cannot operate on the mere designatum of its operand. Analogously, an appropriate designatum for a natural-language demonstrative cannot be a function on the mere demonstratum of the supplementing demonstration. Instead, for any context c there is the aptly suited function @i c that assigns to any individual concept (any content suitable for either a definite description or a demonstration) the object determined by that concept in the particular circumstance c W -at-c T of c (and to any non-concept itself). An account of ‘dthat’ as designating @i c with respect to c could be made to yield exactly the right intension (function from circumstances to designata) for supplemented ‘dthat’-terms. In fact, doing so would make ‘dthat’ an indexical modal functor exactly analogous to the sentential operator ‘actually’ (whose extension with respect to a context c is the function @p c that assigns to any proposition its truth-value in the particular possible world c W of c). Kaplan's thesis KT1 virtually cries out for @i c to serve as the mere demonstrative's designatum.23

Yet Kaplan is barred from taking ‘dthat’ and natural-language demonstratives to be functors. The problem is that the propositions expressed by sentences invoking ‘dthat’ could not then be singular propositions—any more than the contents of sentences beginning with ‘actually’ are truth-values rather than propositions (although again, this could be made to yield exactly the right intension). Instead of Ortcutt himself, the proposition expressed by ‘Dthat [the suspicious-looking guy I saw yesterday wearing a brown hat] is a spy’ would include among its constituents, if ‘dthat’ were semantically a functor, the content of the operand description ‘the suspicious-looking guy I saw yesterday wearing a brown hat’ as well as the content of the functor itself (perhaps something like the operation of assigning to any such individual concept the individual it determines in the particular circumstance c W -at-c T ). This violates (D2) and would thus destroy KT2, and therewith tarnish the spirit of Kaplan's general account. The cost of mediation between KT1 and KT2 is not cheap: a demonstrative is regarded as a syncategorematic incomplete symbol, as mere punctuation.24

Another problem with Frege's account, inherited by the envisaged account of demonstratives as designating @i c , is that the mere demonstrative is ‘context-sensitive’

on Frege's account only in the sense that its sense and designatum are functions from contextually variant elements. The central insight of Kaplan's account of indexicality is that indexicality is not a matter of expressing functions from contextually variant elements, but a matter of taking on different contents altogether in different contexts. This observation goes significantly beyond Hans Kamp's original insight that indexicality requires double indexing of extension both to contexts and to circumstances which may vary independently of context. Not only does the extension, but also the content, of an indexical depend upon, and vary with, a context of use.25 On Frege's account, the content of ‘that’ is the same in every context: the identity function on demonstration contents. Although ‘context-sensitive’ in one obvious sense—the function in question is a function on a contextually variant element—a mere demonstrative on Frege's account is not indexical in Kaplan's sense. Likewise, although on Frege's account a supplemented demonstrative, ‘that’0x0023220x0003b4, is ‘context-dependent’ in one obvious sense—the argument to the function designated by ‘that’ is given by the demonstration 0x0003b4—it is not indexical in Kaplan's sense. It is crucial to Kaplan's account that the supplemented demonstrative be indexical. The content of ‘that’0x0023220x0003b4 in any context is the demonstratum of 0x0003b4in that context, and consequently varies with the context. For these various reasons (and more), Kaplan is barred from taking the mere demonstrative—the word itself—to have a meaning in isolation.

But the demonstrative ‘that’ is surely not meaningless in isolation. It has a definite meaning, one that remains unchanged from one utterance to the next, a meaning that is shared by demonstratives in other languages. And as with any indexical, the meaning of a demonstrative looks to the context to secure a content, and thence, a designatum. Far from being an ‘incomplete symbol’, a demonstrative—the word itself—is a designating singular term if anything is. When Ralph points to Ortcutt and declares, ‘He is a spy!’ the word ‘he’ surely designates Ortcutt. Furthermore, even if the pointing itself is regarded as somehow designating Ortcutt, intuitively it is the word ‘he’ rather than some hybrid consisting of the word and the pointing that semantically designates Ortcutt. Again, Kaplan's account of demonstratives as syncategorematic punctuation, rather than as fully designating singular terms, is not merely somewhat counter-intuitive. It is clearly incorrect.

Does Frege's Puzzle provide adequate grounds to segregate demonstratives from indexical words like ‘I’ and ‘yesterday’ in requiring Frege's syntactic incompleteness thesis? Kaplan's complaint concerning the alternative Bare Bones Theory has considerable force. The mere fact that separate occurrences of a demonstrative within a single context frequently differ in their demonstrata is not an adequate explanation of the apparent informativeness of ‘That=that’, any more than the apparent informativeness of ‘Hesperus is Phosphorus’ is adequately explained by noting that a single object typically has one name rather than two. Even sophisticated speakers aware of the co-designation of two occurrences of ‘that’ in a particular context deem it possible to believe that that 1 is the same as itself without believing that it is that 2 . Frege's Puzzle is concerned with the contents of such sentences as ‘Hesperus is Phosphorus’ and ‘This is that’ and not merely with their syntax. The Puzzle is: How can

the expressed propositions differ in the ways that they do from those expressed by ‘Hesperus is Hesperus’ and by an utterance of ‘That=that’ while pointing to the same object twice in the same way—as, perhaps, by pointing simultaneously with both hands?26 Kaplan's explanation in the case of demonstratives is that the complete sentence is supplemented by distinct demonstrations with distinct contents, and though the two supplemented demonstratives have the same content in the relevant context, they differ in the manner in which they semantically present their common content as a function of context. The Bare Bones Theory also distinguishes the two occurrences of ‘that’ in regard to meaning, but that difference is described in terms of the different sequential order in which their demonstrations are performed, ignoring the epistemologically crucial contrast between the actual contents of those demonstrations. And, it should be added, the Bare Bones Theory cannot provide any explanation in terms of character or content of the uninformativeness of an utterance of ‘That is that’ while pointing with both hands, nor of the difference in informativeness between the two utterances of ‘That is that’, since the sentence is assigned the same character and the same content.

The Bare Bones Theory attempts to solve Frege's Puzzle by postulating distinct words with distinct meanings where there is only one word with one meaning. At bottom, this is the same general strategy employed in both Frege's and Kaplan's solutions. It is a strategy forced on anyone attempting to solve the Puzzle in terms of meaning. But it violates a linguistic variation on Occam's Razor: Thou shalt not multiply meanings beyond necessity. Worse, it flagrantly violates a further, particularly imposing variation of Occam's Razor: Thou shalt not multiply expressions beyond plausibility. Kaplan laments the fact that his preferred solution to the puzzle about ‘That 1 =that 2 does not extend to ‘Hesperus is Phosphorus’, since the two names, unlike the supplemented demonstratives, share the same character (ibid., pp. 562–563). Rather than contort our linguistic intuitions in order to accommodate an explanation that does not in any event work in the general case, it would be wiser to extract from the case of proper names an important lesson concerning Frege's Puzzle and devices of direct reference generally: The epistemologically significant ways in which the same proposition is differently presented, or differently taken, are not always a matter of semantics (linguistic meaning).

The sins of the Bare Bones Theory are not limited to its violation of the linguistic variations on Occam's Razor. That theory ignores demonstrations altogether, and consequently ignores their properly semantic role in the proper use of a demonstrative. One potential problem with the Bare Bones Theory is that a demonstration's demonstratum need not be active or even present in the context. This point is illustrated by one of Kaplan's examples (used for a slightly different purpose). I may demonstrate Alonzo Church by pointing to a photograph while uttering ‘He was one of the greatest thinkers of the 20th century.’ Regrettably, Church himself is not present or active in the context; only the photograph is. But the demonstratum is no mere photograph. It is the photograph's subject: Church himself. At most, Church is present by proxy, his photograph representing him not merely in the standard way that a picture represents but also standing in for him. The demonstratum of a particular demonstration may be neither present in the context nor an active participant, nor even present by proxy.27 Consider the following discourse fragment:


(i) Do you recall the suspicious-looking guy we saw yesterday wearing a brown hat? (ii) Well, I think: he's a spy.

Although the ‘he’ in (ii) is anaphoric, it is not a variable bound by its grammatical antecedent in (i), but a syntactically free term designating Ortcutt. Of course, the pronoun ‘he’ does not designate Ortcutt no matter what the context. The anaphora here is of a peculiar variety. In effect, the ‘he’ in (ii) is a demonstrative and the definite description in (i) plays the role of accompanying demonstration.28 The demonstratum is entirely absent from, and inactive in, the context; the demonstrative ‘he’ succeeds all the same. In general, the demonstratum of a particular demonstration need not be present by proxy nor connected to the context in any significant (‘real’) manner, e.g., causally. The demonstratum may be merely that which is demonstrated—witness Kaplan's ‘dthat’-operator, which may be supplemented by material that designates an object from long, long ago and far, far away, merely ‘by description’ (as in ‘Consider whoever was the last child born in the nineteenth Century. It would have been possible that he or she be born instead in the twentieth Century’).

As mentioned, Church's photograph may be employed as a stand in for Church himself. Another feature of the context which is no less relevant to understanding my use of ‘he’ is my demonstration of Church via the photograph. Frege and Kaplan put the demonstration directly into the expression to form a peculiar hybrid: ‘he’0x002322pointing-at-the-photograph. But the demonstration does not belong in the expression. I say we take it back. My alternative proposal is that we put the demonstration exactly where it has belonged all along: in the context. Intuitively, the speaker's hand gestures, fingerpointings, and glances of the eye are features of the context of use, every bit as much as the identity of the speaker and the time and place of the utterance. Consider again Frege's insightful observations: ‘Thus the time of utterance is part of the expression of the thought . . . The case is the same with words like “here” and “there”. In all such cases, the mere wording, as it can be written down, is not the complete expression of the thought; one further needs for its correct apprehension the knowledge of certain conditions accompanying the utterance, which are used as means of expressing the thought. Pointing the finger, gestures, and glances may belong here too.’ I agree with Frege, as against Kaplan, that gestures and fingerpointings belong together with the time and place of an utterance; I disagree with Frege, and Kaplan, that they go into the expression uttered. Rather, they are equally features of the conditions of an utterance that fix the contents of uttered indexicals. My proposal is that a context of use be regarded as sometimes including a demonstration among its features, along with an agent, a time, a place, and a possible world. Not the bare demonstratum, but the demonstration with all its representational content.29

Better yet, since the same demonstrative may recur within a single sentence or stretch of discourse, each time accompanied by a different demonstration (‘That one goes between that one and that one’), the context should include an assignment of a demonstration for each syntactic occurrence of a demonstrative in a sentence—the first occurrence, the second, and so on.30 This fuller notion of a context provides a different explanation from that of Frege–Kaplan of the sense in which demonstratives without accompanying demonstrations are incomplete. The demonstrative itself is
a complete expression, fully assembled and ready to go. Strictly speaking, it is the context that is incomplete. Or if you prefer, it is the occurrence of the demonstrative in the defective context that is incomplete, because of a contextual deficiency. It is like the use of ‘now’ in a timeless universe (‘before’ the Big Bang?), or the use of ‘there’ in Oakland, California—fully complete expressions occurring in defective contexts.31

The demonstration included in a context need not be an actual fingerpointing, or any action or event in the usual sense. The demonstration can be entirely verbalized—witness the discourse fragment displayed above. Kaplan should formalize this by putting the description from (i) directly into (ii) thus:

(ii′)  

I think that dthat [the male x: x is a suspicious-looking guy & we saw x yesterday wearing a brown hat] is a spy.

If the description in (i) is replaced by ‘the present Secretary of State’, Kaplan would need to make a corresponding adjustment to (ii′). But there is no intuitive justification for this dramatic departure from surface syntax. The description in (i) does not occur in (ii), which is a complete sentence by itself. Instead, (i) is part of the context in which (ii) occurs ((i) is the verbal context for the occurrence of (ii)), and the description in (i) is associated with the ‘he’ in (ii), playing the role of accompanying demonstration. As already mentioned, the description in (i) is a verbalized demonstration. If the description is replaced by another, the context for (ii) is changed, and hence so too its content. But (ii) itself remains the same complete sentence with the same English meaning.32

Importantly, the distinction between so-called pure indexicals and demonstratives is a matter of incompleteness not in the expressions, but in their contexts. Demonstratives and ‘pure’ indexicals alike are full-fledged indexicals, complete expressions unto themselves. The demonstratives ‘this’ and ‘that’ are every bit as complete and purely indexical as ‘you’ and ‘I’, as pure as freshly fallen snow. The negative side effects of the syntactic incompleteness thesis are avoided. The strictures of the linguistic variations of Occam's Razor are respected. Forget the Bare Bones Theory. Here is an Indexical Theory of Demonstratives worthy of the epithet.

VII

As mentioned, this Indexical Theory conforms with the linguistic variations of Occam's Razor which Kaplan's theory flaunts.33 But how does Frege's Puzzle with regard to demonstratives fare?

The sentence ‘That is that’ has a single meaning. The sentence is univocal but indexical, expressing different identity propositions in different contexts—some necessarily true, others necessarily false. The invariant meaning presents the content expressed in a given context with its contextual perspective, (roughly) as the singular proposition about the demonstrata of the separate demonstrations assigned by this very context to the first and second syntactic occurrences of ‘that’, that they are one and the very same. One might regard this as a lean and mean way of presenting content as compared with the riches of Kaplan's theory with its multiplicity of demonstration contents. But to see matters thus is to draw a hasty conclusion on the basis of a serious oversight concerning the communicative situation.

One may still appeal to the contents of accompanying demonstrations on the Indexical Theory in an account of Erkenntniswerte. The speakee understands the sentence merely by knowing the relevant character-building content rule. But in witnessing the utterance, the attentive speakee observes not only the sentence uttered but also the demonstrations that are assigned to distinct utterances of demonstratives. Indeed, the speakee must observe the demonstrations to grasp the speech act adequately, since knowing which proposition was asserted—knowing what is said—requires knowing which object was demonstrated. Awareness of the context provides the speakee with a special handle on the demonstrations assigned to each utterance. This ancillary empirical knowledge about which demonstrations are performed in the particular context allows the speakee to make substitutions into the character-building content rule's mode of presentation of the content, plugging in particular demonstrations, with their particular contents, for the meta-level concept the demonstration assigned by this very context. Instead of taking the proposition in terms of its relation to the context, the speakee now takes the proposition in terms of its relation to the particular demonstrations observably included in the context. In effect, the speakee converts knowledge by description of the proposition in terms of the context into knowledge by description in terms of the demonstration, exchanging knowledge by context-specific description for knowledge by demonstration-specific description. The latter, in turn, provides acquaintance with the proposition itself. The epistemic situation is not unlike learning the color of Alonzo Church's hair by being told that Church's hair was the color of snow while simultaneously being shown what snow looks like.

When the speaker utters ‘That is that’ pointing to the same object with both hands simultaneously, the context assigns the very same demonstration to both syntactic occurrences of ‘that’. In such contexts, the proposition expressed is taken by the attentive speakee as a trivial self-identity—in effect, as the singular proposition about the demonstratum of 0x0003b4that it is itself. This special way of taking the proposition is given not by the character itself, which presents the proposition in terms of its relation to the context, but by the character in tandem with the context that includes the observable demonstration 0x0003b4. There are other contexts that assign distinct demonstrations that happen to converge on the same demonstratum. In such contexts, the proposition is taken by the attentive speakee as an identification between objects differently demonstrated—as the singular proposition about both the demonstratum of 0x0003b41 and the demonstratum of 0x0003b42 , that they are one and the very same. Pairs of contexts, one of each sort, may yield exactly the same singular proposition—resulting in Frege's Puzzle. With regard to such context pairs, the uttered sentence ‘That is that’ not only expresses the same content but retains the same meaning. The relevant character-building content rule presents the proposition in terms of the same relations to the respective contexts—as a singular proposition about the demonstrata of whatever demonstrations are assigned to utterances of ‘that’ by the relevant context. In observing those demonstrations, the attentive speakee is enabled to take the proposition in the distinct contexts in terms of its relation to those very demonstrations. The different ways in which the same proposition is taken—what I have elsewhere called proposition guises34 —are provided not by the character-building content rule itself, but in the contents of the demonstrations assigned by the particular context of use. In short, the difference lies not in the semantics but in the contexts, which assign distinct demonstrations to the syntactic occurrences of ‘that’ and thereby provide the attentive speakee with contrasting perceptual perspectives on what is in fact the same proposition presented via the same meaning in the distinct contexts.

This contrasts with Kaplan's account, on which the same mere words are uttered, yet different sentences with different meanings (the different characters resulting from different demonstrations with different contents). While proposition guises can be a matter of linguistic meaning, they are not always so. Where demonstratives are used, they are a matter of ancillary knowledge, of non-linguistic perceptual perspective. The semantics of demonstratives on the proposed Indexical Theory makes essential reference to demonstrations, which are assigned to syntactic occurrences of demonstratives by the context. But that reference is exclusively by description. The semantics makes no essential reference to the contents of those demonstrations, even if they are crucial to the communicative and epistemic situation. The Indexical Theory provides no semantic distinction on which to hang the different ways in which the same proposition might be taken differently in different utterances of ‘That is that’. The various proposition guises are not given in the semantics. They are given in the context—or more accurately, in the union of meaning and context.

In ‘Afterthoughts’, Kaplan says that he accepted the Fregean theory of demonstrations in ‘Demonstratives’ in part because ‘the Fregean idea that that very demonstration might have picked out a different demonstratum, an idea that depended on the separability of a demonstration from a particular context, seemed to track very closely the cognitive uncertainties of “that 1 is that 2. This cognitive value appears in character, and thus as an aspect of meaning’ (p. 588). The Indexical Theory I propose demonstrates that the Fregean idea does not require the detachment of the demonstration from context. Nor must the relevant ‘cognitive uncertainties’ be an aspect of meaning. Meaning has a role to play, and an important role it is. But the epistemologically crucial ways of taking things are given in the context rather than the character-building content rule. Direct-reference theorists who share my skepticism regarding Frege's Solution to Frege's Puzzle with regard to ‘Hesperus’ and ‘Phosphorus’—including Kaplan (ibid., pp. 562–563, 598)—should not be troubled by this aspect of my proposed account. On the contrary, in respecting the strictures of the linguistic variations of Occam's Razor while locating the proposition guises provided through the use of demonstratives in non-semantic, contextual aspects of their use, the account points the way to a similarly non-semantic account of the cognitive role played by proper names, natural-kind terms, and other devices of direct reference.35

VIII

I have not argued that Kaplan's operator ‘dthat’ could not be added to a natural language like English, or even that it would be undesirable to do so. Quite the contrary, it has already proved itself a very useful addition to philosophical English. What I am

asserting is that the operator provides an inaccurate and seriously misleading model of standard uses of the English demonstrative ‘that’. Unlike ‘dthat’, which is syncategorematic, the English demonstrative ‘that’ is standardly used as a complete singular term that semantically designates the relevant demonstratum with respect to a context. In other standard uses, the English word ‘that’ is not itself a singular term but part of a so-called complex demonstrative, ‘that F’, which is a complete, fully designating singular term. It might be better to view the bare demonstrative ‘that’ as a diminution or abbreviation of the demonstrative phrase ‘that object’ or ‘that thing’, making space for the complex phrase ‘that F’ as the underlying general case. There are other uses of phrases of the same surface form as complex demonstratives on which those phrases seem to be instead stylistically altered definite descriptions. (‘David is still hoping to encounter that pupil who will surpass him.’) There may also be uses of words like ‘that’ and ‘she’ on which they function nearly enough like ‘dthat’—as perhaps, ‘A teacher gave Rudolf a low grade and David doubts whether she (the same teacher) graded fairly.’ Such uses deviate from the standard case.36

Following Kaplan's lead, I here introduce an artificial operator, ‘zat’. Unlike its predecessor ‘dthat’, the ‘zat’-operator does not have the logical form of a functor. But like ‘dthat’, neither is it a singular term. Like the logician's inverted iota, it is a variable-binding operator that forms singular terms from open formulas: ‘(zat x)(x is a man & x looks suspicious)’. It is not required, however, that the open-formula matrix, ‘x is a man & x looks suspicious’, be uniquely satisfied for the ‘zat’-term to be a ‘proper’ demonstrative, i.e., to designate. The meaning of a ‘zat’-term is determined by the following replacement for (D) (as well as for (T n )):

(Z)  

With respect to any assignment of values to variables s and any context c, the content of an occurrence of the demonstrative term 0x00231c(zat 0x0003b1)0x0003d5 0x0003b10x00231dis the demonstratum of the demonstration assigned to that occurrence in c, provided there is such a demonstratum and it satisfies 0x0003d50x0003b1with respect to c (i.e., provided 0x0003d50x0003b1is true under the modified version of s that assigns the demonstratum to 0x0003b1and is otherwise the same as s, with respect to both c and the particular circumstance c W -at-c T of c). Otherwise 0x00231c(zat 0x0003b1)0x0003d5 0x0003b10x00231dhas no content.37

As with ‘dthat’, the ‘zat’ operator is a content operator, in that the designatum of 0x00231c(zat 0x0003b1)0x0003d5 0x0003b10x00231dwith respect to a circumstance w-at-t must satisfy the matrix formula 0x0003d50x0003b1with respect to a different circumstance, viz., that of the context. Also like ‘dthat’-terms, ‘zat’-terms are not compositional with regard to content. Though 0x00231c(zat 0x0003b1)0x0003d5 0x0003b10x00231dis a compound term, the content of its matrix formula 0x0003d50x0003b1(under the assignment of values to its free variables) generally forms no part of the content of the ‘zat’-term itself (under that same value assignment), which, provided it satisfies the operand, is simply the demonstratum assigned to the term by the context. The semantic rule (Z) yields the following corollaries, analogous to (D1)–(D3) above:

(Z1)  

The complex demonstrative 0x00231c(zat 0x0003b1)0x0003d5 0x0003b10x00231dis indexical.

(Z2)  

With respect to any context 0x00231c(zat 0x0003b1)0x0003d5 0x0003b10x00231dis directly referential.


(Z3)  

With respect to any context an occurrence of 0x00231c(zat 0x0003b1)0x0003d5 0x0003b10x00231drigidly designates the demonstratum of the demonstration assigned to it in that context, provided such a demonstratum satisfies 0x0003d50x0003b1with respect to c. Otherwise it is a rigid non-designator.

Accordingly, I propose that Kaplan's content rule (T K ) be replaced with the following as governing standard uses of demonstratives:

(T)  

With respect to any context c, the (English) content of an occurrence of the complex demonstrative ‘that’0x002322NP is the demonstratum of the demonstration assigned to that occurrence in c, provided: (i) there is such a demonstratum; and (ii) NP applies to it with respect to c. Otherwise ‘that’0x002322NP has no content. (NP may be deleted to form a bare demonstrative, in which case condition (ii) is regarded as vacuously fulfilled, or simply deleted.)

This rule yields the same corollaries for natural-language complex demonstratives: ‘that’ is a content operator; complex demonstratives are not compositional with regard to content; they are indexical, directly referential, rigid.38 It is presumably Kaplan's intent that his alternative content rule (T K ) is to be extended to cover supplemented complex demonstratives, ‘that’0x002322NP0x0023220x0003b4, by including (T)’s condition (ii).39 This natural extension of (T K ) makes the mere (unsupplemented) complex

demonstrative ‘that’0x002322NP syncategorematic, i.e., a contextually defined incomplete symbol.40 Utterances of the same mere complex demonstrative accompanied by demonstrations of differing content are utterances of strictly different expressions with different meanings. On my alternative proposal, by contrast, a complex demonstrative is a complete singular term each use of which is an utterance of a single expression with a single meaning—though its content varies with context and its use is felicitous only in those contexts in which it is accompanied by a demonstration.

We have already seen numerous philosophically significant consequences of regarding natural-language complex demonstratives in accordance with (T), i.e., on the model of ‘zat’-terms: Frege's syntactic incompleteness thesis is rejected; the purity of natural-language syntax is not threatened; complex demonstratives are not syncategorematic; they are both meaningful and univocal; they designate the right object, etc. A treatment of complex demonstratives on the model of ‘zat’-terms yields further philosophically significant consequences. The semantic corollary (Z3) in particular imposes three conditions worthy of special note. Not surprisingly, complex demonstratives are rigid designators.41 More interesting, a complex demonstrative

‘that F’ cannot literally (semantically) designate anything that is not an F. The phrase might be used by a speaker to designate something that is not an F, but this is a matter of ‘speaker reference’ as opposed to ‘semantic reference’. Such a ‘referential’ use is, from the point of view of English semantics, a misuse.42 More interesting yet, a complex demonstrative ‘that F’ may designate something with respect to a possible world w even though the designated object is not an F in w, as long as it is actually an F—for example, ‘If we had not lowered admission standards, then that graduate student would not be in graduate school today.’43 No component of the content of an atomic sentence of the form ‘That F is G’ expresses about the demonstratum that it is F. Yet this is logically entailed. In fact, the sentence presupposes of the demonstratum that it is F, in that unless this is a fact the sentential subject is vacuous and the sentence is without truth value.44

There is another noteworthy consequence. The following English sentence is analytic, in the sense that it is true by virtue of semantics alone:

S

That graduate student (if there is any such thing) is a graduate student.45

The analyticity of S lies behind the logical validity of the argument, ‘Every graduate student is full of angst; therefore that graduate student (assuming he/she exists) is full of angst.’46 Although analytic, the content of S in any context is hardly a necessary truth.47 Indeed, its contingency is a likely source of considerable anxiety for the

demonstrated student. More surprisingly, S, although analytic, expresses an a posteriori truth. For consider a typical context in which the demonstratum is a particular graduate student, David. How does one come to know the following de re fact about David: that he—that very individual (if he exists at all)—is in graduate school? In any number of ways. One might observe his lifestyle, follow him around the university, confiscate his computer disks, subpoena his transcripts, record his nocturnal mutterings. Not, however, by a priori reflection on the issue.48

5 Are General Terms Rigid? (2003) *

Nathan Salmon

I

On Kripke's intended definition, a term designates an object x rigidly if the term designates x with respect to every possible world in which x exists and does not designate anything else with respect to worlds in which x does not exist. Kripke evidently holds in Naming and Necessity, hereafter N&N (pp. 117–144, passim, and especially at 134, 139–140), that certain general terms—including natural-kind terms like ‘water’ and ‘tiger’, phenomenon terms like ‘heat’ and ‘hot’, and color terms like ‘blue’—are rigid designators solely as a matter of philosophical semantics (independently of empirical, extra-linguistic facts). As a consequence, Kripke argues, identity statements involving these general terms are like identity statements involving proper names (e.g., ‘Clark Kent=Superman’) in that, solely as a matter of philosophical semantics, they express necessary truths if they are true at all. But whereas it is reasonably clear what it is for a (first-order) singular term to designate, Kripke does not explicitly say what it is for a general term to designate.1 General terms are standardly treated in modern logic as predicates, usually monadic predicates. There are very forceful reasons—due independently to Church and

Gödel, and ultimately to Frege—for taking predicates to designate their semantic extensions.2 But insofar as the extension of the general term ‘tiger’ is the class of actual tigers (or its characteristic function), it is clear that the term does not rigidly designate its extension, since the class of tigers in one possible world may differ from the class of tigers in another. What, then, is it for ‘tiger’ to be rigid?

In his recent book, Beyond Rigidity (Oxford University Press, 2002), Scott Soames considers the two interpretive hypotheses that he deems the most promising, strongly favoring one of the two (pp. 249–263, 287–288, and passim). On the preferred interpretation, a general term is rigid, by definition, if it expresses a property (e.g., being a tiger) that is essential to anything that has it at all, i.e., a property of an object that the object could not fail to have (except perhaps by not existing). Soames characterizes this hypothesis as a ‘natural extension’ to predicates of N&N’s definition of singular-term rigidity.3 I deem it a non-starter. One obvious problem with the proposal is that color terms then emerge as non-rigid, contrary to Kripke's apparent labeling of them as rigid. Also the definition does not provide any obvious candidate to be the rigid designatum of a predicate like ‘is a tiger’. The proposal might be based on a notion of poly-designation, whereby a predicate ‘designates’ one by one each of the things individually to which the predicate correctly applies semantically, i.e., each of the elements of the semantic extension.4 A predicate for an essential property applies to anything x that has the property in question with respect to every world in which x exists, while a predicate for an accidental property does not do this. But an essential-property predicate equally applies to the other things y in its extension besides x, and does so with respect to worlds in which x does not exist. This interpretation, therefore, does not fit the intended definition of rigid designation.

If the predicate ‘is a tiger’ is to be regarded as designating the property of being a tiger (rather than as multiply designating each individual tiger, and rather than as designating the class of actual tigers), then it would appear that any predicate should be seen as designating the property that it expresses. But in that case, every predicate, even ‘is a bachelor’, emerges as a rigid designator, since the attribute (property or relation) expressed by a predicate with respect to a possible world does not vary from world to world. Nothing special about natural-kind predicates, color predicates, etc. has been identified to demarcate them from the rest. So it is that N&N leaves us with the question: What is for a general term to be a rigid designator?5

One way to proceed that is more promising than the failed strategies Soames considers would be to define a notion of designation (simpliciter) for both singular and general terms in such a way that, applying the intended definition of rigid designation as is, without modification, a natural-kind general term (and a color general term, a natural-phenomenon general term, etc.) designates its designatum rigidly whereas some other sorts of general terms designate only non-rigidly.6 What object, then, should a general term like ‘tiger’ be said to designate? And which contrasting sorts of general terms designate only non-rigidly?

The first question has an obvious and natural response: The term ‘tiger’ designates the species, Tiger (Felis tigris). In general, a biological taxonomic general term should be seen as designating a biological taxonomic kind (a species, a genus, an order, or etc.), a chemical-element general term (‘gold’) should be seen as designating an element (gold), a chemical-compound general term as designating a compound (water), a color general term as designating a color (red), a natural-phenomenon general term as designating a natural phenomenon (heat), and so on. The semantic content of a single-word general term might then be identified with the designated kind (or the designated substance, phenomenon, etc.). So far, so good. But now the threat is faced anew that every general term will emerge as a rigid designator of some appropriately related universal or other. If ‘bachelor’ designates the gendered marital-status category, Unmarried Man, it does so rigidly. Even a common-noun phrase, like ‘adult male human who is not married’, emerges as a rigid designator.

II

Such is the notion of designation for general terms that I proposed in Reference and Essence (pp. 52–54, 69–75), and which I continue to believe is fundamentally correct.7 Soames objects on the grounds that ‘there is no point in defining a notion of rigidity for predicates according to which all predicates turn out, trivially, to be rigid’ (p. 251).8 Ultimately he decides that there is no notion of rigidity that is simultaneously analogous to singular-term rigidity, a natural extension of singular-term

rigidity to general terms, and a notion on which certain general terms (especially, natural-kind terms) are rigid but many other general terms are non-rigid (p. 263). And this, he argues, paves the way for a ‘demotion of the status of rigidity in Kripke's overall semantic picture’ of terms singular and general (p. 264).

I sharply disagree. It is true that Kripke's thesis that proper names and certain general names alike, including natural-kind terms, are rigid designators is secondary to a more fundamental thesis: that these names are non-descriptional.9 However, the corollary that they are therefore rigid is correct, and its philosophical significance should not be missed or undervalued. Soames's discussion suffers from a failure to distinguish sharply between a general term like ‘tiger’ and its corresponding predicate, ‘is a tiger’. Even if every common count noun (whether a single word or a phrase) emerges as a rigid designator on my counter-proposal, it does not follow that every general term is rigid. As Bernard Linsky noted in an unduly neglected paper, some general terms, in fact, are manifestly non-rigid.10 This is most evident with certain English definite descriptions. Definite descriptions are typically singular terms—or alternatively (following the great philosopher-lord), quantificational expressions that go around impersonating singular terms—but some English definite descriptions, unlike ordinary singular terms, function rather as if they were adjectives or, more likely, mass-noun phrases. One example is the description ‘the color of the sky’, as it occurs in the sentence

(P1)  

My true love's eyes are the color of the sky.

Soames sees the definite description in the predicate of (P1) as a singular term rather than a general term (p. 261).11 Yet the copula ‘are’ here cannot be the

pluralization of the ‘is’ of identity, since the color blue is a single universal whereas the speaker's lover's eyes are two particulars, and hence not both identical to a single thing. Nor can the copula be the so-called ‘is’ of constitution. One might argue that the copula in (P1) is a fourth kind of ‘is’, over and above the ‘is’ of predication, the ‘is’ of identity, and the ‘is’ of constitution: the dyadic ‘is’ of possession. Soames is evidently committed to positing such an alternative sense. This rather strained account raises the question of why ‘to have’ should come to masquerade as ‘to be’. It is considerably more plausible that the ‘are’ in (P1) is the very same copula that occurs in

(C)  

My true love's eyes are blue

to wit, our old and dear friend, the ‘is’ of predication (in its pluralized conjugation). This common form of ‘be’ cannot coherently combine with an English expression functioning as a (first-order) singular term to form a meaningful English predicate. Any English term (or English expression that functions as a term when occurring in a predicate) that combines with the ‘is’ of predication to form a monadic predicate, must function as a general term in the predicate so formed.12 (I take these principles to be partly ‘criterial’ of the distinction between singular and general terms.) Just as the adjective ‘blue’ is a general term in (C), so the definite description ‘the color of the sky’ is a general term in (P1). The former rigidly designates the color blue; the latter designates the color non-rigidly.

How can a definite description combine with the ‘is’ of predication while designating something? In the same way as the adjective ‘blue’ or the mass noun ‘water’. Let us formally represent the copula in ‘is blue’ as a predicate-forming operator on adjectives (whether single words or adjective phrases) and mass nouns, ‘is’, and let us represent the ‘is a’ in ‘is a tiger’ as a similar predicate-forming operator on count nouns, ‘is-a’, so that the predicate ‘is blue’ is formalized as ‘is’ and the predicate ‘is an albino tiger’ as ‘is-a’.13 The term ‘the color of the sky’ may then be formally rendered as a second-order definite description:


(0x0003b9F)[is-a2(F) & is(the sky)],

where ‘F’ is a variable ranging over appropriate universals. (The superscript ‘2’ indicates that the resulting predicate is second order.) As a second-order term, the description designates even while combining felicitously with the ‘is’ of predication.14 Indeed, so understood, (C) is a straightforward logical consequence of (P1) taken together with the empirical premiss,

(P2)  

Blue is the color of the sky.

This inference is best seen as a special instance of Leibniz's Law, or Substitution of Equality. In the words of a great English poet, it's easy if you try. According to (P2), the color blue is identical with the color of the sky. Since the speaker's true love's eyes are the color of the sky, it follows by Substitution that those same eyes are blue. All you need (besides love) is to see the copula in (P2) for what it surely is: an ‘is’ of identity, attached to general terms instead of singular terms, and forming a sentence that is true if and only if the terms flanking the ‘is’ are co-designative.

Formalization of the inference might help to make the point:

(P1′)  

(x)[is-a(x)→is(F) & is(the sky)]}(x)]

(P2′)  

blue=2(0x0003b9F)[is-a2(F) & is(the sky)]

0x002234(C′)  

(x)[is-a(x)→is(x)]

(Then again, it might not.) The copula in (P2) is evidently the same ‘is’ of identity that occurs in the conclusion of ‘There are exactly three volumes of Russell and Whitehead's Principia Mathematica; therefore, three is the number of volumes of Principia Mathematica.’ Soames contends instead (pp. 364n9, 289–290) that the syllable/vocable ‘blue’ represents a pair of English homonyms: one an adjective (blue 1 ), the other a noun (blue 2 ) that is parasitic on the adjective. This perspective yields a markedly different rendering of the inference:

(P1″)  

(x)[x is an eye of my true love→Is(x,(0x0003b9y)[y is a color & Is(the sky,y)])]


(P2″)  

blue 2 =(0x0003b9y)[y is a color & Is(the sky,y)]

0x002234(C″)  

(x)[x is an eye of my true love→x is blue 1 ],

where the dyadic predicate ‘Is’ occurring in the premisses represents the alleged ‘is’ of possession. This argument, however, is invalid as it stands. The argument (and also the parallel invalid argument obtained by interchanging the major premiss and conclusion) may be validated by supplementing the premisses with a striking Carnapian ‘meaning postulate’ (perhaps as a tacit premiss): ‘Something is blue iff it is blue’, taken in the alleged sense of

(P3)  

Something is predication blue 1 iff it is possession blue 2 ,

and formalized as

(P3″)  

(x)[x is blue 1Is(x, blue 2 )].

But how plausible is it that both of the words ‘is’ and ‘blue’ making up the English predicate are ambiguous (quite independently of a third meaning, the ‘is’ of identity), and in such a way that, solely as a matter of English semantics, the predicate applies under one meaning exactly when it applies under the other as well? Indeed, solely as a matter of English semantics, the two alleged readings would have to be logically equivalent—sharing not only the same semantic extension, and not only the same modal intension, but even the very same logical content, i.e., the same function from models to intensions.15 This degree of duplication—duplication of spelling, phonetics, structure, etc., and in addition, duplication of logical content—strongly suggests that something has gone wrong in the analysis. Rather than exposing an unnoticed convergence, our distinction without a difference more likely indicates an erroneous proliferation (‘is predication blue 1 vs. ‘is possession blue 2). The fact that the word ‘blue’ can occur alternatively as a noun or as an adjective does not imply that the word is ambiguous with regard to semantic extension or intension, let alone that there are two words ‘blue’ rather than one—let alone that there is in addition to the standard ‘is’ of predication another predicative ‘is’, the alleged ‘is’ of possession. To quote Kripke (slightly out of context): ‘It is very much the lazy man's approach to philosophy to posit ambiguities when in trouble. . . . [The] ease of the move should counsel a policy of caution: Do not posit an ambiguity . . . unless there are really compelling theoretical or intuitive grounds to suppose that an ambiguity really is present’ (‘Speaker's Reference and Semantic Reference’, p. 19).

III

Robert May has argued in response to these considerations that insofar as ‘the color of the sky’ is to be classified either as a singular term or as a general term, it is a singular term even in (P1).16 He endorses this conclusion on the ground that definite descriptions are nominal phrases that can occur in positions occupied by singular terms—as, for example, in ‘Max and the color of the sky are two of my favorite things.’ In addition, May cites the particular sentences, ‘Max is the man for the job’ (due to James Higgenbotham) and the sarcastically understated ‘Max isn't the best cook in town’, as further examples—allegedly like (P1)—of the ‘is’ of predication combined with an English singular term rather than a general term to form an English monadic predicate.

As a rejoinder to May's objections, and in order to clarify the position I am defending, I offer the following observations:

(i) The possibility of grammatically occupying singular-term position is a necessary condition on singular terms, not a sufficient condition. Mass terms in English, for example, can occur in singular-term position (‘Water is H 2 O’, ‘Max and gin are two of my favorite things’), but they also occur in general-term position, combining with the ‘is’ of predication to form English monadic predicates (‘The liquid in this cup is water’). Likewise, canonical color terms and number terms (‘three’) can occur in singular-term position (as in (P2) and ‘Nine is the number of planets’), but they also combine with predicational ‘be’ to form a predicate (as in (C) and ‘The planets are nine’17 ). Contrary to May, the latter is something singular terms cannot do, at least not while functioning as singular terms, or even as first-order restricted quantifiers in the manner of Russell and Montague. (See note 1 above. The fact that mass terms and the like can occur grammatically in singular-term position in addition to general-term position might be taken as independent grounds for recognizing at least some general terms as second-order singular terms.)

(ii) English also includes sentences like ‘What I am is nauseous’, in which the subject is a general term—or, at least, would appear to be one. Indeed, this sentence appears to be an identity statement, and its subject a second-order definite description (or, alternatively, a second-order restricted quantifier). Insofar as English includes second-order definite descriptions, phrases like ‘the color of the sky’, ‘Henry's favorite beverage’, and ‘the chemical compound composed of two parts hydrogen, one part oxygen’ are as good candidates as any.18 Although these descriptions can occur

in singular-term position, they also combine with the ‘is’ of predication to form monadic predicates, wherein they cannot function as singular terms. In fact, at least some of these same definite descriptions appear to function as mass-noun phrases and/or as color-term noun phrases. (Consider (P2′) and ‘Water is the chemical compound composed of two parts hydrogen, one part oxygen’.) As such, these descriptions would be general terms rather than singular.

(iii) The copula in May's examples—‘Max is the man for the job’ and ‘Max isn't the best cook in town’—is normally and plausibly construed as the ‘is’ of identity rather than the ‘is’ of predication. For example, ‘Max is the man for the job’ is logically equivalent to its converse, ‘The man for the job is Max’, and also to Russellian paraphrases of its identity construal—‘Someone is both a unique man for the job and Max’, ‘Max, and no one else, is a man for the job’, etc. Likewise, ‘Max is the man for the job’ supports Leibniz's-Law substitution, e.g., ‘Therefore, Max speaks Japanese iff the man for the job speaks Japanese.’ By contrast, (P1), on its relevant reading, is not equivalent to *‘Something is both a unique color of the sky and each of my true love's eyes.’19 Neither does (P1) support logical substitution (e.g., #‘Therefore, my true love's eyes have cataracts iff the color of the sky has cataracts’). Since the copula in (P1), on its relevant reading, cannot be read as the ‘is’ of identity, and should be read instead as the ‘is’ of predication, the definite description does not function in (P1) as a singular term.

(iv) May's claim that some first-order definite descriptions, like ‘the man for the job’, can combine with the ‘is’ of predication to form an English monadic predicate, rather than with the ‘is’ of identity, is controversial. (See notes 12 and 13 above.) If the thesis is correct, the description in the predicate so formed is equivalent to a predicative indefinite description—as perhaps the indefinite description in ‘is a unique man for the job’. A predicative indefinite description (e.g., the phrase ‘a tiger’ in the predicate ‘is a tiger’) is not a singular term, and does not function as one in its containing predicate. May's examples therefore cannot be instances of a monadic predicate formed by combining the ‘is’ of predication (functioning as such in the predicate) with a singular term (functioning as such in the predicate).20

(v) That ‘blue’ and ‘the color of the sky’ are general terms is a fact about logical form. It is not a fact about syntactic form—or about grammar in a syntactic sense of the term (which does not conform to current usage in theoretical linguistics). The following sentences, on their standard readings, have the same syntactic form.

(1)  

Henry's favorite shirt is the color of the sky

(2)  

Henry's favorite color is the color of the sky

Each is a copular sentence constructed from a definite description of the form 0x00231cHenry's favorite N0x00231d as subject, the appropriate conjugation of the verb ‘be’ as copula, and the definite description ‘the color of the sky’ as predicate nominal. Nevertheless, they differ sharply in logical form. Sentence (1) is a monadic predication, whereas sentence (2) is (equivalent to) an identity/equation, on a par with (P2) and with May's examples (e.g., ‘Max is the man for the job’). Correspondingly, (2) is logically equivalent to its converse and supports Leibniz's-Law substitution; (1) is not and does not.

It would be a mistake to infer that, since they differ in logical form, (1) and (2) also differ in syntactic/grammatical form. Compare the following two sentences, on their standard readings.

(3)  

Henry's favorite shirt is blue

(4)  

Henry's favorite color is blue

These sentences are semantically related exactly as (1) and (2). All four sentences, (1)–(4), share a common syntactic structure. Like the pair (1) and (2), (3) and (4) differ in the replacement in their subjects of ‘shirt’ by ‘color’ (count nouns both), and are otherwise structurally identical. Here the lexical switch in the subject issues a categorial (non-structural) switch in the predicate. The word ‘blue’ occurs as an adjective in (3), as a noun in (4), reflecting the change in logical form. This grammatical switch in the predicate does not occur with (1) and (2). As already noted, abstracting from their meanings and their logic—which are indeed very different—(1) and (2) share the same syntactic analysis in terms of both constituent structure and lexical and phrasal categories. Yet the same change in logical form that occurs in (3) and (4) also occurs in (1) and (2), where it is concealed behind a veil of superficial syntactic similarity. Though ‘the color of the sky’ is a nominal phrase, it plays exactly the same logico-semantic role in (1) and (P1) that the adjectival ‘blue’ plays in (3) and (C)—a role reflected in the grammar of the word but not in that of the description.21

Here again, contrary to May, recognition that the copula in (P1), on its standard reading, is the same ‘is’ of predication that occurs in (3) and (C) reveals that the predicate nominal in (P1)—regardless of its syntax—is a general term, since a term that combines with the ‘is’ of predication (without an intervening article) to form a monadic predicate cannot function as a singular term in the predicate so formed.

(vi) Having misclassified ‘the color of the sky’ as a (first-order) singular term, May is prepared to classify the copula in (1) and (P1) as an expression that sometimes operates on a singular term to form a monadic predicate. The predicate-forming operator ‘is’ in (P1′) and (C′) is not an operator of this sort. On the other hand, the envisioned ‘is’ of possession in (P1″) is exactly that. And indeed, May defends the second analysis of the argument about my true love's eyes. May's stance thus fails to appreciate the implausibility of its commitments, e.g., that each of the words making up the English predicate ‘is blue’ has two separate readings (independently of a third meaning—the ‘is’ of identity), but only in such a way that, solely as a matter of English semantics, the two resulting readings of the predicate are logically equivalent.

Given that the noun/adjective ‘blue’ designates the color blue, that the definite description ‘the color of the sky’ designates the color of the sky, and the empirical fact that the sky is blue, the general terms ‘blue’ and ‘the color of the sky’ are co-designative.22 (No surprises here.) But whereas the former is surely rigid, the latter

end p.110

designates red with respect to some worlds, making (P2) contingent. (Again, no surprise.) If the copula in (P2) is indeed an ‘is’ of identity to be placed between general terms, then Kripke's claim is vindicated that identity statements in which rigid general terms occur are, unlike (P2) but like identity statements involving proper names, necessary if true at all. Examples are close at hand: ‘Furze is gorse’; ‘Gold is Au’; ‘Water is H 2 O’. As already noted, even some descriptional general terms, like ‘adult male human who is not married’, are rigid designators. Still, non-rigid general terms are everywhere. These include such definite descriptions as ‘the species that serves as mascot for Princeton University’, ‘the liquid compound that covers most of the Earth’, ‘the most valuable of elemental metals’, ‘the color of the sky’ and so on.23

It was once maintained by many that a general term like ‘blue’ is synonymous with a description like ‘the color of the sky’, that ‘water’ is synonymous with a description, such as perhaps ‘the colorless, odorless, potable, thirst-quenching liquid

that fills oceans, lakes, and streams’, and that ‘pain’ is synonymous with a description of the form ‘the physiological state that occupies such-and-such causal/functional role’. Some consequences of these views are that ‘The sky is blue’ and ‘The oceans are filled with water’ express necessary, a priori truths, whereas ‘Water is the chemical compound of two parts hydrogen, one part oxygen’ and ‘Pain is the stimulation of C-fibers' expresses contingent identities. Today we know better—many of us anyway—thanks in large measure to N&N’s lasting insight that ‘blue’ and ‘water’ and ‘pain’ are, and the allegedly synonymous general-term descriptions are not, rigid designators in the original sense of that term.24 The relevant notion of general-term rigidity results directly from recognizing expressions like ‘blue’, ‘water’, ‘the color of the sky’, and ‘the liquid that sustains terrestrial life’ as general terms designating appropriate universals (colors, substances, etc.), and then applying Kripke's definition of rigidity without modification—with the result that some general terms are rigid, some not. This notion is analogous to singular-term rigidity in every way that matters.25

end p.112


6 A Theory of Bondage (2006)* I

Let A be an assignment of values to variables on which Marlon Brando is the value of ‘x’, and Shirley MacLaine is the value of ‘y’. In classical semantics, the open formula (‘open sentence’)

(1)  

(0x002203x)(y is a sister of x)

is true under our value-assignment A iff there is some element or other i of the universe over which the variables range such that

(2)  

y is a sister of x

is true under the value-assignment Ax i , a variant of A that assigns i instead of Brando as value for ‘x’ and is otherwise the same as A (and so assigns Shirley MacLaine as value for ‘y’). In Tarski's terminology, A satisfies (1) if and only if some modified value-assignment Ax i of the sort specified satisfies (2). Assigning Warren Beatty as value for ‘x’ does the trick.

This simple example demonstrates a fact not often recognized: The quantifier phrase ‘(0x002203x)’ is non-extensional. This follows from the fact that it is not truth-functional. Under the original value-assignment A, ‘(0x002203x)(xx)’ is every bit as false as its matrix, ‘xx’, yet (1) is true even though its matrix is false. The non-extensionality of a quantifier phrase is a surprising but trivial consequence of the way the quantifier works with a variable. The truth-value of (2) under A, and for that matter also the designatum of ‘x’ under A, are irrelevant to the truth-value of (1) under A. What matters are the designata of ‘x’ and ‘y’, and therewith the truth-value of (2), under modified value-assignments Ax i . The original value-assignment A does not satisfy (2), but the value-assignment Ax Beatty does, and that is sufficient for A to qualify as satisfying (1). We achieve satisfaction by offering Brando's role to Beatty.

Under A, ‘x’ designates Brando and ‘y’ designates MacLaine. The variables ‘x’ and ‘y’ both occur in (1). The original value-assignment A satisfies (1), although the particular value of ‘x’ under A and the particular truth-value of (2) under A, do not matter in the slightest. When evaluating (1) under A, MacLaine is present while Brando is nowhere on the set. Under A, (1) makes no mention of Brando. He has nothing to do with the success of (2) under Ax Beatty . Why does he still receive billing? More to the point, how is it that under A (1) makes no mention of Brando even though ‘x’, which occurs twice therein, designates Brando?

Frege admonished that one should never ask for the designatum or content of an expression in isolation, but only in the context of a sentence. This is his celebrated Context Principle.1 Extrapolating from Frege's prohibition, we should not inquire after the designatum of ‘x’ under A. Instead we should inquire after the designatum of the second ‘x’ in (1)—as distinct, for example, from the ‘x’ in (2). If ever there was a case in which Frege's Context Principle has straightforward application, this is it: the bound variable. So let us follow Frege's considered advice and ask: If ‘xas it occurs in (1) does not designate Brando under A, what exactly is the ‘x’ in (1) doing? Likewise, what is the extension of (2), under A, as (2) occurs in (1)?

Classical Tarski semantics does not specify what the second ‘x’ in (1) designates under the original assignment. This is because the second ‘x’ in (1) is not the variablex’, which designates Brando under A. It is a bound occurrence of ‘x’, which does not. Classical semantics imputes semantic extensions to expressions (under assignments of values to variables), not to their occurrences in formulae. Classical semantics does not abide by the Context Principle. But Frege's admonition has a point. One reason for departing from classical semantics—and one possible motivation for the Context Principle—is the desire for universal principles of extensionality for designation and of compositionality for semantic content. (According to extensionality, the extension of a compound expression is a function of the extensions of its meaningful components, including the designata of the component designators. According to compositionality, the semantic content of a compound expression is a function of the contents of the meaningful components.) Even more important is our intuition concerning what is actually being mentioned in a particular context. Consider, for example, the following fallacious inference:

In 1999, the President of the United States was a Democrat.

The President of the United States = George W. Bush.

Therefore, in 1999, George W. Bush was a Democrat.

The invalidity is partially explained by noting that whereas the definite description in the second premiss designates Bush, there is no mention of Bush in the first premiss. The argument's two occurrences of the phrase ‘the President of the United States’ thus do not designate the same thing. Though perhaps incomplete, the explanation is intuitive, even satisfying.

The Context Principle is not a blanket injunction against assigning semantic values to expressions simpliciter. Frege regarded the attributing of semantic values to expressions as legitimate only to the extent that such attribution is derivative from semantic attribution to those expression's occurrences in sentences. One need not adopt Frege's attitude in order to make perfectly good sense of attributing a semantic content and a designatum to an expression-occurrence. From the perspective of classical semantics, semantic attribution to occurrences may be regarded as derivative from the metalinguistic T-sentences (and similar meta-theorems) derived from basic semantic principles. According to Frege, whereas ‘Ortcutt is a spy’ customarily designates a truth-value, the occurrence in ‘Ralph believes that Ortcutt is a spy’ instead designates a proposition (Gedanke). Similarly we may choose to say that whereas ‘the President of the United States’ customarily designates Bush, its occurrence in the major premiss above instead designates the function that assigns to any time t, the person who is President of the United States at t. The semantic value of the description that bears on the truth-value of the sentence is not Bush, but this function.2

My primary objective in what follows is to sketch a proper and natural way of doing quantificational semantics on expression-occurrences. I do this, in part, in the hope of warding off confusion that has resulted from doing occurrence-based quantificational semantics in improper or unnatural ways. In the closing sections below, I apply the occurrence-based semantic apparatus to two separate, seemingly unrelated, contemporary controversies. I do this not because one must adopt occurrence-based semantics in order to obtain the right results in connection with those controversies. On the contrary, in both cases classical expression-based semantics suffices both to obtain and to justify those results, while occurrence-based semantics supplements the case. I do this, rather, because the two controversies are in fact closely related to one another: each is fueled almost entirely by the same pernicious misconception in occurrence-based semantics. In both cases, one needs to get a handle on occurrence-based semantics to see clearly what went wrong on the wrong side of the controversy, and hence in order to provide a full and definitive response.

At least as important—quite apart from and independently of these particular controversies—occurrence-based semantics illuminates. It upholds intuitions about what is actually mentioned, or at least what is not actually mentioned, in sentences like ‘The temperature is rising’ (Barbara Partee3 ) and ‘In 1999, the President of the United States was a Democrat.’ It reveals thereby what is right about the analysis of the fallacy mentioned two paragraphs up. As Frege knew, occurrence-based semantics

reveals that there is a sense in which principles of extensionality and compositionality are upheld, at least in spirit (perhaps even in letter), despite the presence of nonextensional devices (e.g., modal operators, temporal operators, ‘believes that’, or quotation). More important for my present purpose, occurrence-based semantics illuminates just what is going on when a quantifier binds a variable. Properly executed, occurrence-based quantificational semantics directly contradicts prevailing views about bound variables and pronouns. Occurrence-based quantificational semantics also reveals that principles of extensionality and compositionality are upheld with regard to the binding of variables despite the non-extensionality (strictly speaking) of quantifier phrases. It reveals how Frege could have accommodated variable-binding, and more important how he should have done so. It also reveals how Fregean functions from objects to truth-values (‘Begriffe’), and even Russellian functions from objects to singular propositions (‘propositional functions’), emerge from constructions involving bound variables. Even if the Context Principle is wrong and classical expression-based semantics is the ‘right’ or preferred way to do semantics—as I believe—it remains that expression-based semantics is, as Frege insisted, a less discriminating by-product, or sub-theory, of occurrence-based semantics. This alone justifies the present investigation.

Important Cautionary Note Throughout this chapter I distinguish very sharply between an expression (e.g., the variable ‘x’) occurring in a sentence or formula and the occurrence itself (e.g., the second occurrence of ‘x’ in (1)). Equivalently, I draw a sharp distinction between ascribing certain semantic attributes to an expression (of a particular language or semantic system) per se and ascribing those attributes to the expression ‘as it occurs in’, or relative to a particular position in a larger expression (e.g., a sentence) or stretch of discourse.4 It is essential in what follows that the reader be ever vigilant, paying extremely close attention to the distinction between expressions themselves and their occurrences. Many philosophers of language who think, habitually and almost instinctively, in terms of expression-occurrences and their semantic values—especially Fregean and linguistics-oriented philosophers—habitually and almost instinctively reinterpret remarks explicitly about expressions occurring in a sentence as concerning not the expressions but their occurrences. Nearly everyone who thinks about expressions at all typically has at least some inclinations of this sort. How many letters are there in the name ‘Nathan’? The reader with even the slightest inclination to give the incorrect answer ‘six’ is implored to remain on the alert and to make every

effort in what follows to let intellect overcome inclination, instinct, and habit; else much of what is said will inevitably be seriously misunderstood.5

II

I assume the classically defined notion of semantic extension in what follows. Context Principle enthusiasts may take this to be Frege's notion of default or customary Bedeutung. In developing an occurrence-based semantics of variable-binding, I take my cue from Frege's theory of indirect (oblique, ungerade) contexts.

The variables occurring in (2) occur exclusively free there. Assignments of values to variables are assignments of designata to free occurrences. Under the original assignment A, the ‘x’ in (2)—that is, the occurrence of ‘x’ in (2)—designates Brando, the ‘y’ in (2) MacLaine. These are the default or customary designata of the variables ‘x’ and ‘y’ under A, i.e., the designata of occurrences in extensional position and not within the scope of a variable-binding operator.6 The variables have their customary extensions in (2), and (2) is thereby false under A. Not all occurrences of variables have their customary extensions. Some occurrences deviate from the default value. On a natural extrapolation from Frege's explicit remarks, the occurrence of ‘x’ in ‘Ralph believes that x is a spy’ has its indirect designatum (ungerade Bedeutung), under a value-assignment, designating its customary or default sense. This is because the ‘x’ is within the scope of an occurrence of ‘believes that’, which induces a semantic shift, whereby expressions take on their indirect designata in lieu of their customary designata. Alonzo Church has developed this idea by considering assignments of customary-sense values (‘individual concepts’) to variables instead of customary-designatum values.7

Fortunately, the matter of indirect designation does not concern us here. Our concern is with the semantics of ordinary bound variables. The outline is the same. The ‘x’ in (2) is a free occurrence, and consequently it has its customary extension in (2). But neither occurrence of ‘x’ in (1) has its customary extension in (1). This is because both occurrences (‘the two bound variables in (1)’) are within the scope of an occurrence of a shift-inducing operator.

Quantifiers are variable-binding operators. Like ‘believes that’, variable-binding operators induce the variables they bind to undergo semantic shift, but a shift of a different sort from intensional or ‘indirect’ (oblique) operators. The occurrences of ‘x’ in (1) are no longer in default mode, designating their customary extension. They are in bondage. Classical semantics—the semantics of expressions, as opposed to their occurrences—is the customary semantics of default semantic values: the semantics of free occurrences. Classical semantics is thus the semantics of freedom. Bound variables have their bondage semantics, in many respects analogous to the semantics of indirect occurrences. One could say that the special kind of semantic shift that occurs when a quantifier binds a variable is precisely what variable-binding is.

If a free variable has its default or customary extension, which is simply its value under a value-assignment, then what is the extension of a bound variable (of the occurrence, not the variable of which it is an occurrence)? A bound variable ranges over a universe of discourse. It is not that Brando is nowhere on the set. It is that he is part of a cast of thousands. Ranging is not the same thing as designating. The definite description ‘the average man’, as it occurs in ‘The average man sires 2.3 children in his lifetime’, does not designate a peculiar biological being that has very peculiar offspring. It ranges over a universe of relatively normal biological beings, each with a definite whole (non-fractional) number of relatively normal offspring. The description does not designate this universe; it ranges over it. Similarly, the bound variable does not designate the universe over which it ranges.

Bound occurrences of different variables of the same sort range over the same universe. Does the variable also designate? A standard view is that free variables (and occurrences of compound designators containing free variables) designate, whereas bound variables do not. An analogous view is generally assumed with regard to natural-language pronouns like ‘he’: deictic occurrences and some ‘pronouns of laziness’ designate, whereas bound-variable anaphoric occurrences do not. Peter Geach, for example, criticizes ‘the lazy assumption that pronouns, or phrases containing them, can be disposed of by calling them “referring expressions” and asking what they refer to’.8 He says of anaphoric pronoun-occurrences. ‘It is simply a prejudice or a blunder to regard such pronouns as needing a reference at all.’9 Geach's thesis that anaphoric pronoun-occurrences other than pronouns of laziness do not designate is supported by his contention that such pronoun occurrences are bound variables and his insistence that bound variables do not designate. This attitude (which I once shared) betrays a lack of analytical vision. With regard to the issue of whether anaphoric pronoun-occurrences designate, the prejudice or blunder, I contend, is on Geach's side. He is not alone.

A bound variable has its bondage extension, which is different from the variable's customary extension. In general, an occurrence of a meaningful expression in extensional position and not within the scope of a variable-binding operator has its customary extension under a value-assignment, whereas a bound occurrence has its bondage extension.10 The central idea is given by the following principle of identification, analogous to Frege's identification of ungerade Bedeutung with customary sense: The extension of a bound occurrence of an open expression in otherwise extensional position is the function from any potential value of the bound variable to the expression's customary extension under the assignment of that value. It is this function, rather than the extension of the open expression, that bears on the truth-value of sentences in which the open expression occurs bound.

More accurately, the extension of an occurrence depends on the number of variable-binding operators governing it. Let us call the extension, under a value-assignment s, of an occurrence of a well-formed expression 0x0003b6within the scope of an occurrence of a variable-binding-operator phrase 0x00231c(B0x0003b1)0x00231d—where B is a variable-binding operator and 0x0003b1is a variable—and not within the scope of any other occurrence of a variable-binding-operator phrase or other nonextensional operator, the bondage extension of 0x0003b6with respect to 0x0003b1under s. Our theory of bondage starts with, and builds upon, the following principle.

A 1 : The bondage extension of a well-formed (open or closed) expression 0x0003b6with respect to a variable 0x0003b1, under a value-assignment s, is (0x0003bbi)[the customary extension of 0x0003b6under s0x0003b1 i ]—i.e., the function that maps any element i of the universe over which 0x0003b1ranges to the customary extension of 0x0003b6under the modified value-assignment that assigns i to 0x0003b1and is otherwise the same as s.11

The bondage extension of the variable ‘x’ with respect to itself is the identity function on the universe over which ‘x’ ranges.12 Each distinct variable with the same range

thus has the same bondage extension, under any given value-assignment, with respect to itself.

Variables are not the only expressions that have bondage extension. Any well-formed expression that has extension does. (See note 10 above.) Occurrences of open formulae bound through an internal variable-occurrence range over a universe of truth-values. (OK, so it is a baby universe.) The bondage extension of a formula is what Frege misleadingly called a concept (‘Begriff’), i.e., a function from objects to truth-values. Thus the extension of the occurrence of ‘x is bald’ in ‘(0x002203x)(y is a sister of x & x is bald)’, under any particular value-assignment, is the function that maps any bald individual to truth (‘the True’) and any non-bald individual to falsehood (‘the False’). More generally, the bondage extension of a formula 0x0003d5with respect to a variable 0x0003b1, under a value-assignment s, is the characteristic function of the class of objects i from the range of 0x0003b1such that 0x0003d5is true under s0x0003b1 i . For most purposes, the bondage extension may be identified with this class, in lieu of its characteristic function.

The extension of a doubly bound occurrence of a doubly open expression, like ‘x is a sister of y’ or ‘x loves y’, must be sensitive to the particular manner in which its internal variables are bound in a particular occurrence. Otherwise ‘(x)(0x002203y)(x loves y)’ collapses together with ‘(y)(0x002203x)(x loves y)’. How shall this be accomplished?

Let 0x0003b1and 0x0003b2be variables, and let 0x0003d5(0x0003b1, 0x0003b2) be any formula in which both 0x0003b1and 0x0003b2occur free. Suppose an occurrence of 0x0003d5(0x0003b1, 0x0003b2) is within the scope of a quantifier-occurrence on 0x0003b2that is itself within the scope of quantifier-occurrence on 0x0003b1. That is, suppose we are considering a doubly embedding formula of the form


(B0x0003b1)( . . . (C0x0003b2)[ . . . 0x0003d5(0x0003b1, 0x0003b2) . . . ] . . . )

Whereas the occurrence of 0x0003d5(0x0003b1, 0x0003b2) still ranges over a universe of truth-values, it occurs here doubly bound: by B with respect to 0x0003b1and by C with respect to 0x0003b2. We call the extension, under a value-assignment s, of an occurrence of a well-formed expression 0x0003b6in extensional position within the scope of an occurrence of a variable-binding-operator phrase 0x00231c(C0x0003b2)0x00231d, itself within the scope of an occurrence of a variable-binding-operator phrase 0x00231c(B0x0003b1)0x00231d—where B and C are variable-binding operators and 0x0003b1and 0x0003b2are variables—but not within the scope of any other occurrence of a nonextensional operator, the double bondage extension of 0x0003b6with respect to <0x0003b1,0x0003b2> under s. Doubly bound occurrences are governed by the following principle.

A 2 : The double bondage extension of a well-formed (open or closed) expression 0x0003b6with respect to an ordered pair of variables <0x0003b1,0x0003b2>, under a value-assignment s, is (0x0003bbi)(0x0003bbj)[the customary extension of 0x0003b6under s0x0003b1 i 0x0003b2j ]—i.e., the function that maps any element i from the range of 0x0003b1to the function that maps any element j from the range of 0x0003b2to the customary extension of 0x0003b6under the doubly modified value-assignment that assigns i to 0x0003b1,j to 0x0003b2, and is otherwise the same as s.13

This singulary function to singulary functions may be replaced with its corresponding binary function. In the special case where 0x0003b6is a formula 0x0003d5(0x0003b1, 0x0003b2) , the latter function maps any pair of objects, i and j (from their respective ranges), to the truth-value of 0x0003d5(0x0003b1, 0x0003b2) under s0x0003b1 i 0x0003b2j . For most purposes, we may go further and replace this binary function with the class of ordered pairs that it characterizes.

The double bondage extension of the variable ‘x’ with respect to the pair <‘x’, ‘y’> is not the same as its double bondage extension with respect to the converse pair <‘y’, ‘x’>. This is just to say that the extension of a bound occurrence of a variable within the scope of a pair of variable-binding operator-occurrences depends on the order of the variable-binding operator-occurrences. Replacing singulary functions to singulary functions with binary functions, the extension of the second ‘x’ in ‘(x)(0x002203y)(x loves y)’ is the binary function, the former of i and j, the extension of the second ‘y’ (indeed of both occurrences of ‘y’) is the binary function, the latter of i and j. By contrast, the extension of the second ‘x’ in ‘(y)(0x002203x)(x loves y)’ is the function, the latter of i and j, the extension of the second ‘y’ the function, the former of i and j.14

The process iterates. The occurrence of the open formula ‘x is positioned between y and z’ in ‘(z)(0x002203x)(0x002203y)(x is positioned between y and z)’ ranges over a universe of truth-values. Its extension is the triple bondage extension with respect to the ordered triple <‘z’, ‘x’, ‘y’>. The general notion of n-fold bondage extension is defined as follows.

Def For n≥0, the n-fold bondage extension of a wfe 0x0003b6with respect to an n-tuple of variables <0x0003b1 1 ,0x0003b1 2 ,. . .,0x0003b1 n >, under a value-assignment s= def the extension under s of an

occurrence of 0x0003b6within the scope of exactly n occurrences of variable-binding-operator phrases, 0x00231c(B 1 0x0003b11 )0x00231d,0x00231c(B 2 0x0003b12 )0x00231d,. . .,0x00231c(B n 0x0003b1n )0x00231d, in that order, and not within the scope of any other occurrence of a nonextensional operator.

Identifying the 0-fold bondage extension with the customary extension, the basic tenet of our theory of bondage may be characterized by the following recursion:

A 0 :  

The 0-fold bondage extension of a well-formed (open or closed) expression 0x0003b6with respect to the 0-tuple <−>, under a value-assignment s, is the customary extension of 0x0003b6under s.

A (n+1) :  

For n≥0, the (n+1)-fold bondage extension of a well-formed (open or closed) expression 0x0003b6with respect to an (n+1)-tuple of variables <0x0003b1 (n + 1) ,. . .,0x0003b1 2 0x0003b11 >, under a value-assignment s, is (0x0003bbi)[the n-fold bondage extension of 0x0003b6with respect to the sub-tuple obtained by deleting 0x0003b1(n + 1) under the value-assignment s′ that assigns i to 0x0003b1(n + 1) and is otherwise the same as s].15

This function may be replaced by its corresponding (n+1)-ary function. In the special case where 0x0003b6is a formula, the latter function maps an appropriate (n+1)-tuple to 0x0003b6's truth-value under the assignment of those objects as the values of the externally bound variables. For most purposes, we may go further and replace this function with the class of ordered (n+1)-tuples that it characterizes. The notions of bondage extension and of double bondage extension, characterized above, fall out as special cases of this recursion.16

There are the makings here of a hierarchy analogous to Frege's hierarchy of indirect senses. Our hierarchy is completely harmless. The (n+1)-fold bondage extension gives back the n-fold bondage extension once the free variables of 0x0003b6have been exhausted.17

Consider a concrete example. Suppose the universe over which the variables ‘x’ and ‘y’ range is the set of people. The occurrence of ‘x loves y’ in ‘(x)(0x002203y)(x loves y)’ ranges over a universe of truth-values. Its extension is the double bondage extension of ‘x loves y’ with respect to <‘x’, ‘y’>. This is the binary function that maps pairs of people to truth if the first person loves the second, and to falsehood otherwise. The extension of the occurrence of ‘(0x002203y)(x loves y)’ in ‘(x)(0x002203y)(x loves y)’ is the bondage extension of ‘(0x002203y)(x loves y)’ with respect to ‘x’: the characteristic function of the class of lovers. The sentence is true iff this class is universal over the set of people. By contrast, the extension of the occurrence of ‘x loves y’ in ‘(y)(0x002203x)(x loves y)’ is the double bondage extension of ‘x loves y’ with respect to <‘y’, ‘x’>. This is the binary function that maps pairs of people to truth if the second person loves the first, and to falsehood otherwise. The extension of the occurrence of ‘(0x002203x)(x loves y)’ in ‘(y)(0x002203x)(x loves y)’ is the bondage extension of ‘(0x002203x)(x loves y)’ with respect to ‘y’: the characteristic function of the class of beloveds. The sentence is true iff this class is universal over the set of people.

One may choose to follow Frege in saying that any expression that has an extension designates the extension. For Frege, this entails that any expression-occurrence that has an extension—whether it is the customary extension or a non-customary extension—is a designator of that extension. Then a bound occurrence of an open expression (such as an individual variable) has its bondage designatum with respect to a variable (on an analogy to Frege's notion of ungerade Bedeutung, or indirect designatum), which is simply the bondage extension. A singly bound variable (the occurrence) would thus designate the identity function on the universe over which the variable (the expression) ranges. In the standard, and most natural, possible-worlds semantics of modality, the range of the individual variables varies from one possible world to the next. (A so-called possibilist, or fixed-universe, modal semantics is an alternative option.) Whereas a free occurrence of ‘x’ is a rigid designator under a value-assignment of its value, a singly bound occurrence of ‘x’ (on a variable-universe modal semantics) would be regarded as designating identity functions on different universes with respect to different possible worlds. The variable ‘x’, which occurs bound in (1), is itself rigid, but its occurrences in (1) (unlike the occurrence of ‘y’), insofar as they are designators, are non-rigid.

If one holds with Frege that an expression designates its extension, one may say that the open formula (1) customarily designates truth under A. As already noted, our original value-assignment A does not satisfy (2); (2) customarily designates falsehood under A. But falsehood is not what (2) designates as it occurs in (1). Like the occurrences of ‘x’ in (1), the occurrence of (2) in (1) is bound, through its occurrence of ‘x’, by the initial quantifier occurrence. It therefore ranges over a universe of truth-values. Under A, the occurrence of (2) in (1) designates (non-rigidly) the characteristic function of the class of MacLaine's siblings. And (1) designates truth under A as long as (and only as long as) this class is non-empty.

III

The foregoing is an outline of a Fregean extensional-semantic theory for both bound and free expression-occurrences. It can be extended into a Fregean theory of sense for bound and free expression-occurrences. To do so in a thoroughgoing Fregean manner, one should follow Church's idea of considering assignments of customary-sense values to variables in lieu of assignments of customary-designatum values.

Russell's intensional-semantic theory avoids this. On a Russellian theory, variables are logically proper names, or directly referential. That is, the semantic content (‘meaning’) of a variable, under an assignment of values to variables, is simply the variable's designatum (the assigned value) rather than a sense. The content of (2) under A is the false singular proposition about MacLaine and Brando, that she is a sister of his. Suppose that the universe over which ‘x’ ranges is the set of people. Then the content of (1) under A is a somewhat different, more general proposition, having just two components. The first component is the propositional function that maps anyone i to the singular proposition that MacLaine is a sister of i. Or it is the concept (or something similar) corresponding to this, that of having MacLaine as sister. The second component is the content of ‘(0x002203x)’.18 The proposition so constituted is the singular proposition about MacLaine that she is a sister of someone or other.

This is a theory of semantic content for expressions, not for expression-occurrences. Russellian intensional semantics violates strong compositionality, according to which the semantic content of a compound expression is not only a function of, but indeed a composite entity whose components are, the semantic contents of the compound expression's meaningful components. The Russellian content of ‘x’—of the variable itself—is, in some natural sense, a component of the Russellian content of (2), but it is no part of the Russellian content of (1), even though ‘x’ itself is as much a component of (1) as it is of (2). Likewise, the Russellian content of (2) is not a component of the Russellian content of (1).

To satisfy extensionality and compositionality, the notion of a component of a compound expression must be understood to be not an expression but an expression-occurrence. So understood, it is not unreasonable to hope to satisfy compositionality, and even strong compositionality. What we seek is a kind of hybrid Frege–Russellian intensional occurrence-based semantics—a Russellian theory of content that conforms to Frege's Context Principle.

Here is an excessively brief sketch. In Frege–Russellian occurrence-based semantics, what we have been calling ‘the content of ‘x’ ’ under a value-assignment is the customary content of ‘x’, i.e., the content of its free occurrences (not within quotation marks or the like). Bound variables have their bondage semantics. Suppose again that the universe over which the variables ‘x’ and ‘y’ range is the set of people.

The customary content of the open formula ‘x loves y’ under an assignment of values to variables is a singular proposition about the values of ‘x’ and ‘y’. This proposition is the content of free occurrences of ‘x loves y’, not of bound occurrences. The occurrence of ‘x loves y’ in ‘(y)(0x002203x)(x loves y)’ is in bondage, ranging over a universe of singular propositions. Its content, under an assignment s of values to variables, is the double bondage content of ‘x loves y’ with respect to <‘y’, ‘x’> under s. This is the function that maps a pair of people, i and j, to the customary content of ‘x loves y’ under the doubly modified value-assignment sxjyi that assigns j as value for ‘x’ and i as value for ‘y’, and is otherwise the same as s—i.e., the binary Russellian propositional function (0x0003bbij)[the singular proposition that j loves i]. More accurately, the content of the occurrence of ‘x loves y’ in ‘(y)(0x002203x)(x loves y)’ is the binary-relational concept, being loved by, that corresponds to the double bondage content.

The content of the occurrence of ‘(0x002203x)(x loves y)’ in ‘(y)(0x002203x)(x loves y)’ is the bondage content of ‘(0x002203x)(x loves y)’ with respect to ‘y’. This is the propositional function (0x0003bbi)[the singular proposition that someone or other loves i]. Or rather, the content of the occurrence of ‘(0x002203x)(x loves y)’ in ‘(y)(0x002203x)(x loves y)’ is the concept corresponding to this propositional function: that of being loved by someone or other. This concept is composed of the content of the occurrence of ‘x loves y’ and the customary content of ‘(0x002203x)’, the latter being the second-order concept, someone or other. The customary content of ‘(y)(0x002203x)(x loves y)’ is the proposition composed of the content of the occurrence of ‘(0x002203x)(x loves y)’ and the customary content of ‘(y)’: that everyone is loved.

Similarly, the singular proposition that we have been calling ‘the content of (2)’ under a value-assignment is the customary content of (2), i.e., the content of its free occurrences, not of its bound occurrences. The occurrence of (2) in (1) is in bondage, ranging over the universe of singular propositions of the form, Maclaine is a sister of i, (i.e., the class of propositions p such that for someone i,p=the singular proposition about MacLaine and i, that she is a sister of i.) The content under A of the occurrence of (2) in (1) is (0x0003bbi)[the customary content of (2) under the modified value-assignment Ax i ]. This is the Russellian propositional function that maps i to the singular proposition that MacLaine is a sister of i. Or rather, the content under A of the occurrence of (2) in (1) is the concept corresponding to this propositional function, that of having MacLaine as sister.

Russellian occurrence-based semantics obtains as customary content for (1) under A the same proposition that Russell's expression-based semantics obtains as (1)’s content (simpliciter) under A. Unlike the latter, occurrence-based semantics does this by composition, generating a proposition by combining the semantic contents of the sentence's meaningful components—not the component expressions but the component occurrences.

IV

Unlike classical Russell–Tarski expression-based semantics, the Frege–Russell occurrence-based semantics sketched above evidently conforms to Frege's Context

Principle and to (modestly restricted) principles of extensionality, compositionality, and even strong compositionality.19 I should nevertheless strongly advise classical semantics to continue disregarding the Context Principle. This is not because I think it incorrect to attribute semantic values to expression-occurrences. The two approaches, though different, are not intrinsically in conflict. Contrary to the Context Principle, semantics may be done either way. Semantics may even be done both ways simultaneously, assigning semantic values both to expressions and to their occurrences within formulae or other expressions, and without prejudice concerning which is derivative from which. Frege's occurrence-based semantics in fact assigns semantic values both to expressions and their occurrences, even while honoring his Context Principle. His notions of customary designatum, indirect sense, doubly indirect designatum, and the like, are semantic values of the expression itself. The customary designatum is the designatum of the expression's occurrences in ‘customary’ settings, i.e., its occurrences that are in extensional position and not within the scope of a variable-binding operator. (See note 15 .) And despite its pedigree, the Context Principle is not sacrosanct. Translating the term ‘extension’ of conventional expression-based semantics into ‘customary extension’, and so on for the other semantic terms (‘designate’, ‘content’, and so forth), occurrence-based semantics emerges as a conservative extension of conventional expression-based semantics. Occurrence-based semantics may be unorthodox and unconventional, but it is only somewhat unorthodox and only somewhat unconventional. As mentioned, expression-based semantics is its less discriminating by-product.

The principal reason I nevertheless advocate expression-based semantics over occurrence-based semantics is that the latter inevitably invites serious confusion. It led Frege to his view that each meaningful expression has not only a sense, but an indirect sense, and also a doubly indirect sense, and indeed an entire infinite hierarchy of indirect senses.20 Occurrence-based semantics has also led to the miscataloging

of various terms. In particular, it has led to the misclassification of various non-compound singular terms as non-rigid, and of various compound terms (for example, complex demonstratives and ‘that’-clauses in attributions of belief) as restricted quantifiers (often mislabeled generalized quantifiers). Though not Frege's, these errors have been committed by followers in Frege's footsteps, reinforcing a current quantifiermania. The misclassifications, and other confusions like them, come about when a philosopher of language fails to distinguish sharply between an expression and its occurrences.21

I shall first take up the misclassification of compound terms. This arises when a language philosopher erroneously imputes an open expression's customary semantics to the expression's occurrences in a sentence. I have in mind the recent rash of arguments to the effect that compound terms of a certain grammatical category (for example, ‘that’-clauses), because they can be quantified into (‘Every boy believes that his dad is tougher than every other boys' dad’), cannot be singular terms, or cannot be directly referential singular terms, and should be regarded instead as restricted quantifiers.

The general form of the argument originates with Benson Mates, who employed it as an objection to the Fregean (and Strawsonian/anti-Russellian) thesis that definite descriptions are compound singular terms, and that a definite description designates the individual that answers to the description if there is a unique such individual and

designates nothing otherwise, yielding a sentence with no truth-value.22 Although initially plausible, the Fregean thesis apparently falters when a definite description is quantified into, as in:

(3)  

Every [some/at least one/more than one/exactly one/not one] male soldier overseas misses the only woman waiting for him back home.

If the definite description ‘the only woman waiting for him back home’ were a singular term, then (3) should not be true—indeed, on the Frege–Strawson theory, it should be neither true nor false—if the description has no designatum. But (3) could well be true, Mates argues, even though one cannot assign a designatum to the open definite description ‘the only woman waiting for him back home’ as occurring in (3), any more ‘than one can assign a truth-value to “it is less than 9” as occurring in “If a number is less than 7, then it is less than 9”.’23

Let us take a close look at the objection. As Mates notes, the definite description ‘the only woman waiting for him back home’ occurring in (3) is open. The pronoun ‘him’ occurring in the description corresponds to a variable bound by an external quantifier. The pronoun may be assigned any one of various soldiers as designatum. If the phrase ‘the only woman waiting for him back home’ is indeed a singular term, it designates different women under different such assignments. What about the occurrence of the description in (3)? Our theory of bondage demonstrates that Mates overstates the case when he says that one cannot assign anything to the occurrence as its designatum. The occurrence has its bondage extension with respect to ‘him’, and may be regarded as designating the function that assigns to any male the only woman waiting for him back home, if he left exactly one woman waiting for him back home, and assigns nothing otherwise. This much may be said, though: The occurrence of the description in (3) does not designate any particular woman who answers to the description.

Now suppose (3) is true. How does it follow that the description occurring in (3) is not a singular term?

It does not—not without the aid of some additional semantic machinery. What does follow is that if definite descriptions are singular terms, the occurrence of the description in (3) does not designate the description's customary designatum under any particular designatum assignment. But no one ever said that it did. The Fregean thesis is that definite descriptions—the expressions themselves—are singular terms. If one is not careful to distinguish between an expression and its occurrences, one might misconstrue this as the thesis that every occurrence of a definite description designates the object that answers to the description. (Recall the Cautionary Note in Section I.) But it is well known that Frege, with his doctrine of indirect designation, rejected the latter thesis. For (3) to be true, every male soldier overseas must miss the woman who is value of the function designated by the occurrence of the definite description when that soldier is assigned as argument. As long as the function is defined for every male soldier overseas, this presents no particular problem.

To bridge the gap between the current sub-conclusion and the Fregean thesis in Mates's crosshairs, the objection tacitly invokes the following semantic theorem:

M: Any sentence 0x0003d50x0003b2[of a restricted class C], containing an occurrence of a genuine singular term 0x0003b2not within the scope of an indirect, intensional, or quotational operator, is true [either true or false] only if that same occurrence of 0x0003b2designates the customary designatum of 0x0003b2.24

Assuming Mates does not misconstrue the Fregean/Strawsonian thesis, his objection assumes (M) (or something very much like it) as its major premiss, or assumes that his Fregean opponent is committed to it. As we have noted, if the description ‘the only woman waiting for him back home’ is a genuine singular term, its occurrence in (3)—since an external quantifier-occurrence quantifies into it—does not designate the description's customary designatum under a particular designatum-assignment. Yet (3) may be true. Given (M), it directly follows that the description is not a genuine singular term.

The argument is fallacious. Other versions of Mates's objection are equally fallacious. Those other versions make, or require, semantic assumptions analogous, or otherwise very similar, to (M).25 What the proponents of the style of argument generally fail to recognize is that, insofar as there are semantic theorems like (M) concerning singular terms, there are analogous semantic theorems concerning quantifiers,26 as well as other sorts of expressions that have semantic extension.

This makes for the possibility of an exactly analogous argument for the conclusion that quantifiers also cannot be quantified into, and therefore definite descriptions (or ‘that’-clauses, and so forth.) are not quantifiers either, or anything else for that matter. Something has gone very wrong. Restricted quantifiers can be bound by other quantifiers—as, for example, in ‘Every male soldier overseas misses some woman waiting for him back home.’ For that matter, so can singular terms—witness the case of the individual variable. Somewhere a fatal error has been committed.

In every application of which I am aware, the assumed semantic ‘theorem’ is in fact false and the proponents of the target thesis (e.g., that definite descriptions or ‘that’-clauses are singular terms) do not endorse it. If (M) were sound, it would establish more generally that the very notion of an occurrence of an open singular term bound (‘quantified into’) by an external quantifier is semantically incoherent. Despite the objection's popularity, ordinary mathematical notation is rife with counter-examples to its major premise—for example the ‘x2’ in ‘(0x002203x)(x2=9)’. The most glaring counter-example is the paradigm of an open designator: the individual variable. To use Mates's own example, if the occurrences of ‘y’ in the true sentence ‘(y)(y<70x002283y<9)’ (let this be 0x0003d50x0003b2, with 0x0003b2= ‘y’) designate anything, they designate not the customary designatum of ‘y’ under a particular value-assignment, but the bondage extension with respect to ‘y’ itself: the identity function on the range of ‘y’. Yet the variable ‘y’ is a genuine singular term if anything is.27 (See the appendix.)

The mistake directly results from imputing the semantic attributes of an expression to its occurrences, including even bound occurrences. The mistaken ‘theorem’ can be corrected, and even generalized:

M′: An assignment s of values to variables satisfies a formula 0x0003d50x0003b2, of the restricted class C, containing a free occurrence of a singular term 0x0003b2not within the scope of any nonextensional operator (other than classical variable-binding operators), only if that same occurrence of 0x0003b2designates the customary designatum of 0x0003b2under s.

This corrected version effectively blocks the objection.28 Fregean theory may also countenance a second variation of (M):

M″: Any sentence 0x0003d50x0003b2[of a restricted class C], containing an occurrence of a genuine singular term 0x0003b2not within the scope of any nonextensional operator (other than classical variable-binding operators), is either true or false only if that same occurrence of 0x0003b2designates.

As mentioned earlier, according to the occurrence-based semantics sketched above, the occurrence of the open definite description in (3) designates a particular partial function.

It is a trivial matter to extend the theory of bondage from Section II above to include definite descriptions as singular terms, which, if open, can be quantified into. A definite description 0x00231c(0x0003b90x0003b1)0x0003d5 0x0003b10x00231dcustomarily designates under a value-assignment s the unique object i that is an element of the class characterized by the extension of its occurrence of 0x0003d50x0003b1, if there is a unique such i, and customarily designates nothing under s otherwise. A free occurrence of a definite description in extensional position designates the description's customary designatum. The extension of a bound occurrence in otherwise extensional position is then the appropriate bondage extension.29 One may consistently add the corrected Mates theorem (M′) into the mix. On this theory of bondage, quantification into singular terms is not only permitted, it is encouraged.

Saul Kripke has sermonized, ‘It is important, in discussion of logico-philosophical issues, not to lose sight of basic, elementary distinctions by covering them up with either genuine or apparent technical sophistication.’30 The distinction between an expression and its occurrences is elementary and fundamental. The Fregean/Strawsonian thesis that Mates aims to refute is that definite descriptions are singular terms. It is no part of the Fregean thesis that every occurrence—even a bound occurrence—of a definite description in otherwise extensional position in a sentence designates the description's customary designatum. The latter thesis is neither Frege's nor Strawson's; it is Strawman's.

There remain significant differences between the Fregean theory sketched above and the Russellian theory that Mates and company prefer. If every male soldier overseas left exactly one woman waiting for him back home, and he does indeed miss her, then contrary to Mates, Frege's theory, no less than Russell's, deems (3) true. If every male soldier overseas left exactly one woman waiting for him back home, but at least one male soldier overseas does not miss the woman he left behind, then both Frege and Russell deem (3) false. But suppose at least one male soldier overseas left no woman, or two women, waiting for him back home. On Russell's theory, (3) is false in this third case as well as the second. On Frege's theory it is not, although it is not true either. This verdict is a straightforward result of (M′) together with the theory's other semantic principles. The third case, not the first, is the deciding case. To this day, it remains unclear whether the falsity verdicts of Russell's theory, or those of Frege's, are the correct ones.

V

Besides the misclassification of various compound terms, there has also occurred a miscataloging of certain directly referential singular terms as non-rigid definite descriptions, again partly as a result of a failure to distinguish sharply between the term and its occurrence. Here the confusion is traceable to a larger confusion, between an entire sentence and its occurrence in a discourse. Consider the following discourse fragment:

(4)  

(i) A comedian composed the musical score for City Lights. (ii) He was multi-talented.

The particular sentence (4ii) is ordinarily regarded as an open formula with a free variable, ‘he’. As Geach has noted, the pronoun evidently functions differently as it occurs in (4). Geach takes the pronoun-occurrence to be a variable-occurrence bound by a prenex occurrence of the restricted existential quantifier ‘a comedian’, as in the following:

(4G)  

[a x: comedian(x)] (x composed the musical score for City Lights & x was multi-talented).31

Gareth Evans mounted solid evidence against Geach that the scope of ‘a comedian’ in (4) does not extend beyond (4i), and so the phrase does not bind the ‘he’ in (4ii)—this despite the fact that the ‘he’ is anaphoric upon the phrase ‘a comedian’.32 Following Evans, an anaphoric pronoun-occurrence whose grammatical antecedent is a quantifier-occurrence within whose scope that pronoun-occurrence does not stand is often called an E-type pronoun (alternatively a donkey pronoun, because of particular examples originally due to Walter Burley).33 The ‘he’ in (4) appears to be a free occurrence of a closed singular term rather than a bound variable. E-type pronoun-occurrences, according to Evans, are ‘assigned a reference and their immediate sentential contexts can be evaluated independently for truth and falsehood’. Evans takes the ‘he’ in (4) to be a rigid singular term whose reference is fixed by the

description ‘the only comedian who composed the musical score for City Lights’. He thus represents (4) as having the following logical form:

(4E) (i)  

[a x: comedian(x)] (x composed the musical score for City Lights).

(ii)  

dthat[ [the y: comedian(y)] (y composed the musical score for City Lights) ] was multi-talented.

The bracketed expression in the first sentence is a restricted existential quantifier phrase, which may be read ‘a comedian x is such that’. The innermost bracketed expression in the second sentence may be read ‘the only comedian y such that’. The full ‘dthat’-term—which might be read ‘that comedian who composed the musical score for City Lights’ (a closed expression)—is alleged to be the formal counterpart of the ‘he’ in (4ii).

Michael McKinsey, Scott Soames, Stephen Neale, and others argue that the ‘he’, as it occurs in (4), is not merely co-designative, but synonymous in content, with ‘the only comedian who composed the musical score for City Lights’. For although the ‘he’ in (4) designates Charlie Chaplin with respect to the actual world, (4) may also be evaluated with respect to other possible worlds. Consider a possible world W in which, say, Buster Keaton composed the musical score for Chaplin's classic silent film. The discourse fragment (4) is true with respect to W iff Keaton is a multi-talented comedian in W, never mind Chaplin.34 With respect to W, it is argued, the ‘he’ in (4) designates Keaton instead of Chaplin, just as the description does. The entire discourse fragment is thus depicted as having the following logical form, in contrast to (4E):

(4M) (i)  

[a x: comedian(x)] (x composed the musical score for City Lights).

(ii)  

[the y: comedian(y)] (y composed the musical score for City Lights) was multi-talented.

The full definite description in (4Mii) is alleged to be the formal counterpart of the ‘he’ in (4).35

The argument is mistaken. That the pronoun ‘he’ (the expression) is rigid is confirmed by positioning it in the scope of a modal operator-occurrence:

A comedian composed the musical score for City Lights. That he was multi-talented is a contingent truth.

The second sentence here does not impute contingency to the fact that whichever comedian composed the music for City Lights was multi-talented. (something about chaplin himself: If it did, it would presumably be false.) Instead it expresses that, although in fact multi-talented, he might not have been.36

This does not mean that Evans was right and Geach wrong. The pronoun-occurrence in (4) is more plausibly regarded as a variable-occurrence bound by a restricted quantifier implicit in (4ii), perhaps ‘a comedian who composed the musical score for City Lights’. The entire discourse fragment is plausibly regarded as having an underlying logical form more like the following, where items in boldface correspond to explicit elements in the surface form (4):

(4′) (i) [a x: comedian(x)] (x composed the musical score for City Lights).

(ii) [a y: comedian(y); y composed the musical score for City Lights] (y was multi-talented).

The open formula ‘y was multi-talented’ occurring in (4′ii) makes an explicit appearance in the surface form, as (4ii). The rest of (4′ii) does not. On this analysis, an E-type pronoun-occurrence is a species of bound-variable occurrence, as Geach has long maintained. In fact, the conjunction corresponding to (4′) is equivalent to (4G) (and to the second conjunct (4′ii) alone). Contrary to Geach, however, the anaphora between an E-type pronoun and its antecedent is not the same relation as that between a bound variable and its binding operator. Instead the E-type pronoun is bound by an absent operator recoverable from the antecedent.

One important advantage of this analysis over both (4E) and (4M) is that the mere grammar of (4) does not support an inference to a uniqueness claim of the sort presupposed or otherwise entailed by the use of ‘the only comedian that scored the music for City Lights’. Though this may not be obvious with (4) (since, typically, if someone scored the musical score for a particular film, then no one else did), it is with the following discourse:

A comedian panned the musical score for City Lights. He was jealous. Another comedian also panned the musical score for City Lights. He wasn't jealous; he was tone-deaf.

Another important difference is that there is no definite description in (4′) to be regarded as a formal counterpart of the ‘he’ in (4). There is no non-rigid designation of Chaplin in (4′). There is no designation at all of Chaplin in (4′), except by the variables ‘x’ and ‘y’ under appropriate value-assignments. The rigidity of ‘he’ suggests that its formal counterpart in (4′) is simply the last occurrence of ‘y’.37


Recall again the cautionary note of Section I. It is extremely important here to distinguish sharply between the English sentence (4ii) and its occurrence in the discourse-fragment (4). The former is the natural-language analog of an open formula. That is the sentence itself—an expression—whose logical form is given, nearly enough, by ‘y was multi-talented’. The occurrence of (4ii) in (4) is a horse of a different color. Here the surface form of an occurrence is not a reliable guide to the logical form. The occurrence of (4ii) in (4) corresponds not merely to ‘y was multi-talented’ but to the whole of (4′ii), in which a restricted quantifier binds the open formula. Though superficially an occurrence of an open formula, the underlying logical form is that of a closed sentence, which ‘can be evaluated independently for truth and falsehood’. In effect, the second sentence-occurrence in (4), though syntactically an occurrence of (4ii), is semantically an occurrence of (4′ii). One could say that the sentence (4ii) itself is bound in (4), though not by any element of (4i)—indeed, not by any element of the surface form of (4). One might even say that the occurrence of (4ii) in (4) is a pro-clause of laziness; although syntactically an occurrence of (4ii), it has the logical form of the whole consisting of (4ii) together with a binding quantifier phrase. The quantifier phrase itself, though invisible, is present behind the scenes.38


 If the occurrence of ‘y was multi-talented’ in (4′ii) is to be regarded as having an extension, it has the open formula's bondage extension: the function that maps individuals in the range of ‘y’ who were multi-talented to truth and maps those who were not to falsehood. The whole of (4′ii)—and hence the occurrence of (4ii) in (4)—is true iff the class characterized by this function includes a comedian who composed the musical score for City Lights. As was noted, the occurrence of (4ii) in (4) is thus true with respect to the possible world W iff Keaton was multi-talented in W.

The very fact that the occurrence of (4ii) in (4) has these modal truth-conditions despite the rigidity of ‘he’ indicates that, contrary to Evans and several of his critics, the ‘he’ in (4) is not a closed-term occurrence but a bound variable. One can say with some justification that the ‘he’ in (4)—the occurrence—is a non-rigid designator. But this is not because the occurrence designates Chaplin with respect to one possible world and Keaton with respect to another. It does neither. Where it occurs free—as for example in a deictic use (and not as a pronoun of laziness)—‘he’ is a rigid designator of its customary extension under a designatum-assignment. If the pronoun-occurrence in (4) is to be regarded as designating at all, it designates the pronoun's bondage extension: the identity function on the range of ‘he’. Insofar as the occurrence is non-rigid, it is so only because it has its bondage extension, ranging over different universes with respect to different possible worlds.

Appendix

Jeffrey King, as cited in note 22 above, applies a version of Mates's objection against the thesis that demonstratives are directly referential singular terms. Quantification into a complex demonstrative is odd at best. Although King assumes it is permissible, almost all his examples involve, or appear to involve, a stylistically altered definite description rather than a genuine demonstrative, e.g., ‘Every professor cherishes that first publication of his.’ (Compare with (3).) Where the phrase ‘that first publication of his’ occurs as a genuine demonstrative, it should be possible to delete the word ‘first’ by pointing to the publication in question. But this is problematic with King's example.

The issue is significant, but set it aside. King explicitly aims to establish the conclusion that at least some complex demonstratives (the expressions) are not singular

terms at all, let alone directly referential singular terms. His argument employs the following tacit premise: (K1) Any sentence 0x0003d50x0003b2containing a directly referential occurrence of singular term 0x0003b2not within the scope of an indirect, intensional, or quotational operator expresses as its semantic content a singular proposition in which the designatum of that same occurrence of 0x0003b2occurs as a component. The conclusion King derives using this premise is that bound occurrences of complex demonstratives are not directly referential occurrences, that is the occurrence's semantic content is not the expression's customary designatum. Although King evidently believes this refutes the target thesis, strictly speaking the target thesis is perfectly compatible with this conclusion—just as Mates's sub-conclusion before invoking (M) is compatible with the Fregean thesis that definite descriptions are singular terms. An additional premiss is required to validate King's argument against the target thesis: (K2) If a singular term 0x0003b2is directly referential, then every occurrence in a sentence of 0x0003b2not within the scope of an indirect, intensional, or quotational operator is a directly referential occurrence.

King has confirmed in correspondence that he accepts (K2) as well as (K1). He adds that he believes both are partly stipulative, by virtue of the meaning of ‘directly referential’. (He also adds that (K2), because it concerns expressions as well as expression-occurrences, is likely to confuse.) Taken together, (K1) and (K2) yield the direct-reference analogue of Mates's semantic theorem: (K) Any sentence 0x0003d50x0003b2containing an occurrence of a directly referential singular term 0x0003b2not within the scope of an indirect, intensional, or quotational operator expresses as its semantic content a singular proposition in which the designatum of that same occurrence of 0x0003b2occurs as a component. This theorem may be taken as premise in place of (K1) and (K2).

Jason Stanley has confirmed in correspondence that in his review he interprets King's objection as tacitly invoking (K) as a stipulative premiss—or alternatively, (K1) and (K2). Stanley, ibid., maintains that whereas Mates's original argument and others like it fail—essentially on the same grounds argued in the text above—King's variant of Mates's argument is nevertheless decisive against the thesis that demonstratives are directly referential singular terms. Stanley's position is based on his contention that an intensional semantics of content (as opposed to classical, extensional semantics in the style of Tarski) does not relativize content to assignments of values to variables. Contrary to Stanley, however, wherever there is variable binding, the natural method of systematically assigning contents involves doing so under value-assignments. Church's ‘The Need for Abstract Entities in Semantic Analysis’ and the Russellian intensional semantics sketched in Section III above both do so explicitly.39 Mates's argument cannot be made to succeed simply by choosing to speak of the semantic content of a definite description occurrence and the individual of which that content is a concept, rather than speaking of the occurrence designating the individual.

Contrary to both King and Stanley, (K) is not an analytic or stipulative truth. In fact, it has extremely dubious consequences, for example that variables are not directly referential—assuming that a bound variable, since its semantic content is not

the variable's customary designatum, is not a ‘directly referential occurrence’. (This is how both King and Stanley understand the phrase.) More specifically, both (K2) and (K) are evidently falsified by the same paradigm-case as (M): bound variables. Furthermore, proponents of the direct-reference theory, though they may accept (K1), do not endorse either (K2) or (K)—again, witness the case of bound variables. Contrary to Stanley, King's argument and Mates's original argument thus evidently fail for the same general reason.40

Stanley responds that both (K2) and (K) are true despite bound variables because the lower-case letter ‘x’ (qua variable) ambiguously represents two distinct expressions: ‘x’-bound and ‘x’-free. (He maintains that this alleged ambiguity is a corollary of (K).) The bondage extension of a variable is indeed distinct from its customary extension, and one might choose to express this (I believe misleadingly) by saying that the variable is ambiguous, having a bondage reading distinct from its customary or default reading. (It is incorrect to express this by saying that a bound occurrence and a free occurrence of ‘x’ are occurrences of different expressions.) Expressing the point in terms of an ‘ambiguity’ between customary and bondage readings, however, is ineffective as a defense of King's objection. The bondage semantics of any open expression deviates from the customary semantics, for example, ‘the only woman waiting for him’, ‘his first publication’, and so forth. Insofar as open expressions are deemed ipso facto ambiguous, the thesis that King's argument aims to refute is that demonstratives on their customary readings are directly referential singular terms. The alleged bondage reading is irrelevant.

Part II Apriority

7 How to Measure the Standard Meter (1987)*

Nathan Salmon

I

There is one thing of which one can say neither that it is one meter long, nor that it is not one meter long, and that is the Standard Meter in Paris.—But this is, of course, not to ascribe any extraordinary property to it, but only to mark its peculiar role in the language-game of measuring with a meter-rule.

So says Wittgenstein (Philosophical Investigations §50). Kripke sharply disagrees:

This seems a very ‘extraordinary property’, actually, for any stick to have. I think [Wittgenstein] must be wrong. If the stick is a stick, for example, 39.37 inches long (I assume we have some different standard for inches), why isn't it one meter long? (Naming and Necessity, Harvard University Press and Basil Blackwell, 1972, 1980, at p. 54).

Kripke goes on to argue that it not only would be correct to say of the Standard Meter that it is exactly one meter long, but the very fact about the Standard Meter that it is exactly one meter long, although it is only a contingent fact, is in some sense knowable a priori:1

We could make the definition more precise by stipulating that one meter is to be the length of S at a fixed time t 0 . . . . [A] man who uses the stated definition [is] using this definition not to give the meaning of what he called ‘the meter’, but to fix the reference. . . . There is a certain length which he wants to mark out. He marks it out by an accidental property, namely that there is a stick of that length. Someone else might mark out the same reference by another accidental property. . . . Even if this is the only standard of length that he uses, there is an intuitive difference between the phrase ‘one meter’ and the phrase ‘the length of S at t 0. The first phrase is meant to designate rigidly a certain length in all possible worlds, which in the actual world happens to be the length of stick S at t 0 . On the other hand, ‘the length of stick S at t 0 does not designate anything rigidly. . . . [T]he ‘definition’, properly interpreted, does not say that the phrase ‘one meter’ is to be synonymous (even when talking about counterfactual situations) with the phrase ‘the length of S at t 0 but rather that we have determined the reference of the phrase ‘one meter’ by stipulating that ‘one meter’ is to be a rigid designator of the length which is in fact the length of S at t 0 . So this does not make it a necessary truth that S is one meter long at t 0 . . . .

What, then, is the epistemological status of the statement ‘Stick S is one meter long at t 0 for someone who has fixed the metric system by reference to stick S? It would seem that he knows it a priori. For if he used stick S to fix the reference of the term ‘one meter’, then as a result of this kind of ‘definition’ (which is not an abbreviative or synonymous definition), he knows automatically, without further investigation, that S is one meter long. On the other hand, even if S is used as the standard of a meter, the metaphysical status of ‘S is one meter long’ will be that of a contingent statement, provided that ‘one meter’ is regarded as a rigid designator: under appropriate stresses and strains, heatings or coolings, S would have had a length other than one meter even at t 0 . . . . So in this sense, there are contingent a priori truths. (ibid., pp. 54–56.)

. . . The case of fixing the reference of ‘one meter’ is a very clear example in which someone, just because he fixes the reference in this way, can in some sense know a priori that the length of this stick is a meter without regarding it as a necessary truth. (ibid., p. 63)2

Wittgenstein's claim that the sentence in question is unassertable because of the Standard Meter's ‘peculiar role in the language-game’ goes much further than the doctrine held by the empiricists that such definitions are devoid of proper cognitive, extra-linguistic factual content. By contrast with Wittgenstein, the empiricists argued that the sentence does indeed express a priori knowledge, but only because it does not express a matter of fact and instead expresses a relation of ideas (or a linguistic convention devoid of cognitive, factual content, etc.). Kripke's claim that the meter sentence is contingent a priori is significant, in part, because it contradicts this empiricist tradition. If Kripke is correct, the meter sentence expresses a matter of contingent fact. My chief concern in this paper, however, is not with the relation of either Wittgenstein's or Kripke's views to the doctrine of empiricism (vexing issues in themselves), but more directly with the apparent divergence between Kripke and Wittgenstein over the question of the assertability and epistemic justification of the meter sentence.

Either Wittgenstein is wrong or Kripke is wrong. For surely if one who defines ‘meter’ as the length of the standard S at t 0 can thereby know a priori that S is exactly one meter long at t 0 , as Kripke claims, then pace Wittgenstein, one can correctly say of the standard that it is indeed one meter long at t 0 . This follows from the trivial fact that knowledge entails truth and truth entails (is?) assertability. Who is right and who is wrong?

It must be admitted that Kripke has more plausibility on his side than Wittgenstein does. Still, my answer is that Kripke and Wittgenstein are probably both wrong to some extent. To the extent that Wittgenstein is wrong, some of what Kripke says

is right. More interestingly, the extent to which Kripke is right suggests that in some sense, a significant part of what Wittgenstein says may also be right. Frankly, I suspect Wittgenstein is ultimately completely wrong regarding the Standard Meter. Nevertheless, some of what I shall say here provides a measure of support (of some sort) for Wittgenstein's paradoxical observations concerning the Standard Meter. Specifically, I shall propose an epistemic paradox that might, to some extent, vindicate Wittgenstein's enigmatic remark. I make no claim, however, to be faithfully capturing Wittgenstein's intent. In the passage from which Wittgenstein's remark was extracted, he is discussing issues concerning our use of language as a means of representation, and is not explicitly concerned with the epistemological issues I will enter into here.

II

I argued in Frege's Puzzle3 that the disputed meter sentence is (apparently contrary to Wittgenstein) true, but (apparently contrary to Kripke) contingent a posteriori rather than contingent a priori. In judging the sentence contingent, I followed Kripke in gainsaying the traditional empiricist claim that such definitional sentences do not express matters of extra-linguistic fact, but I went further than Kripke by rejecting even the less controversial (not to say uncontroversial) doctrine that such sentences express a priori knowledge.4

I shall not rehearse the full argument for aposteriority. Instead, I shall merely sketch the main premisses, and leave their defence as a homework exercise for the reader. (Warning: This exercise should not be attempted by the squeamish.) For this purpose let us call the length at t 0 of S (that is, the length one meter or 39.3701 inches), ‘Leonard’. Leonard is an abstract quality, a species of the generic Lockean primary quality length. We assume that the measurement-term ‘meter’ is introduced in such a way that a phrase of the form 0x0023080x0003b1meters0x002309, where 0x0003b1is a term referring to some number n, is itself a singular term referring to the length that is exactly n times as great as Leonard.5 We assume further that the sentence ‘The length at t 0 of S, if S exists, is one meter’ has as its cognitive information content a Russellian singular proposition (David Kaplan) in which Leonard occurs directly as a constituent.6 (This move in the argument presupposes a highly controversial theory of the nature of propositions, but Kripke is not prepared to reject it.) Let us call this singular proposition ‘Peter’. For simplicity, we may assume that Peter has only two constituents: Leonard and the complex property of being the length of S at t 0 if S exists. (The fact that Peter actually has a somewhat more complex structure does not matter a great deal to the argument.) Peter is true in all and only those possible worlds in which the very stick S either does not exist at all, or does exist and has at t 0 the very length Leonard. To assert, believe, or know Peter is to assert, believe, or know of the length Leonard that if S exists, it is precisely that long at t 0 . Therefore, the reference-fixer knows Peter, which is the cognitive content of the meter sentence, a priori only if he knows of Leonard without appeal to experience (beyond the experience needed merely to apprehend the proposition) that if S exists, it is precisely that long at t 0 . That is, the reference-fixer knows the content of the meter sentence a priori only if he knows of Leonard that S, if it exists, is precisely that long at t 0 , without his belief that this is so being justified by means of experience. Yet it would seem that no matter what stipulations one makes, one cannot know without resorting to experience such things as that S, if it exists, has precisely such-and-such particular length at t 0 . It would seem that one must at least look at S’s length, or be told that it is precisely that long, etc. Therefore, it would seem that the meter sentence is not a priori but a posteriori.7

Notice that someone who has heard of the stick S but has not yet seen it could still introduce the term ‘meter’ by means of the description ‘the length of S at t 0.8 If

the reference-fixer in this case has a wildly mistaken impression as to S's actual length (and so uses the description referentially, in Donnellan's sense, to refer to a very different length), or has no opinion whatsoever regarding S's length (and so uses the description attributively), it would clearly be incorrect to describe him or her as knowing a priori of Leonard that S, if it exists, is exactly that long at t 0 . It is only after the reference-fixer sees S's length for himself (or is told it, etc.) that the proposition Peter becomes a piece of knowledge. In his description of the reference-fixing situation, Kripke had in mind a case in which the reference-fixer sees S there in front of him and uses the description referentially to refer to that length.9 In such a case, it is correct to say that the reference-fixer knows Peter, but, it would seem, only because he has had the experience needed to acquire this knowledge.

The reference-fixer can know without looking at (or being told, etc.) S's length that the length at t 0 of S, if it exists, is the length he means (in his present idiolect, as determined by his own overriding intentions) by ‘one meter’. Perhaps this even qualifies as genuine a priori knowledge; it depends on whether one's knowledge of one's own intentions is ultimately justified by appeal to experience. For the sake of argument, let us agree that it is a priori. The reference-fixer could infer from this that the length at t 0 of S, if it exists, is one meter (and thereby know of Leonard that S, if it exists, is precisely that long at t 0 ) if only he knew of Leonard that the phrase ‘one meter’ refers to it (in his present idiolect, if S exists). But this is precisely what the reference-fixer apparently cannot know, without having an appropriate experience in which S plays a significant role. Pending this additional experience, all that the reference-fixer knows is the general proposition that the phrase ‘one meter’ refers (in his present idiolect) to whatever length S has at t 0 , if S exists (and is non-referring otherwise).10 In fact, the natural order of things is just the reverse: the reference-fixer


would ordinarily rely on additional experience to discover first that S has Leonard as its length at t 0 , and then infer that ‘one meter’ refers to Leonard. Both pieces of knowledge are apparently a posteriori.

If the claim that the meter sentence is a priori is to be maintained in the face of these considerations, its defence must come from fastening onto an important epistemic distinction: the distinction between experience that plays a peculiar role in the epistemic justification of a belief (which is relevant to the question of whether the knowledge is a priori or a posteriori), and experience that merely serves to place the believer in a position to apprehend the proposition in the first place (by giving him or her the requisite concepts, for example), and does not play the relevant role in the epistemic justification of the belief. Thus, for example, the fact that one must have some experience in order to acquire the concept of a bicycle, and so to apprehend the proposition that all bicycles are bicycles, does not alter the fact that the proposition is known a priori. One might maintain that the reference-fixer's visual experience of S in the introduction of ‘meter’ likewise enables the reference-fixer to apprehend Peter but plays no further role in justifying that belief.

The case for apriority along these lines, however, is far from clear. The reference-fixer's visual experience of S can play an important role in enabling him to apprehend propositions directly concerning S, but it does play a crucial role in justifying his belief of Peter. Suppose the reference-fixer has got himself into a position of being

able to apprehend propositions directly concerning Leonard somehow other than by looking at S and conceiving of Leonard as the length of S. He comes into the situation of the introduction of ‘meter’ already grasping the generic concept of length. Suppose that he conceives of Leonard as ‘this length here’, pointing to some object other than S yet having the very same length. Even if the reference-fixer came to believe of Leonard (so conceived) that S, if it exists, is also exactly that long at t 0 , but did so somehow solely through contemplation and reflection on his concepts without experiential justification (i.e., not by estimating S's length from its appearance etc.), he still could not properly be said to know this of Leonard. At best, it seems more like extremely lucky guesswork. It is only by seeing S and its length that the reference-fixer comes to know that S (if it exists) is just that long.

Whereas the reference-fixer's visual experience of S certainly plays a crucial role in the justification of his belief of Peter, it is arguable that the experience need not play the sort of role that would disqualify the belief from being a priori knowledge. The issue is quite delicate; a great deal depends on the exact meaning of ‘a priori’. It is even possible that the issue is, to some extent, merely verbal. Ordinarily, at least, it would be quite odd to say that one can know a priori concerning a certain length that a particular stick (if it exists) is exactly that long. I conjecture that Kripke, in his discussion, either failed to distinguish properly between the a posteriori content of the meter sentence, i.e. Peter, and the arguably a priori truth that the length at t 0 of S is referred to (in the reference-fixer's present idiolect) as ‘one meter’ (or something similar, such as the proposition that the meter sentence is true in the reference-fixer's idiolect), or else he failed to appreciate that the reference-fixer's visual experience of S in the very introduction of the term ‘meter’ is a crucial part of the justification for the reference-fixer's belief of Peter.11

I claimed in Frege's Puzzle that actual measurement of S's length by someone is required in order for anyone to know that S has Leonard as its length. I did not mean that one must do the measuring oneself. One could be told S's length by someone else who actually measured it, etc. But I thought that at some point an actual measurement by someone was required. Kripke allows in his discussion that the inch may already be in use as a unit of length, independently of the introduction of the meter by the reference-fixer. One function that is filled by the institution of using a unit of length, such as the inch, is that it provides standard or canonical names for infinitely many otherwise unnamed abstract entities (the particular lengths), exploiting names already in use for the numbers (‘39.37 inches’, etc.). It seems plausible that if one is a member of a community of speakers for whom there are one or more units of length in use at a particular time, then at least in the typical sort of case, one would count as knowing exactly how long a given object is only if one is in a position to specify the object's length correctly by means of one of its standard names, given in terms of a conventional unit and the (or at least a) correspondingly appropriate numerical expression. It would follow that one counts as knowing exactly how long S is at t 0 only if one is able to specify S's length in some such manner as ‘39.37 inches’ or ‘3.28 feet’, etc. Having this ability would seem to depend on S's length having been previously measured—either by oneself, or by an informant, or by someone else who is the ultimate source of the information.

By the time Frege's Puzzle made its appearance in print, I realized that this piece of reasoning was flawed by overstatement. When one looks at an ordinary, middle-sized object, one typically sees not only the object; one typically also sees its length. To put it more cautiously, one typically thereby enters into a cognitive relation to the length

itself, a relation that is analogous in several respects to ordinary visual perception, but that (because perceiving subjects may stand in the relation to abstract qualities like lengths) may not correspond exactly with the relation, standardly called ‘seeing’, between perceivers and the concrete objects they see. One also typically thereby sees (perhaps in some other extended sense) the fact that the object has that very length. Of course, merely perceiving an object will not always result in such empirical knowledge. Perhaps in order to see an object's length one must be able to take in the object lengthwise, from end to end, in one fell swoop. Perhaps the visual presentation cannot be under circumstances that create optical illusions (such as might be created by surrounding the object with miniature artifacts, each reduced to the same scale, etc.). Perhaps not. In any case, if the reference-fixer does indeed see S under the required circumstances, he can thereby know of its present length, Leonard, that S is presently exactly that long.12 No physical measurement is required beyond merely perceiving the object (taking it in lengthwise in one fell swoop, etc.). But some sensory experience in which S plays a crucial role seems to be required. The meter sentence is apparently a posteriori, even if physical measurement is not required for its verification.

The error in my argument for the necessity of measurement was the plausible assumption that to know of Leonard that S (if it exists) is exactly that long at t 0 is to know exactly how long S is at t 0 (provided it exists). I suppose that anyone who knows exactly how long a given object is ordinarily knows of its length that the object is exactly that long. But the converse is not universally true; one can know of an object's length, just by looking at the object (and its length, under appropriately favorable circumstances), that the object is exactly that long. Assuming there is a unit of length in use independently of the object in question, one does not thereby learn exactly which length the object's length is, as one would (for example) by physically measuring the object in terms of the conventional unit. Knowing exactly how long something is typically requires more than merely perceiving the object.

III

This brings us to Wittgenstein's paradoxical observation concerning the unassertability of the meter sentence. Wittgenstein claims that one can say of S neither that it is one meter long, nor that it is not one meter long. With part of this, there can be no quarrel. One assuredly cannot properly say of S that it is not one meter long, since that would be straightforwardly false. Why, then, can one not properly say of S that it is one meter long?

Let us modify Kripke's story slightly. Suppose there is no standard unit of length in use by the reference-fixer's community. Suppose the reference-fixer is a very clever caveman who is attempting to devise for the first time a precise method for specifying various lengths. He hits on the brilliant idea of establishing a convention of specifying every length whatsoever as a multiple (whole or fractional) of some one, specially

selected length, which will serve as the standard unit of length. He arbitrarily selects for this purpose the length at that moment t 0 of a particularly straight and sturdy stick S that he picks up from among a pile of sticks and holds in his hands. He calls its length ‘one meter’. His fellow tribesmen agree to his scheme. The length at t 0 of stick S, i.e. Leonard, happens to be 39.3701 inches, though of course, no one is in a position prior to the reference-fixer's flash of brilliance to specify its length using inches or any other unit of measurement, since there was no such thing until the historic moment t 0 . Using a compass and a straightedge, the reference-fixer carefully scratches calibrations onto the stick, marking them ‘½’, ‘¼’, ‘¾’, etc., down to a very fine degree, say 128ths. The clever caveman knows that with this new tool, given any middle-sized object and sufficient time, anyone can now determine the object's length with a very high degree of precision. His people have a new prize possession, the only standard measuring rod on Earth. Soon the measuring rod is in such great demand that every household has its own, carefully crafted duplicate—each carefully measured against the original. A new institution has been born: measuring with a meter-rule.

Does the reference-fixer in this case know at t 0 that S is exactly one meter long? Yes, simply by looking at it. Surely he need not measure S against itself in order to determine its length as a multiple of the standard length. In fact, there is no clear sense to be made of the idea of measuring the standard itself by means of itself, or even against any of its facsimiles. Its length is the standard length, by stipulation. If the reference-fixer can know of S's length, Leonard, just by looking, that S is presently exactly that long, then in some sense he cannot fail to know that S's length is exactly one times that length—except by not seeing it under appropriately favorable circumstances. Physical measurement is not only unnecessary; the very notion is in some sense inapplicable to this case.13

But an interesting philosophical difficulty arises once we say that the reference-fixer does know that S is exactly one meter long. He has deliberately established a convention of measuring objects in order to determine their lengths, and of specifying those lengths as multiples of a standard unit of length. Within the framework of this institution or ‘language-game’, one counts as knowing how long something is (as opposed to merely knowing of its length that the object is that long), typically, if and only if one is in a position to specify its length correctly as a multiple of the standard length (for example, as ‘3 and 27/32 meters')—within the degree of precision epistemically accessible to the community in the current state of scientific knowledge. It would seem that anyone who can correctly specify that a given object is exactly n meters long (with sufficient epistemic justification, understanding what the specification means,

etc.) knows exactly how long that object is. Thus, if the reference-fixer knows that S is precisely one meter long, it would seem that he knows precisely how long S is. If Kripke's claim in this connection were correct, the reference-fixer would know exactly how long S is (provided it exists) a priori! This would be quite astonishing, but we have seen that Kripke's claim seems incorrect. In order to know that S is exactly one meter long, the reference-fixer must look at (or be told, etc.) S's length. However, we still get a rather curious result, not unlike Kripke's claim that the reference-fixer knows S's length a priori: if the reference-fixer knows without measuring and just by looking that S is precisely one meter long, then he knows precisely how long S is without measuring and just by looking.

Indeed, knowing that a given object's length is exactly n times that of another object (the standard) cannot give one knowledge of how long the first object is unless one already knows how long the second object is. If one knows only that the length of the first is n times that of the second without knowing how long the second object is, one knows only the proportion between the lengths of the two objects without knowing how long either object is. Thus, if measurement is ever to give one knowledge of how long an object is, one must already know how long the standard itself is. Yet we have just seen the reference-fixer could not have come to know exactly how long S is by actually measuring S. Physical measurement is out of the question. If he has this knowledge, he must have acquired it simply by looking at S’s length, under appropriately favorable circumstances.

Suppose the reference-fixer wishes to know exactly how long his spear is. Can he tell just by looking at its length, without taking the trouble to measure? It would seem not. Now that there is an institution of measuring with a meter-rule, he can do much better than estimating the spear's length solely on the basis of its visual appearance. He can physically measure it. In fact, it would seem that he must physically measure the spear if he wishes to know exactly how long it is. Why is measurement not equally required in order for him to know exactly how long S is? Because of its unique role in the language-game of determining length with a meter-rule. Measuring the stick itself is, in some sense, impossible. There is nothing to measure S against that is not itself measured ultimately against S.

The caveman could try to do the same thing for the spear that he did for S. He could scratch calibrations into the spear at its midpoint, and so on, proposing the spear as a second and rival standard of measurement. Would this little exercise make it possible for the caveman to know exactly how long the spear is just by looking at it, as he can in the case of S? If so, then it would seem that he does not need to measure anything—or at least any ordinary middle-sized object—in order to know precisely how long it is. He need only look at it and propose to use its length as a new unit of length. Clearly, this would defeat the purpose of the institution of measuring: it would violate the rules of the language-game. No, if the caveman wishes to know exactly how long his spear is, he must do much better than merely look at it and perform a little ritual. He must measure it against the standard S, or by proxy against one of the many facsimile measuring sticks that have since been constructed, etc.

This makes S epistemically quite unique vis à vis the reference-fixer. No other object is such that he can know precisely how long it is just by looking at it. Once an

institution of measuring lengths is put into operation, knowing how long an object is—at least if the object is something other than the standard itself—requires a little elbow grease. This is true even of the duplicate measuring sticks. But how could S have become knowable in a way that no other object is knowable? The measuring rod S was chosen entirely arbitrarily by the reference-fixer to serve a special purpose: all lengths are to be specified as multiples of its length. Despite its ‘peculiar role in the language-game’, it is still a stick, a physical object subject to the same natural laws and knowable in the same way as any other. If the reference-fixer had selected some other stick in place of S as the standard—as well he might have—the other stick would play the special role in the language-game. Its length, rather than Leonard, would be the one in terms of which all others are to be specified. In order to know precisely how long S is, one would simply have to measure it (or be told by someone who measured it, etc.). The reference-fixer's accidental selection of S as the standard could not have made it knowable in some direct way, quite different from the way it would have been knowable if it had not been selected in the first place. The reference-fixer cannot simply legislate that he knows exactly how long S is, any more than he can legislate that he knows exactly how long his spear is. The accidents and whims of human history and culture do not alter the nature of our epistemic relations to external objects. The laws of epistemology (if there are any such things) are universal. They do not play favorites by singling out this or that arbitrarily selected, inanimate object as epistemically special. If the laws of epistemology say in order that thou knowest how long a physical object is, thou shalt measure it, they do not make an exception in the case of some favorite stick.14

Thus as soon as we say that the reference-fixer knows that S is one meter long, we are embroiled in a paradox. The language-game of measuring with a meter-rule involves a simple criterion for knowing how long something is. In order for the reference-fixer to know how long anything is, he must be able to specify its length in meters and he must know how long the Standard Meter is. Saying that he knows that S is exactly one meter long attributes to him knowledge of exactly how long the Standard Meter is. But he could not have acquired this knowledge through measurement. If he has such knowledge, he can only have acquired it by simply looking at S. This would require S to be what it cannot be: knowable in a unique way in which no other object is knowable and in which it itself would not be knowable if it had not been arbitrarily selected as the standard. These considerations invite the skeptical conclusion that the reference-fixer does not know after all that S is exactly one meter long. This, in turn, leads to an even stronger skeptical conclusion. For if the reference-fixer does not know how long S is, he cannot know, and cannot even

discover, how long anything is. Measuring an object's length using S only tells him the ratio of that object's length to the length of S.

The problem leads to an even more disturbing result. Suppose we grab the bull by the horns and deny that the reference-fixer knows the length of S or of anything else. Even if we say merely that S is in fact exactly one meter long, while not suggesting that the reference-fixer knows this, we pragmatically implicate that we know that S is exactly one meter long, thereby opening the door to the same skeptical paradox. For if we know that S is exactly one meter long, then (assuming S's length were the ultimate unit of length-measurement, in terms of which all other such units are ultimately defined) we must have come to know precisely how long S is simply by looking at its length, without measurement. This would make S inexplicably unique, differing in epistemic accessibility from all other objects, and from what it would have been if it had not been selected as the standard, solely by virtue of the special role it has arbitrarily come to occupy as the result of an accident of human history and culture. Since this is impossible, we are drawn to the skeptical conclusion that we do not know, and cannot discover, how long anything is! If this argument is sound, we are epistemically unjustified in saying of S that it is exactly one meter long at t 0 . This comes very close to Wittgenstein's enigmatic claim.

There is a more general form of skepticism, of which the problem of the Standard Meter is only a special case. Analogous skeptical doubts can be raised in connection with other standards, such as the period of the earth's rotation on its axis, midnight Greenwich time, and so on. We may call the general form of skepticism exemplified by these examples Does-anybody-really-know-what-time-it-is skepticism.

This general problem arises in a particularly sharpened form in connection with the transcendental number 0x0003c0. Let us assume that the Greek letter ‘0x0003c0’ was introduced as a standard name for the ratio of the circumference of a circle to its diameter, analogously to the introduction of ‘meter’. We may then raise questions analogous to those raised in connection with the Standard Meter. First, do mathematicians know that 0x0003c0is the ratio of the circumference of a circle to its diameter? Notice that this is separate from the question of whether mathematicians know that ‘0x0003c0’ refers to the ratio of the circumference of a circle to its diameter—which clearly should be answered affirmatively. What we are asking here is whether there is any number that mathematicians know to be the ratio of the circumference of a circle to its diameter. Questions arise concerning the various modes of acquaintance by which mathematicians are familiar with 0x0003c0. If mathematicians conceive of 0x0003c0as the ratio of the circumference of a circle to its diameter, or even as the sum of a particular convergent series, is their (or our) knowledge of 0x0003c0not merely what Russell called ‘knowledge by description’? Or are mathematicians also acquainted with 0x0003c0in some more direct fashion, something like the way in which we are acquainted with 3 or 4 (or even 3.1416)? Presumably, despite the doubts that this line of questions raises, many will insist that mathematicians do know of 0x0003c0that it is the ratio of the circumference of a circle to its diameter. Indeed, the conventional wisdom is that mathematicians know a priori that 0x0003c0is the ratio of the circumference of a circle to its diameter. Very well, then, do they know exactly what number this ratio is? What exactly is the value of ‘0x0003c0’? The very question seems to demand what it is impossible to produce: a specification of 0x0003c0by means of its full decimal expansion. Providing the decimal expansion of a particular constant is analogous to measuring a particular object to determine its length. It is not enough here (perhaps by contrast with the case of measuring) merely to be able to set upper and lower bounds within a desired (non-zero) margin of error. Whatever margin of error one chooses, there remain infinitely many numbers that have not yet been ruled out. Given that the ratio of the circumference of a circle to its diameter lies somewhere among infinitely many other numbers between these bounds, do mathematicians know which number it is? Since one cannot know the full decimal expansion of 0x0003c0, there seems to be a sense in which no one can know what number 0x0003c0is.15 It would follow that no one knows, or can even discover, given the diameter of a circle as a rational number, what the circumference is, or what the internal area is, etc. The well-known formulas for computing these values yield only their proportion to the unknown quantity 0x0003c0.

The threat of Does-anybody-really-know-what-time-it-is skepticism gives a point (whether or not it is the intended point) to Wittgenstein's counsel that we not say of S that it is exactly one meter long. Our not saying this about S would indeed mark its peculiar role in the ‘language-game’ of determining how long objects are with a meter-rule. But how does this help to solve the paradox? It does not.16

IV

The paradox revolves around the epistemic notion of knowing how long a given object is. This concept is philosophically problematic in precisely the same way as the concept of knowing who someone is. In fact, both concepts should be seen as special cases of a more general epistemic notion: that of knowing which F a given F is, where ‘F’ is some sortal. Knowing-who is the special case where ‘F’ is ‘person’; knowing-how-long is the special case where ‘F’ is ‘length’.17 A number of philosophers have held that the locution of ‘knowing who’ is highly interest-relative. Relative to some interests, simply knowing a person's name qualifies as knowing who he or she is: relative to other interests, it does not.18 If this is correct, then the locution of ‘knowing how long’ is equally interest-relative. In some contexts, knowing a length's standard name in the metric system counts as knowing which length it is; in other contexts, it does not. One way of spelling out this idea (though not the only way) is to claim that the locution of ‘knowing which F’ is indexical, expressing different epistemic relations with respect to different contexts.19

Interest-relative notions can easily lead to paradox, if we shift our interests without noticing it. Epistemic notions, if they are interest-relative, lead to skeptical paradox. Someone whose epistemic situation remains unchanged may be correctly described, relative to one set of interests, as knowing something that, relative to another set, he or she cannot be correctly described as knowing. The appearance of contradiction is due to a sort of equivocation, similar to that typified by the sentence ‘Now you see it; now you don't’. If the indexical (or interest-relative) theory of knowing which F is correct, the skeptic is not really denying what we claim when we claim to know something.

The skeptic merely has different interests; he or she is changing the subject. There is no disagreement between us as to the facts of the matter.

It seems likely that the paradox outlined in the preceding section arises from some equivocation of this sort. In describing the caveman's situation, we invoke a notion of knowing-how-long for which a necessary and sufficient condition is, roughly, the ability to produce a standard name of the object's length, in terms of the standard unit, while understanding the meaning of that name. Within the confines of the caveman's language-game, knowing how long something is just is knowing the proportion of its length to Leonard. For every object but one, satisfying this condition requires actual physical measurement. but the reference-fixer trivially satisfies the necessary and sufficient condition for knowing how long S itself is, provided he sees its length. Knowing his own intention in introducing the term ‘meter’ gives the reference-fixer the ability to produce the standard name of S's length; seeing S's length gives him the understanding he needs of that standard name. (See footnote 10 .) In the sense of ‘measurement’ in which knowing how long something is requires measurement against the standard, merely looking at the standard's length (under the appropriately favorable circumstances) counts as measuring the stick itself. In S's case, merely looking is a sort of limiting-case of measuring. The laws of epistemology are not violated; it is just that there are different ways of obeying them.

When we explicitly ask, on the other hand, whether the reference-fixer knows how long the standard itself is, we shift our focus from within the confines of his language-game to looking in on him from the outside. Without taking notice we have raised the ante. From our newer, broadened perspective, knowing how long S is seems to require physically measuring it against a higher standard—one that supersedes and overrides the reference-fixer's standard, one that (by hypothesis) is not available to the reference-fixer himself.

If we raise the same question with respect to our own, or our scientists', current standard, we may raise the ante beyond what anyone is currently in a position to pay. Perhaps there is a legitimate sense in which no one now knows exactly how long a meter is. Likewise, perhaps there is a sense in which no one can know exactly what number 0x0003c0is. But if there is a sense in which these instances of Does-anybody-really-know-what-time-it-is skepticism are true, what is true in this sense need not concern us. It is like shouting ‘Fire!’ in a crowded theatre merely because someone is lighting a cigarette. There is still the standard, everyday sense, in which everyone of course knows how long the Standard Meter is and everyone of course knows what number 0x0003c0is: the Standard Meter is exactly one meter long, and 0x0003c0is the ratio of the circumference of a circle to its diameter. We can expand on this by producing a meter-rule and thereby showing how long the Standard Meter is, or by producing a partial decimal expansion of 0x0003c0or instructions for computing its value to whatever number of places is desired. That is all one can have. To demand more than this is to change the rules of the game in such a way that nobody can win. At the other extreme, there are no doubt contexts in which it is true to say that the caveman knows how long his spear is just by looking at it. (‘I'll get more respect when everyone sees how long my spear is.’) The important fact is that we stand in such-and-such perceptual and cognitive relations to particular objects. In some (perhaps extended) sense of ‘see’, the caveman sees his spear's length by looking at the spear itself (lengthwise, in one fell swoop, etc.). Some of us are acquainted with 0x0003c0only by knowing an approximation to its decimal expansion. Perhaps there is even a (possibly metaphorical) sense of ‘see’ in which we may be said to see the ratio of the circumference of a circle to its diameter simply by looking at a diagram. In the end, what does it matter whether we dignify how we stand with the honorific ‘knowing which F’?

If all of this is correct, there may be a better reason for not saying of the Standard Meter that it is exactly one meter long. In the circumstances of everyday, non-philosophical commerce, the proposition that the standard is just that long is something nearly everyone counts as knowing. But (in part for that very reason) merely uttering the sentence ‘The Standard Meter is exactly one meter long’ tends to raise the ante to a level at which its utterance becomes epistemically unjustified—and threatens to invoke the skeptic's favorite level, at which its utterance is in principle unjustifiable. If saying something that is trivially true leads us to say further things that sound much more alarming than they really are, it may be better to say nothing. In any event, this provides one sort of rationale for not saying of the Standard Meter that it is one meter long.

As I have said, however, I do not pretend that this rationale bears any significant resemblance to Wittgenstein's. It is unclear to me whether Does-anybody-really-know-what-time-it-is skepticism is connected with the issues discussed in and around Philosophical Investigations §50. If 0x0003c0occupies a unique role in the language-game of mathematics, analogous to the peculiar role of the Standard Meter in the language-game of measuring with a meter-rule, its peculiar role is (happily) not marked by any prohibition against saying that it is the ratio of the circumference of a circle to its diameter. Moreover, if the rationale I have suggested does bear some significant resemblance to Wittgenstein's, then his arresting remark itself is also something that sounds much more alarming than it really is, and in the absence of at least the minimal sort of explicit epistemological stagesetting I have provided here, is probably better left unsaid.

8 How Not to Become a Millian Heir (1991)*

Nathan Salmon

I

Millianism is a highly contentious doctrine in the theory of meaning. It is the thesis that the contribution made by an ordinary proper name to securing the information content of, or the proposition expressed by, a declarative sentence in which the name occurs (outside of the scope of such nonextensional operators as quotation marks), as the sentence is used in a possible context, is simply the name's referent (bearer) in the given use.1 The unpopularity of the doctrine stems heavily—perhaps primarily—from the fact that it leads to a serious philosophical difficulty discovered by Gottlob Frege, and which I have dubbed ‘Frege's Puzzle’: Let a and b be distinct but co-referential proper names such that the identity sentence 0x00231ca=b0x00231d contains information that is knowable only a posteriori, and can therefore be informative. Then how can this sentence 0x00231ca=b0x00231d differ at all in cognitive information (propositional) content from 0x00231ca=a0x00231d, which is a priori and uninformative?

In Frege's Puzzle2 I proposed an analysis according to which the puzzle relies on three components: (i) a compositionality principle that propositions formed in the very same way from the very same components are the very same proposition; (ii) the principle, which I call ‘Frege's Law’, that declarative sentences sharing the same cognitive information (propositional) content do not differ in informativeness or epistemological status; and (iii) the observation that there are co-referential proper names a and b (for example, ‘Hesperus’ and ‘Phosphorus’) such that 0x00231ca=b0x00231d is

informative and a posteriori even though 0x00231ca=a0x00231d is always uninformative and a priori. Together these assertions comprise the main premisses of a powerful argument against Millianism. Most Millians, if forced to give direct response, would probably reject Frege's Law. And taken in one sense, I would agree. I argued, however, that properly understood, Frege's Law should be seen as analytic, and that the only objectionable assertion is the first half of (iii). There can be no co-referential names a and b such that 0x00231ca=b0x00231d is either a posteriori or informative in the only senses of ‘a posteriori’ and ‘informative’ that are relevant to Frege's Puzzle.

Howard Wettstein and Kai-Yee Wong have recently argued independently that the Millian ought to embrace the first half of (iii) and reject the second half.3 They claim that Millians (at any rate Millians of my ilk), if we are to be consistent, should maintain that for any proper name a—or at least any proper name that refers to an empirically observable entity like a person or a planet—the reflexive identity sentence 0x00231ca=a0x00231d is typically neither a priori (in something like the traditional sense) nor trivial.

II

Wettstein makes this dramatic claim in the course of an argument that Millians should reject the view, which he calls ‘the mental apprehension picture of reference’, that using a proper name competently to refer to its referent requires special epistemic contact with the referent (either through the user's association of nontrivial individuating or other substantive properties with the name, or through a special causal connection with the referent). I quote at length:

Frege's data themselves—the idea that two names can, unbeknownst to the competent speaker, co-refer—don't seem all that dramatic. Is it, after all, so obvious, that we should know of any two co-referring names that they co-refer? But put Frege's data together with the mental apprehension picture and sparks fly . . . [The] mental apprehension conception is what propels the puzzle. Were we to radically deny the former and adopt an epistemically innocent way of thinking about reference, as I have suggested we should, Frege's data would present no special problem . . .

I argued above that Frege's puzzle, so called, is generated not by Frege's data alone, but only in conjunction with the mental apprehension conception of reference. Is it so obvious, I asked, that there is something deeply puzzling about the very idea that a speaker can be competent with two co-referring names, and not know that they co-refer? The radical change in perspective I've been encouraging makes even more dramatic the dissolution of the puzzle. . . . If one can refer to something without anything like a substantive cognitive fix on the referent . . ., then why should it be the slightest bit surprising that a speaker might be competent with two co-referring names, but have no inkling that they co-refer? . . .

Rejecting [the mental apprehension picture], we can now see that there is no presumption whatever that co-reference should somehow be apparent to the competent user . . .

Indeed, if there is any presumption to speak of here, it is . . . that co-reference, except under unusual circumstances, will not be apparent . . . What is . . . surprising perhaps—and here we turn the tables on Frege—is that ‘a=a’ identities are not, in general, trivial . . . [The] mere presence of the same name, indeed the same name of the same party, surely does not make the identity trivial. (Wettstein ‘Turning the Tables on Frege’, pp. 331–332)

That Wettstein's diagnosis of Frege's Puzzle, and his related stance on the alleged informativeness of 0x00231ca=a0x00231d, are based on a misunderstanding of the import of the puzzle is proved by the fact that the puzzle arises with equal force even against versions of Millianism (such as Wettstein's) that explicitly reject the ‘mental apprehension picture’ of referential competence that Wettstein opposes (see note 3 ). Moreover the puzzle, in its usual formulations (‘Hesperus’–‘Phosphorus’, ‘Superman’–‘Clark Kent’, etc.), does not constitute an objection to orthodox Fregean theory, despite the latter's commitment to the offending picture of referring.4 Wettstein is correct that competence in the use of a pair of co-referential names generally neither requires nor guarantees knowledge of their co-reference. Even without rejecting the offending picture of referring, however, this observation is not particularly puzzling. Indeed, in the younger days of his Begriffsschrift, Frege invoked the possibility of ignorance of co-reference, in tandem with something like the offending picture, as an essential part of a solution to Frege's Puzzle.5 If anyone has ever argued that a competent user's failure to recognize the co-reference of two names in his or her repertoire, together with

principles like (i) and (ii), spell serious trouble for Millian theory, I am unaware of it. Certainly Frege did not.6

In missing the puzzle's point, Wettstein fails to appreciate the puzzle's force. The puzzle arises within Millian theory, and it is a puzzle for the Millian whether or not he or she rejects the picture of referential competence that Wettstein criticizes. Either way, Millian theory allows that the assertion that the names ‘Hesperus’ and ‘Phosphorus’ are coreferential is a posteriori and informative (to the competent user who is unaware of their co-reference). The puzzle arises from the fact that, evidently, a sentence like ‘Hesperus is Phosphorus’ (and its Leibniz's-Law consequences, e.g. ‘Hesperus is a planet if Phosphorus is’) is potentially informative, not merely because it may impart the a posteriori linguistic information about itself that it is true (and hence that ‘Hesperus’ and ‘Phosphorus’ are co-referential) but, in part, because the information (proposition) semantically contained in the sentence—the nonlinguistic information that Hesperus is Phosphorus—is a posteriori. In the very act of presenting the puzzle, the author of ‘Uber Sinn und Bedeutung’ chastised the author of Begriffsschrift for mistaking the former information for the latter, and (as the Church–Langford translation argument demonstrates7 ) the later author was right to do so. The nontrivial character of the information that ‘Hesperus’ and ‘Phosphorus’ are co-referential is irrelevant to Frege's Puzzle.8

One might attempt to defend Wettstein's conflation of semantics with astronomy by pointing out that although the sentence ‘Hesperus and Phosphorus are identical’ differs in content from ‘ “Hesperus” and “Phosphorus” are co-referential’, these two sentences cannot differ in informativeness for anyone competent in the use of the two names. For such a user knows that ‘Hesperus’ refers (in English) to Hesperus and that ‘Phosphorus’ refers to Phosphorus, and from these the bridge principle that ‘Hesperus’ and ‘Phosphorus’ are co-referential (in English) if and only if Hesperus is Phosphorus trivially follows. This sort of consideration raises extremely delicate issues.9 It is enough for present purposes to note that the observation that a competent user need not be aware of the co-reference of ‘Hesperus’ and ‘Phosphorus’ cannot be made to generate a problem for Millianism unless it is relied upon, assuming background knowledge of something like the bridge principle, to establish as a separate and further fact that

‘Hesperus is Phosphorus’ is informative, in the sense that its semantic content can be new information to one who already knows that Hesperus is Hesperus. It is the latter putative fact, and not the former observation, that generates the puzzle. It would be odd to attempt to establish the putative fact by means of the observation; indeed the putative fact seems obvious enough without supporting evidence, and is generally taken for granted.10 Notice also that the same observation could not be used, in the same way, to establish the putative fact that ‘Hesperus is Phosphorus’ is a posteriori. For the bridge principle itself is also a posteriori.11

The contrasting sentence ‘Hesperus is Hesperus’, where both occurrences of the sequence of letters ‘Hesperus’ are used in the same way, with the same semantic reference, is uninformative in the only sense relevant to Frege's Puzzle: the proposition the sentence (so used) semantically contains is a trivial truism. The fact that it may not be apparent on a given occasion that both occurrences of ‘Hesperus’ are being so used is irrelevant.12

III

Wong's challenge to my claim that ‘Hesperus is Phosphorus’ is a priori correctly focuses on the epistemological status of the semantically contained proposition. That proposition, according to Millianism, is the singular proposition about the planet Venus that it is it. On my account, this proposition consists of Venus taken twice and the binary relation of identity (more accurately, identity at t, where t is the present time). Furthermore, according to my account, when we grasp such a proposition, we take the proposition in some particular way, by means of something like a particular mode of familiarity with it. Though I was deliberately vague about what ways of taking a proposition are or amount to, it is critical to my attempt to rescue Millianism from puzzles like Frege's that whenever someone grasps a familiar proposition but fails to recognize it (as the one encountered on such-and-such earlier occasion, or as a trivial truism, etc.), he or she takes the proposition in a new and different way. I also said that a true proposition is a priori if it is in principle knowable solely on the basis of reflection on its components (conceptual or otherwise), without recourse to sensory experience, and that a true sentence is derivatively a priori if its semantically contained proposition is a priori.

Wong agrees, initially for the sake of argument, that my characterization of a priority more or less captures (or at least does not conflict with) the traditional notion.13 His objection is that, given my account of our grasp of propositions in general, and given my account of the singular proposition about Venus that it is it in particular, that proposition does not satisfy my own characterization of a priority. For in order to know the proposition it is not sufficient on my account to reflect on its components, if one does not take the proposition in an appropriate way. In particular, taking this proposition in the way one would were it presented by the very sentence ‘Hesperus is Phosphorus’, an empirical investigation would be required to establish it as a piece of knowledge. Wong also questions the correctness of my characterization of a priority, arguing that, assuming my account of our grasp of propositions, ‘a priority, as an epistemic notion, should be sensitive to the ways in which a proposition is taken or grasped’, so that ‘it may be mistaken to characterize a priority as applying primarily to propositions, as Salmon does’.

My account of the structure of the singular proposition about Venus that it is it may be crucial to the objection. As Wong notes, others such as Ruth Barcan Marcus and Pavel Tichy had urged before me that the proposition semantically contained in ‘Hesperus is Phosphorus’ is a priori.14 However, in so doing these writers drew no distinction between the singular proposition about Venus that it is it and the singular proposition about Venus that it is selfidentical.15 The latter proposition, on my account, differs from the former in having only two components: Venus and the property of being selfidentical (at t).16 One could not object, in the same way, that the singular proposition consisting of Venus and selfidentity is knowable only a posteriori if it is taken one way rather than another. Thus Marcus and Tichy may be immune from Wong's objection.

The objection depends on a misinterpretation of my characterization of a priority. Wong says that, given a natural understanding of the phrase ‘in principle’, ‘to say that [a certain proposition] is in principle knowable solely on the basis of reflection is to say that, provided that one has the modicum of logicality needed and has reflected “hard enough” on [that proposition], one cannot fail to know [that proposition].’ This does not accord with my intent. Indeed, any but the most trivial of mathematical theorems would almost certainly fail such a test. The notion of a priority does not demarcate a kind knowledge automatically attained once certain (nonexperiential) sufficient conditions are fulfilled. Instead it characterizes a kind of knowledge in terms of the necessary conditions for its attainment. The phrase ‘on the basis of’ does not mean merely the same as ‘by means of’; it pertains to epistemic justification. A piece of knowledge is a priori if sensory experience need not play a certain key role in its justification. Exactly what this special role is may be extremely difficult to specify.17

If sensory experience can play no role at all, beyond merely enabling one to grasp the proposition in question (say, by giving one the requisite concepts), the proposition qualifies as a priori. This is what I claim for the singular proposition about Venus that it is it. It is a truth of logic. It may be that in order to know this logical truth without recourse to experience on must not take it a certain way (e.g. the way one might take it were it presented through the sentence ‘Hesperus is Phosphorus’). One can know the proposition on the basis of reflection (including the faculty of reason) alone by taking it the way one would if one stipulated that one is considering a certain trivial truism—as in ‘Consider the fact about Venus that it is it.’ That fact is thus knowable without recourse to sensory experience.18

Wong anticipates a reply along these lines. He responds that it is not clear that such a reply does not risk trivializing the notion of a priority, on the grounds that even a sentence like ‘Peter is at location l at time t’ might emerge as a priori, since its content can be expressible by the arguably logically true sentence ‘I am here now’.19 And indeed, Frege's Puzzle allowed (p. 180) that the latter sentence may be a priori. More recently, I have come to have doubts about this. In the first place, it would be decidedly mysterious if one could know of one's current location, without the slightest experiential contact with one's surroundings, that one is at that location.20 There is no like mystery in the fact that one can know without such contact that one is wherever one is, and that the sentence ‘I am here’ is therefore true with respect to one's context (wherever that may be). In the second place, I have become convinced that the particular sentence ‘I am here now’, in its normal use, is not logically true, and that this is demonstrated by Gerald Vision's example of the standard telephone answering-machine message: ‘I am not here now’. I believe this example is best thought of as a genuine case of assertion in absentia, in which the agent of the context is (just as he or she says) not present at the context of his or her speech act (and indeed, is generally not even aware at the time of performing it).21 One can always invent an artificial sentence that succeeds where the natural-language sentence fails. Thus let  ‘C i ’ indexically refer with respect to any context to the context itself. Then ‘I am the agent of C i ’ is perhaps a logical truth, since by semantics alone it is true with respect to every context, no matter what the range of possible contexts.22 But by the same token, it is by no means clear that the semantically contained proposition is not a priori. Let ‘Clarence’ name a particular context in which Peter is agent. If ‘I am the agent of C i ’ is a priori in the sense relevant to Frege's Puzzle, then so is ‘Peter is the agent of Clarence’. There is no problem here. Likewise, suppose I am wrong about ‘I am here now’. If it is a priori, then so is ‘Peter is at l at t’ (provided the latter is true). But then if ‘I am here now’ is a priori, it is not at all obvious that the resulting a priority of ‘Peter is at l at t’ would trivialize the notion of a priority. Such sentences as ‘Peter is 5′9″ tall’, ‘Mary was born in Seattle’, ‘Water runs downhill’, etc. would remain a posteriori. If it is supposed to be clear that ‘I am here now’ is logically true and yet ‘Peter is at l at t’ not a priori in the relevant sense, the result would be that some logically true sentences are not a priori in the relevant sense (and whose contents, with respect to particular contexts, are thus not themselves logical truths), and are only ‘a priori’ in some alternative sense (e.g., in the sense that one can know by semantics alone that the sentence in question is true in every context). Such a result does not strike the present writer as untenable.23

Having said this much, I must add that I am not unsympathetic to Wong's suggestion that a priority and a posteriority might be taken as relative statuses, so that a single proposition may be said to be a priori relative to one way of taking it and a posteriori relative to another. Still, relativization of the notions of a priority and a posteriority does not replace the absolute notions. A true and knowable proposition is a priori in the absolute sense if and only if it is a priori relative to some ways of taking it, and a posteriori in the absolute sense if and only if it is not a priori relative to any way of taking it. It is this absolute notion of a priority that corresponds to the traditional notion—which is that of a property of propositions and not that of a binary relation between propositions and ways of taking them (or a property of pairs consisting of a proposition and a way of taking the proposition)—but the relativized notions, being more discriminating, doubtless deserve their own niche in general epistemology. As Wong suggests, the relativized notions may even form the basis of a justification, of sorts, for the traditional view held by Frege (and once endorsed by Kripke) that ‘Hesperus is Phosphorus’ is ‘a posteriori’.24

All the same, the proposition that Hesperus is Phosphorus is trivial, “given” information that is knowable a priori in the traditional (absolute) sense, and the sentence ‘Hesperus is Phosphorus’ is therefore uninformative and a priori in the only sense relevant to Frege's Puzzle.

end p.168


9 Relative and Absolute Apriority (1993)*

Nathan Salmon

I

The theory of direct reference is the theory that proper names and other simple singular terms are nondescriptional in content. Propounders and expounders have agreed that one of the theory's remarkable consequences, discovered by Kripke, is that such identity sentences as ‘Hesperus is Phosphorus’ and ‘Cicero is Tully’ semantically contain necessary truths even though they are a posteriori and informative.1 Whereas the possibility of necessary a posteriori truth—of facts that could not have been otherwise yet cannot be known except by empirical means—is philosophically remarkable for its own sake, the claim that the direct-reference theory yields this consequence is especially dramatic. Gottlob Frege, in the opening paragraph of ‘Über Sinn und Bedeutung’, noted the aposteriority and syntheticity of such sentences as ‘Hesperus is Phosphorus’ and ‘Cicero is Tully’ in generating what I call ‘Frege's Puzzle’, which forms the core of his principal argument against Millianism—a version of direct-reference theory according to which the sole contribution made by a proper name, as occurring in a typical context, to the proposition content of the sentence in which it occurs is its referent (bearer, denotation, designatum). Frege asks: If Millianism is correct, how can ‘Cicero is Tully’ differ in epistemological status from the a priori ‘Cicero is Cicero’? Certainly there is considerable tension between direct-reference theory and the evident a posteriori informativeness of identity sentences like ‘Cicero is Tully’. How is this apparent conflict to be resolved?

A word of caution: One can maintain that ‘Cicero is Tully’ is ‘a posteriori’ or ‘informative’, and mean by this that the linguistic fact that the sentence ‘Cicero is Tully’ is true (in English) is a nontrivial fact that is knowable only on the basis of experience.2 But it is hardly remarkable that there are necessary truths that are ‘a

posteriori’ or ‘informative’ in this attenuated sense. Nor could the claim that ‘Cicero is Tully’ is ‘a posteriori’ in that sense, once properly understood, be regarded as threatening the theory of direct reference. Which sentences of English are true, or necessary, is an empirical matter concerning the relationship between English and the world; all true sentences of English are ‘a posteriori’ in the attenuated sense. By the same token, which sentences of English are true, or necessary, is, at least to a large extent, a contingent matter. The claim that ‘Cicero is Tully’ is necessary even though a posteriori and informative is philosophically significant, at least initially, because it concerns the means by which one might come to know the nonlinguistic, necessary truth that Cicero is Tully.

One pioneering direct-reference theorist provided (in a footnote) an intriguing account of how the claim that identity sentences like ‘Cicero is Tully’ are a posteriori might be reconciled with Millianism. Keith Donnellan says:

I introduce the expression ‘exotic necessary truths’ not just to dramatize the interest of Kripke's discovery [that certain sentences involving rigid designators turn out to express necessary truths although the fact that they express truths is to be learned by empirical means]. The more obvious term ‘a posteriori truths’ obscures an important point. If we distinguish a sentence from the proposition it expresses then the terms ‘truth’ and ‘necessity’ apply to the proposition expressed by a sentence, while the terms ‘a priori’ and ‘a posteriori’ are sentence relative. Given that it is true that Cicero is Tully (and whatever we need about what the relevant sentences express) ‘Cicero is Cicero’ and ‘Cicero is Tully’ express the same proposition. And the proposition is necessarily true. But looking at the proposition through the lens of the sentenceCicero is Cicero’ the proposition can be seen a priori to be true, but through ‘Cicero is Tully’ one may need an a posteriori investigation. (‘Kripke and Putnam on Natural Kind Terms’, in C. Ginet and S. Shoemaker, eds, Knowledge and Mind, Oxford University Press, 1983, pp. 84–104, p. 88 n)3

By contrast, in developing and defending a version of Millianism, I argued in Frege's Puzzle that such identity sentences as ‘Cicero is Tully’ are both a priori and uninformative—indeed analytic—since the proposition content of ‘Cicero is Tully’ is just the singular proposition about Cicero that he is him, a trivial truism that is in principle knowable with complete certainty solely on the basis of reflection (including

the faculty of reason), without recourse to any experience beyond what may be needed simply to be able to apprehend singular propositions involving Cicero.4 Donnellan and I thus seem to have provided two competing Millian accounts of the epistemological status of such sentences as ‘Cicero is Tully’. This raises the question of which account, if either, is correct.

II

It must be admitted that for such sentences as ‘Cicero is Tully’, understanding and reason alone are not sufficient without empirical investigation to reveal their truth. In order to know the proposition content independently of experience, one must also apprehend that proposition in a way that is sensitive to its special logical status. This fact, however, does not establish that such sentences are a posteriori rather than a priori. Even a straightforwardly analytic and a priori sentence can share the property that one must apprehend its content in a special way in order to know that proposition independently of experience. Kripke provides the basis for one such example:

A speaker . . . may learn ‘furze’ and ‘gorse’ normally (separately), yet wonder whether these are the same, or resembling kinds. (What about ‘rabbit’ and ‘hare’?) It would be easy for such a speaker to assent to an assertion formulated with ‘furze’ but withhold assent from the corresponding assertion involving ‘gorse’. The situation is quite analogous to that of [a speaker who uses ‘Cicero’ and ‘Tully’ normally but sincerely and reflectively assents simultaneously to ‘Cicero was bald’ and ‘Tully was not bald’]. Yet ‘furze’ and ‘gorse’, and other pairs of terms for the same natural kind, are normally thought of as synonyms.(‘A Puzzle about Belief’, p. 134)

Kripke's speaker presumably learned the words ‘furze’ and ‘gorse’ on separate occasions by something like ostensive definitions, without thereby learning that the two words are co-extensional, let alone synonymous. Has the speaker therefore failed to learn one or both of the words? Not necessarily. Most of us learn one of the two words by ostensive definition, and the other as a word that is interchangeable with the first, in a sort of verbal (non-ostensive) definition. We might be told something like ‘Furze is that stuff growing over there’, and later ‘ “Gorse” is another word for furze.’ Alternatively, we might be told ‘Gorse is that stuff growing over there’, and later ‘ “Furze”

is another word for gorse.’ If either of these words can be learned by ostensive definition, then both can be. Kripke's speaker has done so. If those words are indeed synonyms,5 then the sentence ‘Furze is gorse’ is analytic and a priori. But Kripke's speaker, while assenting to ‘Furze is furze’, does not assent to ‘Furze is gorse’. Why not? Not because the words are not synonyms in the speaker's idiolect. It is not as if he or she misunderstands ‘gorse’ to mean heather. The speaker has correctly learned both ‘furze’ and ‘gorse’. If they are synonyms in English, they are therefore synonyms also in the speaker's idiolect. The problem is that the speaker does not realize that. He or she understands both ‘Furze is furze’ and ‘Furze is gorse’ without recognizing their synonymy. In particular, he or she understands ‘Furze is gorse’, but fails to recognize the proposition thus expressed as the logical truth that furze is furze.

The general phenomenon is not restricted to natural-kind terms. As I have argued elsewhere, someone may also fail to apprehend the content of the sentence ‘Catsup is ketchup’ in the right way if he or she learned ‘ketchup’ and ‘catsup’ independently—not by being told that they are synonyms but, for example, by consuming the condiment and reading the labels on the bottles, in a sort of ostensive definition.6 The sentence ‘Catsup is ketchup’ is unquestionably analytic—despite the fact that the speaker, who correctly understood both words even before learning of the identity, might sincerely say, ‘I'm fond of ketchup, but I find the taste of catsup repugnant.’ In fact, it is arguable that ‘ketchup’ and ‘catsup’ are not two words, but alternative spellings of a single word. Indeed, a native Santa Barbaran who has learned in a physics lecture while studying in Oxford that ‘colour’ is the English word for the property of reflecting electromagnetic radiation in the visible spectrum may be surprised to learn the truth of ‘Colour is color’. To push the point even further, the same Santa Barbaran, whose limited experience of tomatoes consists in seeing them sliced and put into salads, on later consuming a tomato-based sauce in Oxford could be similarly surprised to learn the truth of ‘Tomatoes are tomatoes’, if it is pronounced: To-mae-toes (American) are to-mah-toes (British, or American affectation). This despite the fact that, however it is pronounced, the sentence has the logical form of a valid sentence: All F's are F's.7

Sentences like ‘Cicero is Tully’, on my view, belong very much with these examples. If they are exotic philosophically, then they are not only exotically necessary but exotically analytic, a priori, and, in the relevant (semantic) sense, uninformative: They are analytic, a priori, uninformative sentences for which understanding and reflection does not suffice for recognition of their truth.8 If ‘Cicero is Tully’ seems somehow more exotic than ‘Ketchup is catsup’, it is chiefly because the names ‘Cicero’ and ‘Tully’ are not mere etymological variations, so that one might more naturally come to learn both without thereby becoming aware of their co-reference. Even for etymologically unrelated co-referential names, however, one can—and indeed one very often does—learn one of the two names by means of its co-reference with the other. I suspect that this is precisely the way most of us learn the name ‘Tully’.9

III

Quoting the passage from Donnellan, as well as passages from other pioneering direct-reference theorists and a passage from my former self, I claimed in Frege's Puzzle (pp. 78–79) that my account of the epistemological status of such sentences as ‘Cicero is Tully’ differed significantly from that of these other theorists.10 Rod Bertolet and Saul Kripke have independently objected that Donnellan's account in terms of the sentence relativity of the concepts of apriority and aposteriority is in fact

entirely within, and in significant respects truer to, the spirit and fundamentals of my own theory.11 For a priori knowledge involves knowledge, and knowledge involves belief. And Frege's Puzzle also argued that belief is the existential generalization (on the third argument place) of a ternary relation BEL among believers, propositions, and some third type of thing, perhaps something like ways of taking propositions. My account thus makes such epistemic concepts as apriority and aposteriority relative concepts. As I have just admitted, one must take the proposition content in a particular way in order to recognize that a given sentence is true without an empirical investigation, simply by understanding it (reflecting on its content, etc.).

I did not argue, however, that belief is sentence relative. In fact, I do not say that belief is a ternary relation. Belief, on my view (as on the views of Frege, Alonzo Church, et al.), is a binary relation between believers and propositions. If the concept of belief is considered to be a relative concept on my account, it is not sentence relative but way-of-taking relative: one believes a given proposition under one way of taking it but not under another (where we understand ‘A believes p under x’ to mean that BEL[A, p, x]). More generally, our ‘epistemic access to propositions’ (Bertolet) is not sentence relative but way-of-taking relative. For ‘Paderewski’-type reasons, ways-of-taking propositions cannot be identified with sentences in a language (and indeed ways-of-taking things generally cannot be identified with expressions generally).12 Sentences are too coarse-grained. Furthermore, even in the more typical case (‘Cicero was talented’ rather than ‘Paderewski was talented’), a sentence in a language does not determine a unique way of taking its content except relative to a particular speaker.13

One can define, in a fairly natural and straightforward way, something like a sentence relative notion of sentential apriority—I shall call it s-apriority—in terms of the traditional (proposition-based rather than sentence-based) notion of apriority and my notion (proto-notion?) of a way of taking a proposition. We may say that a true sentence S is s-apriori with respect to a speaker A if something like the following obtains:

(D1) The proposition content of S (with respect to some [A's] context) is knowable [by A] by reflection (including deductive reasoning) while taking that proposition in the way A does when it is presented to A by means of (A's version of) S, without recourse to experience and without taking the proposition in some alternative way.14

We would then say that a true sentence is s-aposteriori with respect to A if its content (with respect to some [A's] context) is knowable [by A] but the sentence itself is not s-apriori with respect to A. One may similarly define, in a parallel manner, relative notions of s-informativeness and s-triviality. Then presumably, ‘Cicero is Tully’ would be s-aposteriori rather than s-apriori, and s-informative rather than s-trivial, with respect to someone who has learned the names ‘Cicero’ and ‘Tully’ but has not learned that they are two names of the same man. This comes mighty close to the claim that ‘Cicero is Tully’ is ‘a posteriori’ and ‘informative’.

We can also define absolute notions in terms of these relative notions. The most natural definition for absolute sentential s-apriority would be something like the following, where the metalinguistic variable ‘S’ ranges over true sentences:

(D2)  

S is s-apriori (simpliciter) = def. S is [could be] s-apriori with respect to someone or other.

A true sentence would then be s-aposteriori (simpliciter) if its content (with respect to some context and time) is knowable but the sentence itself is not s-apriori (simpliciter), i.e. if it is not [could not be] s-apriori with respect to anyone. Alternatively, one might define an absolute notion of sentential s-apriority in terms of a sentence's being s-apriori with respect to everyone who understands the sentence. This yields a correspondingly wider notion of s-aposteriority simpliciter, defined in terms of a sentence's failing to be s-apriori with respect to someone or other. I choose the former definitions for the absolute notions, in part, because it seems more natural to say that a sentence is s-apriori, than it is to say that it is s-aposteriori, whenever it is s-apriori with respect to at least some speakers, even if it might turn out to be s-aposteriori with respect to other speakers. For in that case, the content is still knowable independently of experience. Under the alternative definitions, situations like ‘Ketchup is catsup’ threaten to preclude any sentence from being deemed ‘s-apriori’.

IV

I willingly concede, and even insist, that all of these epistemic notions are perfectly legitimate, and indeed epistemologically significant. But I would also note several additional features. First and foremost, none of these notions is identical with the traditional, proposition-based notions of apriority and aposteriority. Second, strictly speaking the proposed relative notions are not sentence they are speaker relative. (The ‘s’ in ‘s-apriori’ stands for ‘speaker relative’.) Also, they are probably undefined for cases like that of ‘Tomatoes are tomatoes’ vis à vis my native Santa Barbaran, or of ‘Paderewski is Paderewski’ vis à vis Kripke's character Peter, who does not realize that the pianist and the statesman are one and the same. For there is no single way of taking the trivial proposition that Paderewski is Paderewski that counts as the way that Peter takes it when it is presented to him by means of the sentence ‘Paderewski is Paderewski’. (There are at least three different ways that Peter might take the proposition when it is so presented to him, depending on how he thinks the sentence is intended: The pianist is the pianist; the statesman is the statesman;

the pianist is the statesman—if I may put the point this way.15 ) Furthermore, the proposed absolute notion of s-apriority does not support that claim that ‘Cicero is Tully’ is ‘a posteriori’. A scholar who understands the sentence ‘Cicero is Tully’ and knows that it is true (e.g. any philosopher of language who knows that ‘Cicero’ and ‘Tully’ are co-referential, and to whom the names both refer), at least if that scholar happens to be a Millian, may treat the names more or less interchangeably. Such a scholar is liable to take the proposition that Cicero is Tully, when thus expressed, in much the same way he or she would take it were it put instead by means of ‘Cicero is Cicero’.16 If such patently analytic sentences as ‘Tomatoes are tomatoes’ and ‘Paderewski is Paderewski’ are to be counted s-apriori, then so is ‘Cicero is Tully’. Last but not least, the notions of s-apriority and s-aposteriority are no more (albeit no less) natural or fundamental to the spirit of my view of our cognitive access to propositions than is the corresponding name relative notion of love natural or fundamental to the spirit of Everyman's view of love. (According to the name relative notion of love, Mrs. Jones, who does not realize that the demented grave-robber she loves is none other than her husband, may be described as loving someone qua ‘Jones the Ripper-Offer’ but no longer qua ‘Hubby Dear’.17 ) The proposed relative notions are derivative, contrived, nonbasic.

A less contrived notion would be a way-of-taking relative notion of sentential apriority. We may say that a true sentence S is w-apriori with respect to a way x of taking a proposition—or as I shall say instead, that S is simply a priori with respect to x—if something like the following condition obtains:

(D3) x is a way of taking the proposition content of S (with respect to some context and time) and that proposition is knowable [by the agent of the context] by reflection (including deductive reasoning) while taking the proposition in way x, without recourse to experience and without taking the proposition in some alternative way.

A true sentence would be a posteriori with respect to a way x of taking a proposition if the sentence's proposition content (with respect to some context and time) is knowable and x is a way of taking that proposition, but the sentence itself is not a priori with respect to x. We may thus say that whereas ‘Paderewski is Paderewski’ is a priori with respect to some ways of taking its proposition content, it is still a posteriori with respect to others (the pianist is the statesman).

These way-of-taking relative notions are arguably the basic ones on my view.18 But even they are not identical with the traditional, proposition-based ones. (Compare the relationship between BEL and belief.) More importantly, they do not support

the claim that ‘Cicero is Tully’ is ‘a posteriori’, any more than the proposed absolute notions of s-apriority and s-aposteriority do. As we saw above, although ‘Cicero is Tully’ is a posteriori with respect to some ways of taking its content, a Millian philosopher who both understands the sentence and knows that it is true is liable to take its content in a way with respect to which the sentence is a priori rather than a posteriori. The fact that the sentence is a priori with respect to at least one way of taking its content is sufficient for the sentence to be a priori (simpliciter)—otherwise even ‘Tomatoes are tomatoes’ and ‘Paderewski is Paderewski’ should be counted ‘a posteriori’. Accordingly, if the way-of-taking relative notions of sentential apriority and aposteriority are taken as basic, something like the following definition (where ‘S’ ranges over true sentences) for absolute sentential apriority may be taken in place of more conventional definitions:

(D4)  

S is a priori (simpliciter) = def. S is [could be] a priori with respect to some way of taking a proposition.

As usual, a true sentence would be a posteriori (simpliciter) if its proposition content (with respect to some context and time) is knowable but the sentence itself is not a priori (simpliciter). Here this means that, although its content is knowable, the sentence is not [could not be] a priori with respect to any way of taking a proposition.

Recognition of the fact that ‘Cicero is Tully’ is a priori simpliciter is crucial to finding a philosophically satisfactory solution to Frege's Puzzle: In the relevant sense, ‘Cicero is Tully’ does not differ in epistemological status from ‘Cicero is Cicero’. Combined with results obtained in earlier work, this yields the further result that the theory of direct reference does not have the consequence, which had been claimed, that there are (nontrivial) examples of necessary a posteriori sentences.19 About the closest I am able to come to accommodating the claim that ‘Cicero is Tully’ is necessary even though ‘a posteriori’ is to acknowledge that ‘Cicero is Tully’ is not only necessary but is also [could also be] s-aposteriori with respect to some speakers, in particular with respect to anyone who understands (his or her version of) the sentence without knowing that it is true.

I had criticized Donnellan's account on the grounds that it assumes that ‘Cicero is Tully’ and ‘Cicero is Cicero’ differ in epistemological status, judging ‘Cicero is Tully’ a posteriori even though ‘Cicero is Cicero’ is a priori.20 I am persuaded, however, that

Donnellan should be interpreted instead as making a different claim, one which I may be able to accept. He may be saying, for example, merely that (as we now put it) ‘Cicero is Tully’ is [could be] s-aposteriori with respect to anyone who understands the sentence but does not know that it is true. If so, I was indeed wrong to group him with other direct-reference theorists (such as my former self) who have maintained that ‘Cicero is Tully’ is a posteriori (simpliciter). However, I would still urge the several points made in the opening paragraph of this section in response. The fact that ‘Cicero is Tully’ is s-aposteriori with respect to anyone who understands it without knowing that it is true does not distinguish that sentence from ‘Ketchup is catsup’.

V

Though identity sentences like ‘Cicero is Tully’ are every bit as a priori as the theorems of mathematics, the original motivation for the claim that ‘Cicero is Tully’ is a posteriori probably did not focus on the epistemology of its content. One indication of this comes by way of the complementary claim that had been made by some direct-reference theorists—notably Kripke and David Kaplan—that sentences like ‘The Standard Bar is exactly one meter long’ and ‘Newman-1 will be the first child born in the 22nd Century’ are a priori despite their contingency, if the reference of the term ‘meter’ is fixed by the description ‘the length of the Standard Bar’ and if the name ‘Newman-1’ is similarly ‘defined’ as ‘the first child to be born in the 22nd Century’.21 Those who declare such sentences a priori may not have intended thereby to separate the propositional contents of those sentences on epistemological grounds from knowledge gained by measuring a bar's length or by looking at one's watch at the time of a birth. Direct-reference theorists who deem ‘Cicero is Tully’ a posteriori, or the ‘meter’ and ‘Newman-1’ sentences a priori, sometimes seem to mean something more linguistic. Their principal concern seems to be not with our knowledge of the contents of the sentences in question, but with the means by which we know that the sentences themselves are true. At the same time, they may mean something less epistemological than, for example, the observation that the truth in English of ‘Cicero is Tully’ is knowable only by means of experience. We have seen that the question of whether particular English sentences are true or false—even logically valid sentences—is an empirical matter. This is partly because the question of what any particular English sentence means is itself an empirical matter; even the Queen of England does not have innate knowledge of the language. What originally prompted the claim that the ‘meter’ and ‘Newman-1’ sentences are a priori, however, was the recognition that those sentences belong, in some sense, with those for which knowledge of the meaning—however empirical that knowledge may be—is sufficient to establish

their truth.22 Likewise, the main point behind the claim that ‘Cicero is Tully’ is a posteriori may not be to mark that sentence off from the nonempirical sciences, but instead to mark it off from those sentences for which mere understanding is sufficient to establish their truth.

In what sense is our understanding of a sentence something that is sufficient in some cases and not in others to establish the sentence's truth? Understanding the mathematical equation ‘5,278 + 3,639 = 8,927’ involves knowing that the equation is true in standard mathematical notation if and only if the sum of 5,278 and 3,639 is 8,927.23 One can thereby establish the falsity of the equation by an a priori calculation. But this involves something beyond merely understanding the equation. It involves arithmetic. If the notion of understanding being sufficient to establish truth is to differ in extension from that of semantic content being knowable independently of experience by excluding both this case and ‘Cicero is Tully’, and by including the ‘meter’ and ‘Newman-1’ sentences, the former notion needs to be made more precise, or at least clearer.

Let us draw a distinction between pure semantics and applied semantics. It is a purely semantic fact about English that the definite description ‘the inventor of bifocals’ refers to (denotes, designates) the inventor of bifocals. It is also a semantic fact about English that ‘the inventor of bifocals’ refers to Benjamin Franklin. But the latter is a fact of applied semantics; it obtains partly in virtue of the nonlinguistic historical fact that it was Benjamin Franklin who invented bifocals. Similarly, whereas it is a purely semantic fact about English that ‘Snow is white’ is true if and only if snow is white, it is an applied semantic fact that ‘Snow is white’ is true. Certain sentences are special in that their truth value is settled entirely by pure semantics. It is a purely semantic fact about English for example that ‘Cicero is Cicero’ is true. For this fact is a logical

consequence of the purely semantic fact that ‘Cicero is Cicero’ is true if and only if Cicero is Cicero.

The notion of a sentence's truth being a fact of pure rather than applied semantics is, roughly, a notion of ‘truth solely by virtue of meaning’.24 The epistemologically charged term ‘a priori’ is less appropriate for this notion than the more semantic epithet ‘analytic’. Nevertheless, I have often felt that this form of analyticity as truth-by-virtue-of-pure-semantics may be what is meant by particular uses of ‘a priori’.25 The notion does have an epistemological dimension: for any sentence whose truth value is a logical consequence of pure semantics, anyone competent in the language is ipso facto in possession of sufficient information to determine that truth value by logic—never mind that knowledge of pure semantics for a natural language, and hence competence in the language, is gained only by means of experience.

Correspondingly, what is meant by the claim that ‘Cicero is Tully’ is ‘a posteriori’ may be that the sentence's truth is a fact of applied rather than pure semantics for English. The resulting claim—which is supposed to be a consequence of direct reference—that certain sentences, including ‘Cicero is Tully’, are necessary even though their truth is a fact of applied rather than pure semantics (i.e. synthetic yet necessary) may or may not be as surprising or remarkable in the present philosophical age as the

claim that some necessary truths are knowable only by means of experience. (Consider the mathematical equation, for example, or a priori principles of metaphysics.) But it is hardly devoid of philosophical significance.

Is it the case, though, that the fact that ‘Cicero is Tully’ is true is not a purely semantic fact about English? Certainly a speaker who is in full command of the language may nevertheless fail to know that ‘Cicero is Tully’ is true. Even a master logician who is fully competent in the use of ‘Cicero’, ‘Tully’, and the ‘is’ of identity may be in no position to infer that ‘Cicero is Tully’ is true from the purely semantic fact that ‘Cicero is Tully’ is true if Cicero is Tully. On the other hand, it is a purely semantic fact that ‘Cicero’ refers to Cicero, and it is also a purely semantic fact that ‘Tully’ refers to Tully. The latter, according to the Millian view, is identical with the fact that ‘Tully’ refers to Cicero. And it is a truth of logic that if ‘Cicero’ and ‘Tully’ both refer to Cicero, then there is something to which both names co-refer. Given the purely semantic facts for English, it follows that ‘Cicero is Tully’ is true. Alternatively, it is a fact of pure semantics for English that ‘Cicero is Tully’ is true if Cicero is Tully. According to Millianism, that Cicero is Tully is nothing more than the logical truth about Cicero that he is him. On the Millian theory, then, ‘Cicero is Tully’ is ‘a priori’ even in the sense that its truth is logically settled by pure rather than applied semantics. It is true solely by virtue of meaning.

Why is the master logician unable to infer by modus ponens that ‘Cicero is Tully’ is true from his a priori knowledge concerning Cicero that he is him, if the latter is really nothing less than knowledge of the fact that Cicero is Tully? The answer is that if the logician does not already know that ‘Cicero is Tully’ is true, he or she knows the conditional fact about English that ‘Cicero is Tully’ is true if Cicero is Tully only by taking that proposition in a way that does not reveal the special logical status of its antecedent; the logician does not recognize the antecedent proposition, so taken, as the truism concerning Cicero that he is him. The logician is in the same boat as the speaker who understands ‘Ketchup is catsup’ without knowing that it is true.26

It is difficult for the direct-reference theorist to escape our conclusion: Identity sentences like ‘Cicero is Tully’ are neither informative nor a posteriori, nor s-aposteriori, nor is their truth a matter of applied rather than pure semantics. ‘Cicero is Tully’ and ‘Ketchup is catsup’ are birds of a feather. Both are a priori and s-apriori, uninformative and trivial. Indeed, both are equally analytic.27


10 Analyticity and Apriority (1993)*

Nathan Salmon

The logical positivists invoked various notions of analyticity, or ‘truth by convention’, to explain the special modal and epistemological character of logic and mathematics, as well as of other nonempirically based assertions. The central idea of at least one version of the argument is that the postulates of, for example, arithmetic, do not describe independently existing fact, and instead constitute linguistic conventions, which represent decisions to use expressions in a certain way, with such-and-such meaning. Such decisions are ‘conventions’ in the sense that alternatives were available and furthermore the choices made among the alternatives do not require epistemic justification. Rather, they are to be justified on pragmatic grounds.1

On reflection, the fundamental claim that the postulates of arithmetic (or of any other subject) require no epistemic justification is really quite puzzling. In fact, conventionalism is based on serious philosophical errors. A linguistic convention which is supposed to be justified pragmatically rather than epistemically is not strictly a piece of cognitive information at all. It is not a truth or a fact; it is a decision, a commitment, a resolve. It is precisely because one's stipulations are in this way prescriptive rather than descriptive, that the justification for their adoption is pragmatic rather than epistemic. This feature already poses a significant challenge for the conventionalist account of the arithmetic postulates and of other a priori statements (statements whose contents are knowable independently of experience). The famous Peano Postulates, for example, describe paradigmatic facts concerning natural numbers; it is generally presumed that they state necessary facts that are knowable a priori. Linguistic conventions, while they are not themselves facts, do of course create, or give rise to, facts. That a particular expression, ‘successor’ for example, has the meaning it does—even when that meaning was secured by explicit stipulation—is every bit a knowable fact. But the linguistic convention per se, the resolve to use the expression with that meaning, is not the right sort of thing to be a piece of knowledge, properly speaking. Furthermore, the facts to which conventions give rise are, by the very nature of their source, contingent rather than necessary, and knowledge of those facts

end p.183


is generally a posteriori (epistemically justified only by way of experience) rather than a priori. This poses a further, serious difficulty for the conventionalist's attempt to accommodate the necessary apriority of mathematics. I think it ultimately impossible that these pressing challenges to conventionalism can be satisfactorily met.2

There is a related problem with the conventionalist idea that the postulates of arithmetic, or of some other subject, are conventions for which a pragmatic rather than epistemic justification is appropriate, and with the related notion that, as David O. Brink put it, ‘convention is the mother of necessity’,3 i.e. that the necessity of mathematics has its source in convention. I strongly suspect that these conventionalist ideas involve a conceptual confusion, one that remains widespread in contemporary analytic philosophy. Essentially, it is the failure to distinguish between the semantic cognitive content of a declarative sentence S and the logically independent, metatheoretic proposition that S itself is true.4

To take an example of a widely discussed linguistic convention, consider the sentence

(M)  

The Standard Bar (assuming it exists) is exactly one meter long at time t,

in the context of someone's having introduced the expression ‘meter’ as a word for a unit of length which is exactly the length at time t of a particular stick, the Standard Bar. We assume the Standard has a particular length at t. Let l be that length. The decision to use the word ‘meter’ as a name for l, together with the semantic facts created by this decision, must be sharply distinguished from the independent, pre-existing fact about the Standard Bar that it has the very length l at t. As we have seen, it is arguable—and indeed it is part of at least one version of the conventionalist account—that the decision to use ‘meter’ in this way is not a piece of knowledge, since it is not a natural, extralinguistic fact but a man-made convention, a resolve, and that therefore a pragmatic rather than an epistemic justification is appropriate. The stipulation creates or gives rise to the fact that the phrase ‘one meter’ designates the length l of the Standard at t, and hence also the fact that the sentence (M) is true. Nevertheless, the fact that the Standard has the particular length l at t is in no way a result of linguistic stipulation or decision. That fact, unlike the semantic facts concerning ‘one meter’ and (M), would have obtained regardless of whatever linguistic conventions one might have chosen to adopt. As Saul Kripke observed in opposition to Wittgenstein's cryptic remarks concerning this example, the fact that the Standard

is one meter long at t is surely a statable piece of knowledge, and one that obtains only contingently.5

When philosophical questions concerning the epistemological status of a particular sentence are under investigation—whether it is a sentence from theoretical science, from mathematics, or from everyday life—our concern is not one of providing an historical or causal explanation of how the sentence came to be true (or perhaps I should say assertable), but one of providing a philosophical account of how one might come to know the proposition that is the cognitive content of the sentence. In particular, even if it is taken as settled that the decisions or conventions that resulted in the truth of (M) require only pragmatic justification, and even if it is taken as settled that the resulting fact that (M) is true is thereby knowable somehow a priori, we must consider anew the justification for the fact semantically described or encoded by (M).

How is knowledge of the fact semantically described or encoded by (M) to be justified? Sentence (M) and others like it have been offered by Kripke and David Kaplan, and discussed by many others, as nontrivial counterexamples to the thesis—which was the dominant view among the logical positivists—that any proposition that is knowable a priori is true by necessity.6 The following similar, and in some respects purer, example of what is alleged to be the same phenomenon is due to Kaplan. If one introduces the expression ‘Newman-1’ as a name for the first child to be born in the twenty-second century, then the sentence

(N)  

If anyone will be the first child born in the twenty-second century, it will be Newman-1

is supposed to describe a fact that might have been otherwise yet is knowable a priori by the speaker who adopts this convention.7 If Kaplan and Kripke are correct, one might try to make a case, along the conventionalist's lines, for the claim that (M) and (N) are justified pragmatically rather than epistemically. (I ignore for present purposes the significant fact mentioned above that a decision or convention that is justified pragmatically rather than epistemically is not properly termed ‘a priori’, since it is not strictly a knowable fact at all.) However, Keith Donnellan and a few others, citing the distinction mentioned earlier between the semantic content of a sentence S and

the metatheoretic proposition that S is true, criticized Kaplan's and Kripke's account of the epistemological status of sentences like (M) and (N).8 Exposing a fallacy in Kripke's treatment of the matter, Donnellan argued persuasively that knowledge of the facts described by (M) and (N) are knowable only a posteriori (i.e. by means of experience), requiring a straightforwardly empirical justification.

I believe, with Donnellan and company, that (M) and (N) fail as examples of the contingent a priori.9 The fact described by (M) is a nonlinguistic fact concerning the length of a particular object. That the Standard has length l is paradigmatically a posteriori. In fact, I propose to turn Kaplan and Kripke on their heads by taking these same examples a step further. It is my contention that these very same examples may be seen as demonstrating the falsity of an even more cherished thesis, virtually unchallenged in analytic philosophy: that all analytic sentences—or, if one prefers, all sentences that are true by convention—state facts that are knowable a priori.

Whether (M) and (N) qualify as genuinely analytic, or true by convention, depends in large measure on precisely what is meant in calling a sentence ‘analytic’ or ‘true by convention’. A number of definitions or explications of analyticity have been proposed. My favorite is a proposal by Hilary Putnam. In an exposition of W. V. Quine's famous (if little understood) attack on the analytic–synthetic distinction, Putnam suggests that a sentence may be termed ‘analytic’ if it is deducible from the sentences in a finite list at the top of which someone who bears the ancestral of the graduate-student relation to Carnap has printed the words ‘Meaning Postulate’.10 This definition not only acknowledges the central importance of Carnap's contribution to the role of the analytic–synthetic distinction in analytic philosophy, but it has the additional virtue that it accords to those few among us who bear this special relationship to Carnap an authority that strikes me as only fitting. Unfortunately, there are those who fail to appreciate the virtues of Putnam's definition. For them I should like to propose a variation on Carnap's own explication of analyticity.

In his Introduction to Semantics, Carnap distinguished between what he called pure semantics and descriptive semantics.11 Descriptive semantics was concerned with the

semantical features of a natural language, with all its diachronic vicissitudes, while pure semantics was concerned exclusively with artificial languages (‘semantical systems’) whose semantics is stipulated. The former was an empirical science, whereas the latter consisted entirely of definitions for semantical expressions like ‘designates-in-L’ and ‘true-in-L’ and their logical consequences. Carnap's distinction between descriptive and pure semantics corresponds roughly to the distinction between a law of nature and a law passed by the legislature. Although Carnap did not explicitly propose doing so, his notion of pure semantics might have been extended to cover artificial bits of a natural language, as for example the name ‘Newman-1’ or, perhaps, certain legislative decrees by L’ Academie francaise.

The definition of analyticity that I propose is based on a somewhat different distinction, between what I call pure semantics and applied semantics, analogous to the distinction between pure and applied mathematics. It is a purely semantic fact about English that the definite description ‘the inventor of bifocals’ designates (denotes, refers to) the inventor of bifocals. It is also a semantic fact about English that ‘the inventor of bifocals’ designates Benjamin Franklin. But the latter is a fact of applied semantics; it obtains partly in virtue of the nonlinguistic, historical fact that it was Benjamin Franklin who invented bifocals. Similarly, whereas it is a purely semantic fact about English that ‘Snow is white’ is true if and only if snow is white, it is an applied semantic fact that ‘Snow is white’ is true. As with Carnap's notion, pure semantics, in my sense, consists of appropriate recursive definitions for semantic expressions like ‘true-in-L’ and ‘designates-in-L’ and their logical consequences. For Carnap, however, any semantical matter concerning a natural language—including its pure semantics, in my sense—was ipso facto a matter of descriptive semantics. With my notion of pure semantics, the language L whose semantics is under consideration may be ‘historically given’, the product of natural evolution rather than of legislation. On the other side of the coin, the ‘appropriateness’ of the semantic definitions is crucial for my notion. A definition for truth-in-English that has the consequence that ‘Snow is white’ is true if and only if grass is green, while it may not involve any falsehood, is inappropriate. It has smuggled in some applied semantics.12

Certain sentences are special in that their truth value is settled entirely by pure semantics. It is a purely semantic fact about English for example that ‘All married men are married’ is true. For this fact is a logical consequence of the purely semantic fact that ‘All married men are married’ is true if and only if all married men are married. My proposal, finally, is that we call a true sentence ‘analytic’ if its truth is in this way a fact of pure rather than applied semantics.13 This notion is related to Carnap's

notion of ‘L-truth’, which he proposed as constituting an explication equally of analyticity and of necessity—although L-truth corresponds more closely to (and indeed is an important precursor to) the contemporary notion of logical truth as truth in all models for the language.14

The proposed definition includes certain sentences in addition to those that have the form of a logical validity. A sentence like ‘All husbands are married’, assuming ‘husband’ is synonymous with ‘married man’ also qualifies as analytic under the definition. For it is a purely semantic fact about English that the adjective ‘married’ (correctly) applies to all married individuals, and it is also a purely semantic fact that the noun ‘husband’ applies only to married men. In fact, assuming ‘husband’ and ‘married man’ are synonymous, the purely semantic fact that ‘husband’ applies only to husbands is identical with the fact that ‘husband’ applies only to married men. It is a truth of logic that if ‘married’ applies to all married individuals and ‘husband’ applies only to married men, then ‘married’ applies to any individual to which ‘husband’ applies. Given the further purely semantic fact that the English construction ‘All Ns are A’ is true if and only if the adjective A applies to anything to which the NP N applies, it follows that ‘All husbands are married’ is true. Alternatively, it is a fact of pure semantics for English that ‘All husbands are married’ is true if all husbands are married. That all husbands are married is nothing more than the logical truth that all married men are married. The truth of ‘All husbands are married’ is thus logically settled by pure rather than applied semantics.

Let us return to sentence (N). Given the manner in which the designation of ‘Newman-1’ is fixed, the fact that ‘Newman-1’ designates the first child to be born in the 22nd Century, and hence also the resulting fact that (N) is true, are facts of pure rather than applied semantics. One may also say, therefore, that (N) is analytic; it is, in a straightforward sense, true by convention. Similarly for (M).15 Indeed, the truth of either sentence is settled by ‘pure semantics’ in both Carnap's sense (as extended above to incorporate stipulated bits of natural language) and my own.

The notion of a sentence's truth being a logical consequence of pure rather than applied semantics is, roughly, a notion of ‘truth solely by virtue of meaning’.16 The

epistemologically charged term ‘a priori’ is less appropriate for this notion than the more semantic epithet ‘analytic’. Nevertheless, I have often felt that this form of analyticity may be what is meant by particular uses of ‘a priori’.17 The notion of truth-as-a-consequence-of-semantics-alone does have an epistemological dimension: for any sentence whose truth value is a logical consequence of pure semantics, anyone competent in the language is ipso facto in possession of sufficient information to determine that truth value by logic—never mind that knowledge of pure semantics for a natural language, and hence competence in the language, is gained only by means of experience. This might explain the Kaplan–Kripke stance with respect to (M) and (N). What originally prompted the claim that those sentences are a priori was the recognition that they belong, in some sense, with sentences for which knowledge of the meaning—however empirical that knowledge may be—is sufficient to establish their truth.18

Even if (M) and (N) are declared analytic, it is widely recognized nowadays that it does not follow that their contents are necessary truths. Still, it is usually assumed that the content of any sentence that is true solely by virtue of meaning is a priori. I maintain that (M) and (N), though analytic in the suggested sense, are both contingent and a posteriori; their contents are not only contingent but also knowable only by means of experience. Whereas the philosophical significance of the existence of propositions that are both contingent and a priori is apparent, the philosophical significance of the fact that such conventionally true sentences as (M) and (N) express contingencies even though their truth is a matter of pure semantics is less so. One consequence (noted by Kaplan, in ‘Demonstratives’, p. 540) is that Quine was wrong to see the ‘second grade of modal involvement’ as recasting analyticity, which is a meta-theoretic notion, as the object-language notion of necessity. Carnap was equally wrong to identify necessity with truth by pure semantics.

If I am correct, another consequence is that analyticity, in this sense, is no more a guarantee of apriority (knowability independently of experience) than it is of necessity. In order to explain the special modal and epistemological status of necessary a priori sentences, it is not sufficient to assert (whether rightly or wrongly) that they are analytic, or true by convention.

Consider the following mathematical postulate:

(P)  

0x0003c0is the ratio of the circumference of a circle to its diameter (if there is a fixed such ratio).

It is very plausible that the term ‘0x0003c0’ is, in some sense, defined by (P). This is in fact significantly more plausible than the prospect that the expressions ‘natural number’, ‘0’, and ‘successor’ are somehow implicitly but simultaneously defined by the Peano Postulates.19 For (P) at least determines the extension of ‘0x0003c0’. Indeed, the truth of (P) is analogous in many ways to the truth of (M) and (N). To use Kripke's phrase, the definite description ‘the ratio of the circumference of a circle to its diameter’ fixes the reference of ‘0x0003c0’, without thereby turning ‘0x0003c0’ into a synonym for the description.20 One point of disanalogy with the case of (M) and (N) is that the reference-fixing definite description involved here is a rigid designator; (P) contains a necessary truth. The various analogies with (M) and (N), however, amply demonstrate that the analyticity, or conventional truth, of (P) does not account for its necessity—otherwise (M) and (N) should be necessary as well. An alternative account is required.

A second striking disanalogy with the case of (M) and (N) is that it is not at all plausible that (P) is a posteriori. The epistemic justification of purely mathematical knowledge is very different from that concerning the lengths of bars and the birthdates of persons. On the other hand, the central point of analogy remains: the epistemic justification for the mathematical fact described by (P) is independent of the justification for the metamathematical fact that (P) is true. In order to know that (P) is true, one need only know how ‘0x0003c0’ is defined. That is pure semantics. It is also a posteriori. To say that (P) is not a posteriori, however, is not yet to say that it is a priori. For it is arguable that the content of (P) is not knowable at all. Exactly what is involved in coming to know of the number, 0x0003c0, that it is the ratio of the circumference of a circle to its diameter (assuming there is such a ratio)—and even the question of whether it is possible for us to gain this purely mathematical, nonsemantic knowledge—are vexing matters that raise delicate issues in the philosophy of mathematics and epistemology generally.21 The analyticity of (P) is of no help here.


Part III Belief


11 Illogical Belief (1989)*

Nathan Salmon

I

My purpose here is to present a defense against some criticisms that have been leveled against various doctrines and theses I advanced in Frege's Puzzle,1 and to draw out some philosophically interesting applications and consequences of some of the central ideas utilized in my defense. The two principal objections I shall consider—one of which is offered by Saul Kripke and the other by Stephen Schiffer—as I reconstruct them, tacitly presuppose or assume one or both of a pair of closely related and largely uncontroversial principles concerning belief and deductive reasoning. The first is a normative principle, which I shall call the belief justification principle. It may be stated thus:

Suppose x is a normal, fully rational agent who consciously and rationally believes a certain proposition p. Suppose also that x is consciously interested in the further question of whether q is also the case, where q is another proposition. Suppose further that q is in fact a trivial deductive consequence of p. Suppose finally that x fully realizes that q is a deductive consequence of p and is fully able to deduce q from p. Under these circumstances, x would be rationally justified in coming to believe q on the basis of his or her belief of p (and its deductive relationship to q), or alternatively, if x withholds belief from q (by disbelieving or by suspending judgement) for independent reasons, x would be rationally justified in accordingly relinquishing his or her belief of p.

The second principle is similar to this, except that it is descriptive rather than prescriptive. I shall call it the belief closure principle:

Make the same initial-condition suppositions concerning x vis a vis the propositions p and q as given in the belief justification principle. Under these circumstances, if x consciously considers the question of whether q is the case and has adequate time for reflection on the matter, x will in fact come to believe q in addition to p on the basis of his or her belief of p (and its deductive relationship to q), unless x instead withholds belief from q (either by disbelieving or by suspending judgement) for independent reasons, and accordingly relinquishes his or her belief of p.

The belief justification principle, since it is normative rather than predictive, may seem somehow more certain and on sounder footing than the belief closure principle, but both principles are quite compelling. I shall claim that there are situations that present straightforward counter-examples to both principles simultaneously. Specifically, I claim that these principles fail in precisely the sort of circumstances to which my objectors tacitly apply the principles.

First, a preliminary exposition of the project undertaken in Frege's Puzzle is in order. The central thesis is that ordinary proper names, demonstratives, other single-word indexicals or pronouns (such as ‘he’), and other simple (noncompound) singular terms are, in a given possible context of use, Russellian ‘genuine names in the strict logical sense’.2 Put more fully, I maintain the following anti-Fregean doctrine: that the contribution made by an ordinary proper name or other simple singular term, to securing the information content of, or the proposition expressed by, declarative sentences (with respect to a given possible context of use) in which the term occurs (outside of the scope of nonextensional operators, such as quotation marks) is just the referent of the term, or the bearer of the name (with respect to that context of use). In the terminology of Frege's Puzzle, I maintain that the information value of an ordinary proper name is just its referent.

Some other theses that I maintain in Frege's Puzzle are also critical to the present discussion. One such thesis (which Frege and Russell both more or less accepted) is that the proposition that is the information content of a declarative sentence (with respect to a given context) is structured in a certain way, and that its structure and constituents mirror, and are in some way readable from, the structure and constituents of the sentence containing that proposition.3 By and large, a simple  (noncompound) expression contributes a single entity, taken as a simple (noncomplex) unit, to the information content of a sentence in which the expression occurs, whereas the contribution of a compound expression (such as a phrase or sentential clause) is a complex entity composed of the contributions of the simple components.4 Hence, the contents of beliefs formulatable using ordinary proper names, demonstratives, or other simple singular terms, are on my view so-called singular propositions (David Kaplan), i.e., structured propositions directly about some individual, which occurs directly as a constituent of the proposition. This thesis (together with certain relatively uncontroversial assumptions) yields the consequence that de re belief (or belief of) is simply a special case of de dicto belief (belief that). To believe of an individual x, de re, that it (he, she) is F is to believe de dicto the singular proposition about (containing) x that it (he, she) is F, a proposition that can be expressed using an ordinary proper name for x. Similarly for the other propositional attitudes.

There is an important class of exceptions to the general rule that a compound expression contributes to the information content of a sentence in which it occurs a complex entity composed of the contributions of the simple components. These are compound predicates formed by abstraction from an open sentence. For example, from the ‘open’ sentence ‘I love her and she loves me’—with pronouns ‘her’ and ‘she’ functioning as ‘freely’ as the free variables occurring in such open sentences of the formal vernacular as ‘F(a, x) & F(x, a)’—we may form (by ‘abstraction’) the compound predicate ‘is someone such that I love her and she loves me’. Formally, using Alonzo Church's ‘0x0003bb’-abstraction operator, we might write this ‘(0x0003bbx)[F(a, x) & F(x, a)]’. Such an abstracted compound predicate should be seen as contributing something like an attribute or a Russellian propositional function, taken as a unit, to the information content of sentences in which it occurs, rather than as contributing a complex made up of the typical contributions of the compound's components.

In addition to this, I propose the sketch of an analysis of the binary relation of belief between believers and propositions (sometimes Russellian singular propositions). I take the belief relation to be, in effect, the existential generalization of a ternary relation, BEL, among believers, propositions, and some third type of entity. To believe a proposition p is to adopt an appropriate favorable attitude toward p when taking p in some relevant way. It is to agree to p, or to assent mentally to p, or to approve of p, or some such thing, when taking p a certain way. This is the BEL relation. I do not say a great deal about what the third relata for the BEL relation are. They are perhaps something like proposition guises, or modes of acquaintance or familiarity with propositions,


or ways in which a believer may take a given proposition. The important thing is that, by definition, they are such that if a fully rational believer adopts conflicting attitudes (such as belief and disbelief, or belief and suspension of judgement) toward propositions p and q, then the believer must take p and q in different ways, by means of different guises, in harboring the conflicting attitudes toward them—even if p and q are in fact the same proposition. More generally, if a fully rational agent construes objects x and y as distinct (or even merely withholds construing them as one and the very same—as might be evidenced, for example, by the agent's adopting conflicting beliefs or attitudes concerning x and y), then for some appropriate notion of a way of taking an object, the agent takes x and y in different ways, even if in fact x=y.5 Of course, to use a distinction of Kripke's, this formulation is far too vague to constitute a fully developed theory of proposition guises and their role in belief formation, but it does provide a picture of belief that differs significantly from the sort of picture of propositional attitudes advanced by Frege or Russell, and enough can be said concerning the BEL relation to allow for at least the sketch of a solution to certain philosophical problems, puzzles, and paradoxes—including those in the same family as Frege's notorious ‘Hesperus’–‘Phosphorus’ puzzle.6

In particular, the BEL relation satisfies the following three conditions:

(i)  

A believes p if and only if there is some x such that A is familiar with p by means of x and BEL(A, p, x);7

(ii)  

A may believe p by standing in BEL to p and some x by means of which A is familiar with p without standing in BEL to p and all x by means of which A is familiar with p;


(iii)  

In one sense of ‘withhold belief’, A withholds belief concerning p (either by disbelieving or by suspending judgement) if and only if there is some x by means of which A is familiar with p and not-BEL(A, p, x).

These conditions generate a philosophically important distinction between withholding belief and failure to believe (i.e., not believing). In particular, one may both withhold belief from and believe the very same proposition simultaneously. (Neither withholding belief nor failure to believe is to be identified with the related notions of disbelief and suspension of judgement—which are two different ways of withholding belief, in my sense, and which may occur simultaneously with belief of the very same proposition in a single believer.)

It happens in most cases (though not all) that when a believer believes some particular proposition p, the relevant third relatum for the BEL relation is a function of the believer and some particular sentence of the believer's language. There is, for example, the binary function f that assigns to any believer A and sentence S of A's language, the way A takes the proposition contained in S (in A's language with respect to A's context at some particular time t) were it presented to A (at t) through the very sentence S, if there is exactly one such way of taking the proposition in question. (In some cases, there are too many such ways of taking the proposition in question.)

This account may be applied to the comic-book legend of Superman and his woman-friend Lois Lane. According to this saga, Lois Lane is acquainted with Superman in both of his guises—as a mild-mannered reporter and dullard named ‘Clark Kent’ and as the superheroic defender of truth, justice, and the American way, named ‘Superman’—but she is unaware that these are one and the very same person. Whereas she finds our hero somewhat uninteresting when she encounters him in his mild-mannered reporter guise, her heartbeat quickens with excitement whenever she encounters him, or even merely thinks of him, in his superhero guise. Consider now the sentence

(0)  

Lois Lane believes that Clark Kent is Superman.

Is this true or false? According to my account, it is true! For Lois Lane agrees to the proposition that Clark Kent is Superman when taking it in a certain way—for example, if one points to Superman in one of his guises and says ‘He is him’, or when the proposition is presented to her by such sentences as ‘Clark Kent is Clark Kent’ and ‘Superman is Superman’. That is,


BEL[Lois Lane, that Clark Kent is Superman, f(Lois Lane, ‘Superman is Superman’)].

Lois Lane also withholds belief concerning whether Superman is Superman. In fact, according to my account, she believes that Superman is not Superman! For she agrees to the proposition that Superman is not Superman when taking it in the way it is presented to her by the sentence ‘Clark Kent is not Superman’. That is,


BEL[Lois Lane, that Superman is not Superman, f(Lois Lane, ‘Clark Kent is not Superman’)],

and hence, since Lois Lane is fully rational, it is not the case that



BEL[Lois Lane, that Superman is Superman, f(Lois Lane, ‘Clark Kent is Superman’)].

II

It is evident that these consequences of my account do not conform with the way we actually speak. Instead it is customary when discussing the Superman legend to deny sentence (0) and to say such things as

(1)  

Lois Lane does not realize that Clark Kent is Superman.

According to my account, sentence (1) is literally false in the context of the Superman legend. In fact, (1)’s literal truth-conditions are, according to the view I advocate, conditions that are plainly unfulfilled (in the context of the Superman legend). Why, then, do we say such things as (1)? Some explanation of our speech patterns in these sorts of cases is called for. The explanation I offer in Frege's Puzzle is somewhat complex, consisting of three main parts. The first part of the explanation for the common disposition to utter or to assent to (1) is that speakers may have a tendency to confuse the content of (1) with that of

(1′)  

Lois Lane does not realize that ‘Clark Kent is Superman’ is true (in English).

Since sentence (1′) is obviously true, this confusion naturally leads to a similarly favorable disposition toward (1). This part of the explanation cannot be the whole story, however, since even speakers who know enough about semantics to know that the fact that Clark Kent is Superman is logically independent of the fact that the sentence ‘Clark Kent is Superman’ is true (in English, according to the legend), and who are careful to distinguish the content of (1) from that of (1′), are nevertheless favorably disposed toward (1) itself—because of the fact that Lois Lane bursts into uncontrollable laughter whenever the mere suggestion ‘Clark Kent could turn out to be Superman’ is put to her.

The second part of my explanation for (1)’s appearance of truth is that (1) itself is the product of a plausible but mistaken inference from the fact that Lois Lane sincerely dissents (or at least does not sincerely assent) when queried ‘Is Clark Kent Superman?’, while fully understanding the question and grasping its content, or (as Keith Donnellan has pointed out) even from her expressions of preference for the man of steel over the mild-mannered reporter. More accurately, ordinary speakers (and even most nonordinary speakers) are disposed to regard the fact that Lois Lane does not agree to the proposition that Clark Kent is Superman, when taking it in a certain way (the way it might be presented to her by the very sentence ‘Clark Kent is Superman’), as sufficient to warrant the denial of sentence (0) and the assertion of sentence (1). In the special sense explained in the preceding section, Lois Lane withholds belief from the proposition that Clark Kent is Superman, actively failing to agree with it whenever it is put to her in so many words, and this fact misleads ordinary speakers, including Lois Lane herself, into concluding that Lois harbors no favorable attitude of agreement whatsoever toward the proposition in question, and hence does not believe it.

The third part of the explanation is that, where someone under discussion has conflicting attitudes toward a single proposition that he or she takes to be two independent propositions (i.e. in the troublesome ‘Hesperus’–‘Phosphorus’, ‘Superman’–‘Clark Kent’ type cases), there is an established practice of using belief attributions to convey not only the proposition agreed to (which is specified by the belief attribution) but also the way the subject of the attribution takes the proposition in agreeing to it (which is no part of the semantic content of the belief attribution). Specifically, there is an established practice of using such a sentence as (0), which contains the uninteresting proposition that Lois Lane believes the singular proposition about Superman that he is him, to convey furthermore that Lois Lane agrees to this proposition when she takes it in the way it is presented to her by the very sentence ‘Clark Kent is Superman’ (assuming she understands this sentence). That is, there is an established practice of using (0) to convey the thought that


BEL[Lois Lane, that Clark Kent is Superman, f(Lois Lane, ‘Clark Kent is Superman’)].

III

The last part of the explanation just sketched may be clarified by considering an objection raised by Schiffer.8 Schiffer sees my theory as attempting to explain ordinary speakers' dispositions to utter or to assent to (1) by postulating that in such cases a particular mechanism, of a sort described by H. P. Grice,9 comes into play. The mechanism works in the following way: A speaker deliberately utters a particular sentence where there is mutual recognition by the speaker and his or her audience that the speaker believes the sentence to be false. The speaker and the audience mutually recognize that the speaker is not opting out of Grice's conversational Cooperative Principle (according to which one should make one's conversational contribution such as is required, at the stage at which it occurs, by the accepted purpose or direction of the conversation) and hence that the speaker is subject to the usual Gricean conversational maxims. Yet the speaker and audience also recognize that there is a prima facie apparent violation of the first conversational maxim of Quality: ‘Do not say what you believe to be false.’ The audience infers, in accordance with the speakers intentions, that the speaker is using the sentence not to commit himself or herself to its literal content (which is taken to be false) but instead to convey, or to ‘implicate’, some saliently related proposition, which is easily gleaned from the context of

the conversation. In the case of sentence (1), or this account, the speaker employs this mechanism to implicate that Lois Lane does not agree to the proposition that Clark Kent is Superman when she takes it in the way it is presented to her by the very sentence ‘Clark Kent is Superman’. Schiffer's criticism is that this account flies in the face of the obvious fact that ordinary speakers do not believe (1) to be false, but believe it true.

This criticism is indeed decisive against the explanation described above for our propensity to say such things as (1). But this is not the explanation I proposed in Frege's Puzzle. Oddly, the very example of sentence (1) comes from a particular passage in Frege's Puzzle that explicitly precludes Schiffer's interpretation:

Now, there is no denying that, given the proper circumstances, we say things like ‘Lois Lane does not realize . . . that Clark Kent is Superman’ . . . When we make these utterances, we typically do not intend to be speaking elliptically or figuratively; we take ourselves to be speaking literally and truthfully.(p. 81)

My pragmatic account of the appearance of truth in the case of such sentences as (1) is meant not only as an explanation of the widespread disposition to utter or to assent to (1), but equally as an explanation of the widespread intuition that (1) is literally true, and equally as an explanation of the widespread belief of the content of (1). What is needed, and what I attempt to provide (or at least a sketch thereof), is not merely an explanation of the disposition of ordinary speakers to utter or assent to (1) given the relevant facts concerning Lois Lane's ignorance of Superman's secret identity, but an explanation why ordinary speakers who understand (1) perfectly well, fully grasping its content, sincerely utter it while taking themselves to speaking literally and truthfully, without being exactly similarly disposed toward such synonymous sentences as

Lois Lane does not realize that Superman is Superman

when they also understand these sentences perfectly well and the common content of these sentences is something these speakers believe.10 The particular Gricean mechanism that Schiffer describes is no doubt part of the correct explanation in some cases of how ordinary speakers may use certain sentences to convey what these sentences do not literally mean. But the particular mechanism in question cannot yield a coherent account of why ordinary speakers believe that a given sentence is true. How would the alleged explanation go? ‘Here's why ordinary speakers believe that sentence S is true: They realize that it's false. This mutual recognition of its falsity enables them to use S to convey something true. Their use of S to convey something true leads them to conclude that S is true.’ This alleged explanation is incoherent; it purports to explain ordinary speakers' belief that a given sentence is true by means of their belief that it is false. Clearly, no attempt to explain the widespread view that (1) is literally true can

proceed from the initial hypothesis that ordinary speakers typically believe that (1) is literally false!

Schiffer's criticism concerns only the third part of the explanation sketched in the preceding section: the hypothesis that there is an established practice of using such a sentence as (0) to convey that Lois Lane agrees to the proposition that Clark Kent is Superman when taking it in the way it is presented to her by the very sentence ‘Clark Kent is Superman’. I do not claim that this practice came about by means of a special Gricean mechanism requiring the mutual recognition by the speaker and his or her audience that sentence (0) is literally true. Quite the contrary, I suppose that many ordinary speakers, and most philosophers, would take the proposition that they use the sentence to convey to be the very content of the sentence. That is why they would deem the sentence literally false. Schiffer describes a particular mechanism that allows speakers to use a sentence to convey (‘implicate’) what it does not literally mean by means of a mutual recognition that what is conveyed cannot be what the sentence literally means. I had in mind an alternative mechanism that allows speakers to use a sentence to convey something stronger than what it literally means, thereby creating a mutual misimpression that what is conveyed is precisely what the sentence literally means. There is nothing in the general Gricean strategy (as opposed to the particular strategy involving Grice's first conversational maxim of Quality) that requires ordinary speakers to recognize or believe that the sentence used is literally false. Grice describes several mechanisms that involve speakers' using a sentence mutually believed to be true to convey (‘implicate’) something further that the sentence does not literally mean, and Schiffer himself cites such a mechanism in the course of presenting his objection. Surely there can be such a mechanism that, when employed, sometimes has the unintended and unnoticed consequence that speakers mistake what is conveyed (‘implicated’) for the literal content. Consider, for example, the conjunction ‘Jane became pregnant and she got married’, which normally carries the implicature that Jane became pregnant before getting married. Utterers of this sentence, in order to employ it with its customary implicature, need not be aware that the sentence is literally true even if Jane became pregnant only after getting married. Some utterers may well become misled by the sentence's customary implicature into believing that the sentence literally means precisely what it normally conveys—so that, if they believe that Mary became pregnant only after getting married, they would reject the true but misleading conjunction as literally false. A similar situation may obtain in connection with certain English indicative conditionals (‘If you work hard, you will be rewarded’) and universal generalizations (‘All white male cats with blue eyes are deaf’), which carry an implicature of some salient connection between antecedent and consequent that is more than merely truth-functional ‘constant conjunction’. (The implicated connection need not be the temporal relation of earlier-later, as in the conjunction case.) It is this general sort of situation, or something very similar, that I impute to propositional-attitude attributions.11


Frege's Puzzle makes the suggestion that, in a certain type of case, a simple belief attribution 0x002308c believes that S0x002309 may be routinely used to convey the further information (not semantically encoded) that (assuming he or she understands his or her sentence for S) x agrees to the proposition p when taking it in the way it is presented to x by the very sentence S, where x is the referent of c and p is the content of the nonindexical sentence S.12 The book does not include the much stronger claim that the manner in which such a belief attribution is routinely used to convey this further information must exhibit all of the features that characterize Gricean implicature—let alone does it include the highly specific claim that the phenomenon in question is an instance of Gricean particularized conversational implicature.

I have not thoroughly explored the relation of Grice's many rich and fruitful ideas to the sort of project undertaken in Frege's Puzzle; obviously, there is a great deal more to be investigated. It should be clear, however, that there is nothing in Grice's general apparatus that makes the sort of explanation I have in mind in connection with propositional-attitude attributions altogether impossible. Quite the contrary, some of the central ideas of the Gricean program are obviously directly applicable.

IV

In Frege's Puzzle I explicitly applied the various doctrines and theses sketched in Section I above to Kripke's vexing puzzle about belief.13 Kripke considers a certain Frenchman, Pierre, who at some time t 1 , speaks only French and, on the basis of deceptive travel brochures published by the London Chamber of Commerce and the like, comes to assent to the French sentence ‘Londres est jolie’ (as a sentence of French), which literally means in French that London is pretty. At some later time t 2 , Pierre moves to London and learns the English language by direct assimilation (not by translation in an ESL course). Seeing only especially unappealing parts of the city, and not recognizing that this city called ‘London’ is the very same city that he and his fellow French speakers call ‘Londres’, Pierre comes to assent to the sentence ‘London is not pretty’ (as a sentence of English), while maintaining his former attitude toward the French sentence ‘Londres est jolie’. Kripke presses the following question: Does Pierre believe at t 2 that London is pretty? The puzzle arises from Kripke's forceful demonstration that both the assertion that Pierre does believe this, and the denial that he does, appear deeply unsatisfactory (for different reasons). Likewise, both the assertion that Pierre believes at t 2 that London is not pretty and the denial that he does appear deeply unsatisfactory.

What does my account say about Pierre's doxastic disposition at t 2 vis à vis the propositions that London is pretty and that London is not pretty? I maintain that he believes them both. For he understands the French sentence ‘Londres est jolie’ when he assents to it, fully grasping its content. That content is the proposition that London is pretty. Since he agrees to this proposition when he takes it in the way it is presented to him by the French sentence, he believes it. Exactly the same thing obtains with regard to the negation of this proposition and the English sentence ‘London is not pretty’. Hence he believes this proposition too. In fact, Pierre presumably also assents to the conjunctive sentence ‘Londres is pretty but London is not’, as a sentence of Frenglish, i.e. French-cum-English (French-English ‘word-salad’). And he understands this sentence in Frenglish. Hence he even believes the conjunctive proposition that London is pretty and London is not pretty. If he is sufficiently reflective, he will even know that he believes that London is pretty and London is not pretty. For given adequate time to reflect on the matter he can, with sufficient linguistic competence and ample epistemic justification, assent to the sentence ‘You, Pierre, believe that Londres is pretty but London is not’, taken as addressed to him as a sentence of Frenglish. The tri-part explanation sketched in Section II above may easily be extended to account for our propensity to say such things (in Frenglish) as ‘Pierre does not realize that London is Londres’ despite their falsity.

Kripke objects to the sort of account I offer of Pierre's situation with some trenchant remarks. I quote at length:

But there seem to be insuperable difficulties with [the position that Pierre believes both that London is pretty and that London is not pretty] . . . We may suppose that Pierre, in spite of the unfortunate situation in which he now finds himself, is a leading philosopher and logician. He would never let contradictory beliefs pass. And surely anyone, leading logician or no, is in principle in a position to notice and correct contradictory beliefs if he has them. Precisely for this reason, we regard individuals who contradict themselves as subject to greater censure than those who merely have false beliefs. But it is clear that Pierre, as long as he is unaware that the cities he calls ‘London’ and ‘Londres’ are one and the same, is in no position to see, by logic alone, that at least one of his beliefs must be false. He lacks information, not logical acumen. He cannot be convicted of inconsistency: to do so is incorrect.

We can shed more light on this if we change the case. Suppose that, in France, Pierre, instead of affirming ‘Londres est jolie,’ had affirmed, more cautiously, ‘Si New York est jolie, Londres est jolie aussi,’ so that [according to this account] he believed that if New York is pretty, so is London. Later Pierre moves to London, learns English as before, and says (in English) ‘London is not pretty’. So he now [allegedly] believes, further, that London is not pretty. Now from the two premises, both of which appear to be among his beliefs, (a) if New York is pretty, London is, and (b) London is not pretty, Pierre should be able to deduce by modus tollens that New York is not pretty. But no matter how great Pierre's logical acumen may be, he cannot in fact make any such deduction, as long as he supposes that ‘Londres’ and ‘London’ may name two different cities. If he did draw such a conclusion, he would be guilty of a fallacy.

Intuitively, he may well suspect that New York is pretty, and just this suspicion may lead him to suppose that ‘Londres’ and ‘London’ probably name distinct cities. Yet if we follow our normal practice of reporting the beliefs of French and English speakers, Pierre has available to him (among his beliefs) both the premises of a modus tollens argument that New York is not pretty. . . . (pp. 257–258)

. . . Pierre is in no position to draw ordinary logical consequences from the conjoint set of what, when we consider him separately as a speaker of English and as a speaker of French, we would call his beliefs. He cannot infer a contradiction from his separate [alleged] beliefs that London is pretty and that London is not pretty. Nor, in the modified situation above, would Pierre make a normal modus tollens inference from his [alleged] beliefs that London is not pretty and that London is pretty if New York is. . . . Indeed, if he did draw what would appear to be the normal conclusion in this case . . . , Pierre would in fact be guilty of a logical fallacy. (p. 262)

. . . The situation of the puzzle seems to lead to a breakdown of our normal practices of attributing belief . . . [The view that Pierre believes both that London is pretty and that London is not pretty] definitely get[s] it wrong. [That view] yields the result that Pierre holds inconsistent beliefs, that logic alone should teach him that one of his beliefs is false. Intuitively, this is plainly incorrect. . . . [It is] obviously wrong . . . [a] patent falsehood . . . (pp. 266–267)

. . . when we enter into the area exemplified by . . . Pierre, we enter into an area where our normal practices of interpretation and attribution of belief are subjected to the greatest possible strain, perhaps to the point of breakdown. So is the notion of the content of someone's assertion, the proposition it expresses.

. . . Pierre's [case] lies in an area where our normal apparatus for the ascription of belief is placed under the greatest strain and may even break down.(pp. 269–270)

These passages indicate (or at least strongly suggest) that Kripke rejects as ‘plainly incorrect’ the view, which I maintain, that Pierre believes at t 2 both that London is pretty and that London is not pretty.14

V

Schiffer raises a second objection to the theory advanced in Frege's Puzzle—one that is evidently similar in certain respects to Kripke's, but focuses more on the de re mode than on the de dicto. Schiffer's second criticism concerns such nesting (or second-level) propositional-attitude attributions as

(2)  

Floyd believes that Lois Lane does not realize that Clark Kent is Superman.

Schiffer tells a little story according to which Floyd is an ordinary speaker who is fully aware that the mild-mannered reporter is none other than the man of steel himself, and who is also aware of Lois Lane's ignorance of this fact. Schiffer argues that, whereas sentence (2) is straightforwardly true in the context of this little story—since Floyd believes that sentence (1) is true (and knows that if (1) is true, then Lois Lane does not realize that Clark Kent is Superman)—I am committed by my adherence to my central thesis (which Schiffer calls ‘the ‘Fido’–Fido theory of belief’) to the falsity of (2), and further by my account of the dispositions of ordinary speakers to utter or to assent to (1), to the erroneous claim that Floyd does not believe that sentence (1) is true, and instead believes it to be false.

We have seen in Section III above that, contrary to Schiffer's interpretation, the explanation I offer for Floyd's propensity to utter (1) does not involve the obviously false claim that Floyd believes (1) to be false. How is it that I am committed to the claim that Floyd does not believe that Lois Lane does not realize that Clark Kent is Superman, and hence to the falsity of (2)? Schiffer argues that I am thus committed by invoking a certain principle that concerns de re belief, and which he has elsewhere called ‘Frege's Constraint’.15 Actually, the principle Schiffer explicitly cites is inadequate for his purposes, and should be replaced by a pair of principles which together entail the cited principle. The first might be called ‘Frege's Thesis’ and may be stated (using Schiffer's theoretical apparatus and terminology) as follows:


If x believes y to be F, then there is an object m that is a mode of presentation of y and x believes y under m to be F.

The second principle, which I shall call ‘Schiffer's Constraint’, is the following (again stated using Schiffer's theoretical apparatus and terminology):


If a fully rational person x believes a thing y under a mode of presentation m to be F and also disbelieves y under a mode of presentation m′ to be F, then mmand x construes m and mas (modes of) presenting distinct individuals.

Together these two principles pose a serious obstacle to my taking the position, which seems undeniably correct, that sentence (2) is true. For Floyd, whom we may

suppose to be fully rational, no doubt believes that Lois Lane realizes that Superman is Superman. Yet given that Floyd is aware of Superman's secret identity, there do not seem to be the two modes of presentation required by Frege's Thesis and Schiffer's Constraint in order for Floyd to believe furthermore that Lois Lane does not realize that Clark Kent is Superman.

VI

Let us consider first Kripke's argument against the view that Pierre believes at t 2 both that London is pretty and that it is not. I briefly addressed Kripke's objection in Frege's Puzzle. I shall elaborate here on certain aspects of my reply.16

Kripke's primary critical argument might be stated in full thus:

P1:  

Pierre sees, by logic alone, that the propositions (beliefs) that London is pretty and that London is not pretty are contradictory.

P2:  

If Pierre has the beliefs that London is pretty and that London is not pretty, then he is in principle in a position to notice that he has these beliefs.

Therefore,

C1:  

If Pierre has the beliefs that London is pretty and that London is not pretty, then he is in principle in a position to see both that he has these beliefs and that they are contradictory.

P3:  

But Pierre, as long as he is unaware that the cities he calls ‘London’ and ‘Londres’ are one and the same, is in no position to see that the propositions (beliefs) that London is pretty and that London is not pretty are simultaneously beliefs of his and contradictory, and hence is in no position to see that at least one of his beliefs must be false.

Therefore,

C2:  

As long as Pierre is unaware that the cities he calls ‘London’ and ‘Londres’ are one and the same, it is incorrect to say that he has the beliefs that London is pretty and that London is not pretty.

An exactly similar argument may be stated, as Kripke proposes, replacing the belief that London is pretty with the more cautious belief that London is pretty if New York is, and replacing the logical attribute of contradictoriness with that of entailing that New York is not pretty. Furthermore, in this case we may replace the epistemic state of being in a position to see that at least one of the first pair of beliefs must be false


with the disposition of being such that one would be logically justified in inferring that New York is not pretty from the second, more cautious pair of beliefs.

Both the displayed argument and the one obtained by making the suggested substitutions are extremely compelling. But they are fallacious. I do not mean by this that they proceed from false premisses. I mean that they are invalid: the premisses are all true, but one of the critical inferences is fallacious. Which one?

The fallacy involved may be seen more clearly if we first consider the following simpler and more direct argument:

If Pierre has the beliefs that London is pretty if New York is and that London is not pretty, then (assuming that he consciously considers the further question of whether New York is pretty, that he fully realizes that the proposition that New York is not pretty is a trivial and immediate deductive consequence of the propositions that London is pretty if New York is and that London is not pretty, that he has no independent reasons for withholding belief from the proposition that New York is not pretty, and that he has adequate time for reflection on the matter) he will come to believe that New York is not pretty on the basis of these beliefs, and he would be logically justified in doing so. But Pierre, as long as he is unaware that the cities he calls ‘London’ and ‘Londres’ are one and the same, will not come to believe that New York is not pretty on the basis of his beliefs that London is pretty if New York is and that London is not pretty, and he would not be logically justified in doing so. Therefore, as long as Pierre is unaware that the cities he calls ‘London’ and ‘Londres’ are one and the same, it is incorrect to say that he has the beliefs that London is pretty if New York is and that London is not pretty.

This argument is evidently at least very much like one of Kripke's, and it is valid. I have formulated it in such a way as to make obvious its reliance, in its first premiss, on the belief closure and justification principles. (Let p be the conjunctive proposition that whereas London is pretty if New York is, London is not pretty, and let q be the entailed proposition that New York is not pretty.) I maintain that Pierre's inability to infer that New York is not pretty presents a bona fide counter-example to these principles, so that the first premiss of this argument is false. The theses advanced in Frege's Puzzle show how Pierre's case may be seen as presenting a counter-example. Pierre fully understands the English sentence ‘London is not pretty’ and also the Frenglish sentence ‘Londres is pretty if New York is’, grasping their content. In particular, he understands the Frenglish sentence to mean precisely what it does mean (in Frenglish): that London is pretty if New York is. (He does not misunderstand it to mean, for example, that Rome is pretty if New York is. If any French speaker who has never been to London can nevertheless understand French sentences containing the French name ‘Londres’, Pierre understands the particular sentence ‘Si New York est jolie, Londres est jolie aussi’ as well as its Frenglish translations.) When these sentences are put to him, he unhesitatingly assents; he agrees to the propositions that are their contents when he takes these propositions in the way they are presented to him by these very sentences. Hence he believes these propositions.

Pierre also fully understands the English sentence ‘London is pretty if New York is’, grasping its content. He is fully aware that the proposition so expressed, taken together with the proposition expressed by ‘London is not pretty’, collectively entail

that New York is not pretty. Unfortunately for Pierre, he does not take this conditional proposition the same way when it is presented to him by the different sentences. He mistakes the proposition for two, logically independent propositions—just as he mistakes London itself for two separate cities. This is evidenced by the fact that he harbors conflicting doxastic attitudes toward the proposition. He believes it, since he agrees to it taking it one way (the way it is presented to him by the Frenglish sentence, or by its French translation), but he also withholds belief from it, in the sense specified in Section I above, since he does not agree to it taking it the other way (the way it is presented to him by the English sentence). It is this confusion of Pierre's—his lack of recognition of the same proposition when it is presented to him differently—that prevents Pierre from making the logical connection between his two beliefs and drawing the modus tollens inference. He fails to recognize that his belief that London is not pretty is the negation of the consequent of his belief that London is pretty if New York is.

It is precisely Pierre's sort of situation, in which there is propositional recognition failure, that gives rise to counter-examples to the belief closure and justification principles. The principles can, of course, be weakened to rescue them from vulnerability to this sort of counter-example. One way to do this is to adjoin a further initial-condition supposition: that x recognizes that q is a deductive consequence of his or her belief of p. That is, we must be given not only that x recognizes both that he or she believes p and that p entails q, but furthermore that x also recognizes that p is both a belief of his or hers and entailing of q. Since he is a logician, Pierre knows that the compound proposition that whereas London is pretty if New York is, London is not pretty entails that New York is not pretty, and he also knows (taking this proposition in a different way) that this proposition is something he believes, but since he fails to recognize this proposition when taking it differently, he does not recognize that this proposition is simultaneously something that entails that New York is not pretty and something he believes.17

One might be tempted to defend these disputed instances of the belief closure and justification principles by arguing that if a normal, fully rational agent x knows both that a particular proposition p is something he or she believes and furthermore that p deductively entails another proposition q, then x can easily infer that p is simultaneously both something he or she believes and something that deductively entails q. Since the former conditions are already included as initial-condition suppositions in the belief closure and justification principles, the new initial-condition supposition would be entirely superfluous.

This purported defense of the belief closure and justification principles does not succeed. Notice how it is supposed to go. We might begin by noting that the argument form 0x002308a is F and a is G; therefore a is both F and G0x002309 is valid, since it is simply a special application of the ‘0x0003bb’-transformation rule of abstraction, which permits the inference from a formula 0x0003d5a to 0x002308(0x0003bb x )[0x0003d5x](a)0x002309, i.e. to 0x002308a is an individual such that 0x0003d5it 0x002309(where 0x0003d5a is the result of uniformly substituting free occurrences of a for free occurrences of ‘x’ in 0x0003d5x —or for ‘free’ occurrences of the pronoun ‘it’ in 0x0003d5it ). In particular, then, there is a valid argument from ‘x believes p, and p deductively entails q’ to ‘p is something that x believes and that deductively entails q’. We then invoke the belief closure and justification principles to argue that if x believes the conjunctive proposition that he or she believes p and p deductively entails q, then (assuming the rest of the initial conditions obtain) x will infer that p is something that he or she believes and that deductively entails q, and x would be justified in doing so. This would be a meta-application of the belief closure and justification principles, an application to beliefs concerning inference and belief formation. But this meta-application of these principles is part of a purported justification of these very principles! The problem with this defense of the two principles is that, like the misguided attempt to defend induction-by-enumeration by citing inductive evidence of its utility, it presupposes precisely the very principles it is aimed at defending, and hence suffers from a vicious circularity. If we let x be Pierre, p be the conjunctive proposition that whereas London is pretty if New York is, London is not pretty, and q be the proposition that New York is not pretty, then the resulting instances of the belief closure and justification principles are precisely special instances whose truth is explicitly denied by the sort of account I advocate.

More generally, the theory advanced in Frege's Puzzle distinguishes sharply between a complex sentence 0x0003d5a and the logically equivalent sentence 0x002308(0x0003bb x )[0x0003d5x](a)0x002309 (or 0x002308a is such that 0x0003d5it 0x002309) as regards their proposition content. I have argued elsewhere for this distinction in some detail in connection with sentences 0x0003d5a that involve multiple occurrences of the name a.18 Thus, for example, Pierre no doubt believes

(putting it in Frenglish) that Londres is prettier than London, and (according to my view) he thereby believes the proposition (putting it in proper English) that London is prettier than London, but he does not thereby believe the unbelievable proposition that London exceeds itself in pulchritude (that London is something that is prettier than itself). Likewise, Pierre believes the conjunctive proposition that London is pretty and London is not pretty, but he surely does not believe that London has the unusual property of being both pretty and not pretty.

The fallacy in Kripke's argument, as reconstructed above, occurs in the inference from the subsidiary conclusion C1 and the additional premise P3 to the final conclusion C2. More specifically, the argument would apparently involve an implicit and invalid intervening inference from C1 to the following:

C1′:  

If Pierre has the beliefs that London is pretty and that London is not pretty, then he is in principle in a position to see that these propositions (beliefs) are simultaneously beliefs of his and contradictory, and hence in a position to see that at least one of his beliefs must be false.

This intervening subsidiary conclusion C1′ together with premise P3 validly yield the desired conclusion C2. The implicit inference from C1 to C1′ is, in effect, a meta-application of one of the disputed instances of the belief closure and justification principles. Pierre is indeed in a position to know that he believes that London is pretty and that London is not pretty. Being a logician, he certainly knows that the propositions that London is pretty and that London is not pretty are logically incompatible. But he believes these facts about these propositions only when taking one of them in different ways, believing it to be two logically independent propositions, failing to recognize it as a single proposition. He is in no position to see or infer that these two propositions are simultaneously believed by him and contradictory.

There is a serious residual problem with the account given so far of Pierre's situation. There is an extremely compelling reason to deny that Pierre believes that London is pretty: when the sentence ‘London is pretty’ is put to him (after t 2 ), he sincerely dissents from it in good faith, while fully understanding the sentence and grasping its content. The theoretical apparatus of Frege's Puzzle makes it possible to dispel at least some of the force of this sort of consideration. Using that apparatus, where ‘f’ refers to the function that assigns to a speaker and a sentence of the speaker's idiolect the corresponding third relatum of the BEL relation (e.g., the way the speaker would take the content of the sentence were it presented to the speaker at t 2 by that very sentence), we may say that at t 2


BEL[Pierre, that London is pretty, f(Pierre, ‘Londres is pretty’)],

or in Frenglish,


BEL[Pierre, that Londres is pretty, f(Pierre, ‘Londres is pretty’)],

whereas we must deny that at t 2


BEL[Pierre, that London is pretty, f(Pierre, ‘London is pretty’)].


Pierre believes the proposition that Londres is pretty, taking it as presented by those very words, but he also withholds belief from (in fact disbelieves) the proposition that London is pretty, taking it as presented by those very words. Pierre's doxastic disposition towards the proposition depends entirely on how the proposition is presented to him. The reason offered for denying that Pierre believes that London is pretty is a decisive reason for affirming that he disbelieves that London is pretty (and therefore that he withholds belief), but it is highly misleading evidence regarding the separate and independent question of whether he believes that London is pretty.19

VII

I turn now to Schiffer's criticism that I am committed to the falsity of the true sentence (2). I fully agree with Schiffer that sentence (2) is straightforwardly true in his little story involving Floyd, as long as Floyd understands sentence (1) when uttering it or assenting to it. In fact, far from being committed to the claim that (2) is false, the theory advanced in Frege's Puzzle is in fact committed to precisely the opposite claim that (2) is true! This virtually follows directly from the first condition on the BEL relation given in Section I above, according to which it is sufficient for the truth of (2) that Floyd should agree to the content of (1) when taking this proposition the way it is presented to him by the very sentence (1).20 On my view, then, Floyd does believe that Lois Lane does not realize that Clark Kent is Superman. In addition, I also maintain (as Schiffer correctly points out) that Floyd believes that Lois Lane does

end p.211


realize that Clark Kent is Superman—since Floyd believes the proposition that Lois Lane realizes that Superman is Superman, and on my view this just is the proposition that Lois Lane realizes that Clark Kent is Superman. Thus, I maintain that Floyd both believes and disbelieves that Lois Lane realizes that Clark Kent is Superman.

Schiffer has uncovered a very interesting philosophical problem here. Before presenting my solution, I want to emphasize the generality of the problem. The general problem is not one that is peculiar to my own theory of propositional-attitude attributions (contrary to the impression created by Schiffer's presentation of his criticism), but is equally a problem for the orthodox, Fregean theory, and indeed for virtually any theory of propositional-attitude attributions.

Consider an analogous situation involving straightforward (strict) synonyms. Suppose that Sasha learns the words ‘ketchup’ and ‘catsup’ not by being taught that they are perfect synonyms, but by actually consuming the condiment and reading the labels on the bottles. Suppose further that, in Sasha's idiosyncratic experience, people typically have the condiment called ‘catsup’ with their eggs and hash browns at breakfast, whereas they routinely have the condiment called ‘ketchup’ with their hamburgers at lunch. This naturally leads Sasha to conclude, erroneously, that ketchup and catsup are different condiments, condiments that happen to share a similar taste, color, consistency, and name. He sincerely utters the sentence ‘Ketchup is a sandwich condiment; but no one in his right mind would eat a sandwich condiment with eggs at breakfast, so catsup is not a sandwich condiment.’ Now, Tyler Burge, who has a considerable knowledge of formal semantics and who is well aware (unlike Sasha) that ‘ketchup’ and ‘catsup’ are exact synonyms, would claim that Sasha believes that ketchup is a sandwich condiment but that Sasha does not believe that catsup is, describing his view in exactly so many words.21 Clearly, Burge believes that Sasha believes that ketchup is a sandwich condiment. (See note 23 below.) When queried, ‘Does Sasha believe that catsup is a sandwich condiment?’, however, Burge sincerely responds ‘No’, while fully understanding the question and grasping its content. Given Burge's mastery of English, there would seem to be every reason to say, therefore, that he also believes that Sasha does not believe that catsup is a sandwich condiment. Yet by an argument exactly analogous to Schiffer's, we are apparently barred, by Frege's Thesis and Schiffer's Constraint, from acknowledging this. For we have granted that Burge believes ketchup to be something Sasha believes is a sandwich condiment. If, while remaining fully rational, Burge also believed catsup (i.e. ketchup) not to be something Sasha believes is a sandwich condiment, there would be a violation of the conjunction of Frege's Thesis with Schiffer's Constraint. There are no relevant modes of presenting ketchup that Burge construes as (modes of) presenting different stuff, as are required by Frege's Thesis together with Schiffer's Constraint. The conjunction of Frege's Thesis with Schiffer's Constraint thus apparently prohibits us from acknowledging that Burge does indeed disbelieve what he sincerely claims to disbelieve—that Sasha believes that catsup is a sandwich condiment.

Some philosophers will conclude that, despite his insistence to the contrary, Burge really does not disbelieve that Sasha believes that catsup is a sandwich condiment, and when he protests that he does, he is operating under a misunderstanding of the phrase ‘believes that’. What Burge really disbelieves, they claim, is something linguistic, for example that Sasha believes that the sentence ‘Catsup is a sandwich condiment’ is true in English, or that Sasha satisfies the sentential matrix ‘x believes that catsup is a sandwich condiment’ in English (i.e. that the open sentence ‘x believes that catsup is a sandwich condiment’ is true in English when Sasha is assigned as value for the free variable ‘x’).22 Yet this seems plainly wrong—and therein lies the problem. Burge correctly understands the sentence ‘Sasha believes that catsup is a sandwich condiment.’ He understands it to mean (in English) that Sasha believes that catsup, i.e. ketchup, is a sandwich condiment. He knows enough formal semantics to know that the sentence does not mean instead that Sasha believes that the sentence ‘Catsup is a sandwich condiment’ is true in English, nor that Sasha satisfies the sentential matrix ‘x believes that catsup is a sandwich condiment’ in English. Burge sincerely dissents from this sentence (as a sentence of English) because of his philosophical views concerning belief (which assimilate the proposition so expressed with the false proposition that Sasha accepts, or would accept, the sentence ‘Catsup is a sandwich condiment’, understood in a certain way). Burge's sincere dissent surely indicates a belief on his part (even if it is confused) that Sasha does not believe that catsup is a sandwich condiment—in addition to his correct belief that Sasha does believe that ketchup is a sandwich condiment, and in addition to his (erroneous) linguistic belief that Sasha fails to satisfy the sentential matrix ‘x believes that catsup is a sandwich condiment’ in English. The problem is that this apparently conflicts with Frege's Thesis in conjunction with Schiffer's Constraint.

This time the objection is not an objection to my theory of belief attributions in particular. If Schiffer's second criticism of my theory of belief attributions is sound, any reasonable theory of belief attributions, even a Fregean theory, would be required to deny that Burge believes that Sasha does not believe that catsup is a sandwich condiment.23 Yet surely we are not barred by the demands of reasonableness (and

consistency) from acknowledging that Burge does indeed disbelieve what he claims to disbelieve. Since it proves too much, there must be something wrong with Schiffer's argument. What?24

It is perhaps natural to point an accusing finger at Schiffer's Constraint. Since this principle (in conjunction with Frege's Thesis) apparently bars us—Fregeans, Russellians, and other theorists alike—from acknowledging what is patently true about Burge's beliefs, it would appear that it must be incorrect.

I was careful in Frege's Puzzle to avoid particular commitments concerning the nature of what I call ‘proposition guises’ or ‘ways of taking propositions’ or ‘means by which one is familiar with a proposition’. However, I am prepared to grant, for present purposes, that something along the lines of Frege's Thesis and Schiffer's Constraint is indeed correct.25 Does this, together with the doctrines and theses I advocate in Frege's Puzzle, lead to a commitment to the falsity of (2), as Schiffer argues? If so, then my position is strictly inconsistent since I also maintain that (2) is true.

Contra Schiffer, my granting that something along the lines of Frege's Thesis and Schiffer's Constraint is correct does not commit me to the falsity of sentence (2). For illustration, first instantiate the ‘x’ to Floyd, the ‘y’ to the fact (or proposition) that Clark Kent is Superman, and the ‘F’ to the property of being realized by Lois Lane. On my theory, the fact (or proposition) that Clark Kent is Superman is just the fact that Superman is Superman. The relevant instances of the two principles entail that, since Floyd both believes and disbelieves this fact to be realized by Lois Lane, if he is fully rational he must grasp this fact by means of two distinct modes of presentation of it, he must take this fact in two different ways. I am happy to say that Floyd does. In fact, my theory more or less requires that he does. Unless Floyd himself believes with me what Schiffer calls ‘the ‘Fido–Fido theory of meaning’, he may rationally proclaim ‘The fact that Superman is Superman is trivial and something that Lois Lane realizes, whereas the fact that Clark Kent is Superman is neither; hence they are distinct facts.’ As the discussion in Section I made clear, whatever else my notion of a way of taking an object is, it is such that if Floyd believes that a proposition p is distinct from a proposition q, then Floyd takes these propositions in different ways (even if p=q). If Floyd is sufficiently philosophical, he may mistake the singular proposition about Superman that he is him, when it is presented to him by the sentence ‘Clark Kent is Superman’, for some general proposition to the effect that the mild-mannered reporter having such-and-such drab physical appearance is the superhero who wears blue tights, a big ‘S’ on his chest, and a red cape, etc. Or instead he may mistake the proposition, so presented, for the singular proposition taken in a certain way, or what comes to the same thing, the singular proposition together with a certain way of taking it. This is how he takes the singular proposition when it is so presented. The fact that he knows this proposition to be true does not have the consequence that he sees it as the very same thing, in the very same way, as the corresponding thing (general proposition or singular-proposition-taken-in-a-certain-way) that he associates with ‘Superman is Superman’.

Consider Frege in place of Floyd. On my view, Frege mistook the singular proposition about the planet Venus that it is it to be two different propositions (‘thoughts’). He took this proposition in one way when it was presented to him by the sentence ‘Der Morgenstern ist derselbe wie der Morgenstern’ (the German version of ‘Morningstar is the same as Morningstar’) and in another way when it was presented to him by the sentence ‘Der Morgenstern ist derselbe wie der Abendstern’ (‘Morningstar is the same as Eveningstar’)—despite the fact that he was well aware that the names ‘Morgenstern’ and ‘Abenstern’ refer to (‘mean’) the same planet. That he took this proposition in two different ways is established by the fact that he took it to be two different propositions. Floyd is in a similar state with respect to the singular proposition about Superman that he is him—even if Floyd has not formed a specific view about the nature of propositions in general or about the nature of this proposition in particular, as long as he takes this proposition to be two different propositions. Anyone who does not consciously subscribe to the sort of theory advanced in Frege's Puzzle is likely to

have different perspectives on a given singular proposition of the form x is x when it is presented in various ways, seeing it as a different entity each time.26

Let us return to Frege's Thesis and Schiffer's Constraint. Suppose instead that the ‘y’ is instantiated this time to Superman (or to Clark Kent) and the ‘F’ to the property of being an individual x such that Lois Lane realizes that x is Superman, or being someone that Lois Lane realizes is Superman. Surely Floyd believes Superman to have this property. (We ask Floyd, ‘You know that man who calls himself “Superman”. Does Lois Lane realize that he is Superman?’ If Floyd understands the question, he should answer ‘Yes’.) If at the same time Floyd disbelieves Superman to have this property, yet he remains fully rational, the conjunction of Frege's Thesis with Schiffer's Constraint will have been violated. As Schiffer points out, it will not do in this case to defend my theory by claiming that there are relevant modes of presentation m and m′ of Superman that Floyd grasps but construes as (modes of) presenting different individuals, for there are no such modes of presentation in Schiffer's little story.

Does Floyd disbelieve Superman to be such that Lois realizes that he is Superman? Put another way, does Floyd believe Clark Kent to be someone that Lois Lane does not realize is Superman? I suspect that Schiffer assumed that if I were to concede that Floyd believes Lois Lane does not realize that Clark Kent is Superman, it would simply follow—according to my own theory—that Floyd believes Clark Kent to be someone that Lois Lane does not realize is Superman. That is, Schiffer's second criticism apparently involves an inference from

(2)  

Floyd believes that Lois Lane does not realize that Clark Kent is Superman

to

(3)  

Floyd believes that Clark Kent is someone that Lois does not realize is Superman.

On my theory, it virtually follows from (3) that Floyd believes Clark Kent not to be someone that Lois Lane realizes is Superman. The conjunction of Frege's Thesis with Schiffer's Constraint would thus bar me from acknowledging the truth of (2).

It is an essential part of the theory I advanced in Frege's Puzzle, however, that (3) does not follow from (2). The theory advanced in Frege's Puzzle distinguishes sharply between the proposition that Lois Lane does not realize that Clark Kent is such-and-such and the proposition that Clark Kent is someone that Lois Lane does not realize is such-and-such. These propositions differ in structure. Roughly put, Clark Kent is the subject of the latter proposition, but not of the former. According to my account, Floyd believes that Lois Lane does not realize that Clark Kent is Superman but, at least very likely, he does not also believe of Superman that he is someone Lois Lane does not realize is Superman.

In fact, it is precisely in the implicit inference from (2) to (3) that Schiffer might be invoking the belief closure principle (and perhaps the belief justification principle as well). Here again, the relevant logical entailment is an instance of the inference rule of abstraction. And here again, we seem to have an example of someone believing a proposition while being in no position to infer a simple deductive consequence from the proposition. Worse, if Schiffer's apparent implicit inference from (2) to (3) is indeed based on an application of the belief closure principle, as it seems to be, it is a fallacious application. For one of the initial-condition provisos of the belief closure principle is that the agent is aware of the deductive relationship between his or her current belief and its deductive consequence. But it seems likely in Schiffer's little story that Floyd does not believe that the proposition that Clark Kent is someone that Lois Lane does not realize is such-and-such is a valid deductive consequence of the proposition that Lois Lane does not realize that Clark Kent is such-and-such.27 Given his favorable attitude toward sentence (1), it is evident that Floyd believes that Lois Lane does not realize that Clark Kent is Superman, but he is in no position to infer that Clark Kent is someone that Lois Lane does not realize is Superman, and he would not be logically justified in doing so. For we may suppose that Floyd also believes that Superman is someone that Lois Lane realizes is Superman. On my view, this is just to say that Floyd believes the singular proposition about Superman, i.e. Clark Kent, that he is someone that Lois Lane realizes is Superman. Floyd is not about to relinquish this belief of his. He would indeed be less than fully rational, in the sense used in Schiffer's Constraint, if at the same time he also formed the belief of Superman (i.e. Clark Kent) that he is someone that Lois Lane does not realize is Superman.

Floyd would be less than fully rational, that is, unless he has gained a new mode of familiarity with Superman, an additional mode of presentation, by encountering Superman on another occasion and failing to recognize him, or he somehow mistakes the logically incompatible properties of being someone Lois Lane realizes is Superman and of being someone Lois Lane does not realize is Superman—which are properties that such individuals as you, me, and Superman either have or lack in an absolute de re way—for properties of individuals-under-guises (or equivalently, for binary relations between individuals and ways of conceiving them).28 Either of these predicaments might rescue Floyd from irrationality even when he both believes and disbelieves Superman to be someone Lois Lane realizes is Superman. For present purposes, we may assume that Floyd has acquired neither a new mode of presentation nor this philosophically sophisticated confusion.

Suppose we queried Floyd, ‘You know that man who calls himself “Superman” and “Clark Kent”. Does Lois Lane realize that he is Superman, or does she fail to realize that he is Superman?’ If he understands the question, he should answer ‘She does realize that he is Superman.’ If he were sufficiently philosophical, he might describe his pertinent beliefs by adding, ‘Lois does not realize that Clark Kent is Superman. But if you're asking about the man himself (and not about the man-under-one-of-his-guises), she thinks he is two men. She doubts that he is Superman, but she also realizes that he is Superman. It all depends on the guise under which he is presented to her.’ Floyd cannot fully rationally add to this stock of beliefs a further belief that he would express by ‘That man, Clark Kent, is someone Lois does not realize is Superman.’ If he added this belief to his present stock, without relinquishing any of his current beliefs, he would believe of Superman that he simultaneously is and also is not someone Lois Lane realizes is Superman, that he both is and is not such that Lois Lane realizes that he is Superman. That would indeed be less than fully rational, in the sense used in Schiffer's Constraint (unless Floyd is under the sort of confusion mentioned in the preceding paragraph). To use a piece of terminology recently introduced by Schiffer, Floyd, in both believing and disbelieving that Lois Lane realizes that Clark Kent is Superman, exhibits the belief/disbelief phenomenon with respect to the phrase ‘that Clark Kent is Superman’ (which he does not construe as standing for the same thing as the phrase ‘that Superman is Superman’).29 However, since on my view Floyd (unless he is under the sort of confusion mentioned above) does not disbelieve Clark Kent to be someone that Lois realizes is Superman, he does not exhibit the belief/disbelief phenomenon with respect to the name ‘Clark Kent’ (which he rightly construes as standing for the same individual as the name ‘Superman’). Hence, my theory does not conflict here with the conjunction of Frege's Thesis and Schiffer's Constraint.30

VIII

Although the general philosophical problem uncovered by Schiffer does not refute my theory of propositional-attitude attributions (or Frege's), it does pose a very serious difficulty for—in fact, a refutation of—a proposal originally made by W. V. Quine in 1956 in his classic ‘Quantifiers and Propositional Attitudes’,31 and more recently endorsed (and improved upon) by David Kaplan.32 The proposal is one for translating (or in Quine's case, replacing) constructions involving quantification into intensional or content-sensitive operators by a certain type of construction—which Kaplan calls ‘syntactically de re’—that avoids such quantifying in. In particular, a syntactically de dicto open sentence

c believes that 0x0003d5x ,

where ‘x’ is the only free variable of the open sentence 0x0003d5x , and has only one free occurrence therein (positioned inside the scope of the content-sensitive syntactically de dicto operator ‘c believes that’), is to be replaced by

c believes the property of being an object y such that 0x0003d5y of x

(Quine), or equivalently, to be translated into the syntactically de re

x is believed by c to be an object y such that 0x0003d5y

(Kaplan). The proposed substitutes artfully leave the free variable ‘x’ outside the scope of ‘believe’.33 Accordingly, on this proposal, the syntactically de dicto open sentence

(2′)  

Floyd believes that Lois Lane does not realize that x is Superman

is rewritten as


Floyd believes the property of being an object y such that Lois Lane does not realize the property of being Superman of y, of x

(Quine), or as


x is believed by Floyd to be an object y such that y is not realized by Lois Lane to be Superman

(Kaplan), or more colloquially as

(3″)  

Floyd believes x to be someone that Lois Lane does not realize to be Superman.

Now, in Schiffer's little story, (2′) is true when Superman is assigned as value for the variable ‘x’, i.e. Superman satisfies (2′). Yet Schiffer's argument demonstrates that (3″) is false when Superman is assigned as value for ‘x’, i.e. Superman does not satisfy (3″). If (3″) were true of Superman, Floyd would be less than fully rational, in the sense used in Schiffer's Constraint (unless he is under the confusion mentioned in the preceding section concerning the nature of the property of being someone Lois Lane realizes is Superman), since he would then both believe and disbelieve Superman to be someone Lois realizes is Superman, while lacking the required ‘modes of presentation’ construed as (modes of) presenting distinct individuals. The proposed translation of (2′) into (3″) thus fails, and for precisely the same reason as Schiffer's implicit inference from (2) to (3).34

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S. Schiffer, ‘Naming and Knowing’, in P. French, T. Uehling, and H. Wettstein, eds, 1979, pp. 61–74.

—— ‘The Basis of Reference’, Erkenntnis, 13 (1978), pp. 171–206.  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them

—— ‘Indexicals and the Theory of Reference’, Synthese, 49 (1981), pp. 43–100.  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them

—— ‘The Real Trouble with Propositions’, in R. J. Bogdan, Belief: Form, Content, and Function (Oxford University Press, 1986), pp. 83–118.

—— ‘The “Fido–Fido” Theory of Belief’, in J. Tomberlin, ed., Philosophical Perspectives 1: Metaphysics (Atascadero: Ridgeview, 1987), pp. 455–480.

S. Schwartz, Naming, Necessity, and Natural Kinds (Cornell University Press, 1977).

S. Soames, ‘Lost Innocence’, Linguistics and Philosophy, 8 (1985), pp. 59–71.  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them

—— ‘Direct Reference, Propositional Attitudes and Semantic Content’, in N. Salmon and S. Soames, 1988.

S. Wagner, ‘California Semantics Meets the Great Fact’, Notre Dame Journal of Formal Logic, 27, 3 (July 1986), pp. 430–455.  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them


D. Wiggins, ‘Identity, Necessity and Physicalism’, in S. Korner, ed., Philosophy of Logic (University of California Press, 1976), pp. 96–132, 159–182.

—— ‘Frege's Problem of the Morning Star and the Evening Star’, in M. Schirn, ed., Studies on Frege II: Logic and the Philosophy of Language (Stuttgart: Bad Canstatt, 1976), pp. 221–255.

12 The Resilience of Illogical Belief (2006)*

Nathan Salmon

Although Professor Schiffer and I have many times disagreed, I share his deep and abiding commitment to argument as a primary philosophical tool. Regretting any communication failure that has occurred, I endeavor here to make clearer my earlier reply in ‘Illogical Belief’ to Schiffer's alleged problem for my version of Millianism.1 I shall be skeletal, however; the interested reader is encouraged to turn to ‘Illogical Belief’ for detail and elaboration.

I have argued that to bear a propositional attitude de re is to bear that attitude toward the corresponding singular proposition, no more and no less. If this is right, then according to Millianism every instance of the following modal schema is true:

S:  

Necessarily, 0x0003b1Vs that 0x0003d50x0003b2iff 0x0003b1Vs of 0x0003b2(de re) that 0x0003d5it ,

where 0x0003b1is any singular term of English, V is any of a range of transitive English verbs of propositional attitude (including ‘believe’, ‘disbelieve’, and ‘doubt’), 0x0003b2is any proper name or other Millian term of English, 0x0003d5it is any English ‘open sentence’ in which the pronoun ‘it’ occurs as a free variable—alternatively ‘he’, ‘him’, ‘she’, or ‘her’—and 0x0003d50x0003b2is the same as 0x0003d5it except for having occurrences of 0x0003b2wherever 0x0003d5it has free occurrences of the relevant pronoun.2

Schiffer uses the epithet ‘Frege's constraint’ for a principle that entails the following:

FC: (Necessarily) if x rationally believes y to be F while also disbelieving (or merely withholding believing) y to be F, for some property or singulary-functional concept F, then in so doing x takes y in differing ways, by means of distinct guises (‘modes of presentation’) m and m′; in so doing, x does not construe m and m′ as separate ways of taking a single thing.

I have spent much of the past two decades arguing for a duly qualified version of (FC). The primary rationale is that if x rationally believes y to be F while disbelieving

z to be F, then x, in so doing, takes y and z to be distinct. Insofar as x is rational, he/she thereby takes y and z differently—even if, in fact, y=z. Similarly, if x rationally believes y to be F while also suspending judgment whether z is F, then ordinarily, in so doing x takes y and z differently.

Schiffer derives from these principles the conclusion that my Millianism is inconsistent with the possibility of a certain possible state of affairs (a): Jane's rationally believing, even while she is fully aware that ‘George Eliot’ and ‘Mary Ann Evans’ co-designate, both that Ralph believes that George Eliot was a man and that Ralph does not believe that Mary Ann Evans was a man. For according to Millianism, in situation (a), Jane rationally believes both the singular proposition about Eliot, that Ralph believes she was a man, and its denial. Putting ‘Jane’ for 0x0003b1in (S), ‘George Eliot’ for 0x0003b2, ‘believe’ for V, and ‘Ralph believes she was a man’ for 0x0003d5it , and performing a bit of logic, one obtains the result that, in (a) Eliot is believed by Jane to be such that Ralph believes she was a man. Now putting for 0x0003b2instead ‘Mary Ann Evans’ and for 0x0003d5it ‘Ralph does not believe she was a man’, and drawing analogous inferences, one obtains the additional result that in (a) Eliot is also rationally believed by Jane not to be such that Ralph believes she was a man. Thus, in (a) Jane believes Eliot to be F while also believing Eliot not to be F, for a particular property or concept F. It follows by (FC) that in (a) Jane, insofar as she is rational, takes Eliot in differing ways, by means of a pair of guises that Jane does not thereby take to be of a single individual. But Jane does not do this in (a).

The reductio derivation is in fact fallacious. Specifically, a fallacy is committed when Schiffer erroneously ‘restates’ the relevant half of the first premiss as the thesis that every instance of the following alternative schema is true (putting ‘believe’ for V):

S′  

Necessarily, if 0x0003b1believes that 0x0003d50x0003b2, then 0x0003b2is believed by 0x0003b1to be (something/someone) such that 0x0003d5it .3

Contradiction is indeed derivable from (S′) taken together with Millianism, (FC), and the possibility of (a), exactly in the manner that Schiffer sets out. This is because the relevant instance of (S′) is inconsistent with the facts. The derivation might even be taken as demonstrating this—at least by the Millian's lights. Importantly, Millianism is in no way committed to (S′), not even a Millianism like my own, which is committed to (S). I am committed to the existence of counter-instances of (S′).

The distinction between the de re constructions 0x00231c0x0003b1believes of 0x0003b2that 0x0003d5it 0x00231dand 0x00231c0x0003b2is believed by 0x0003b1to be something such that 0x0003d5it 0x00231dmay seem excessively subtle and delicate, but in the present instance it is crucial. The latter is the passive-voice transformation of a relational predication: Believes r (0x0003b1,0x0003b2, to be something such that 0x0003d5it ), where ‘Believes r ’ is a triadic predicate for a ternary relation between a believer x, an object

end p.225

y, and importantly, a property or singulary-functional concept F that x attributes to y. Schema (S′) is thus indeed a logical consequence of (S) in a special case: if the open sentence 0x0003d5it has monadic-predicational form, ‘It’ + VP, where VP is a monadic predicate in which the pronoun ‘it’ does not occur free. The predicate VP is then a term for a particular property or singulary-functional concept F. If someone x believes the singular proposition expressed by ‘It’ + VP under the assignment of a particular value y to the variable ‘it’, then the proposition believed—that y is F—has the simple structure, <y, F>, so that x indeed believes y to be F.4

Not all de re beliefs about y involve the attribution of a property to y. Many singular propositions involving y have considerably more structure than <y, F>. There are some propositions, expressed by complex sentences 0x0003d50x0003b2, such that someone might rationally believe the proposition even while doubting the consequence expressed by 0x00231c0x0003b2is something such that 0x0003d5it 0x00231d. Some of these propositions are witness to the fact that (S′) is no logical consequence of (S).

One example is due to David Kaplan. If Quine's Ralph believes that this man [pointing at a fuzzy picture of Ortcutt, his face covered by a large brown hat] is taller than Ortcutt, then Ralph believes the singular proposition about Ortcutt, that he (Ortcutt) is taller than he (Ortcutt) is. According to (S), Ralph thus believes that Ortcutt is taller than Ortcutt. But Ralph does not thereby believe Ortcutt to be someone taller than himself; i.e., Ortcutt is not believed by Ralph to be something z such that z is taller than z. The proposition Ralph believes has the binary-relational form: taller-than>—or perhaps, the special monadic-predicational form: <taller-than, Ortcutt0x00226b. It does not have the alternate monadic-predicational form: being taller than oneself>. Putting ‘Ralph’ for 0x0003b1, ‘Ortcutt’ for 0x0003b2, ‘believe’ for V, and ‘He is taller than he is’ for 0x0003d5it , the resulting instance of (S) is true, the resulting instance of (S′) false.5

Schiffer's central example employs another such sentence: ‘Ralph does not believe that Mary Ann Evans was a man.’ This expresses a singular proposition about Eliot, that Ralph does not believe that she was a man, represented by the ordered pair

0x00226aRalph, believing, having been a man0x00226b, being false>. Jane rationally believes this proposition, while also believing precisely what it denies, as expressed by ‘Ralph believes that George Eliot was a man’ and represented by believing, having been a man0x00226b. But Jane does not thereby both believe and disbelieve the singular proposition about Eliot, that she is believed by Ralph to have been a man, as represented by being believed by Ralph to have been a man>. The following dialogue illustrates Jane's pertinent beliefs:

Socrates  

‘Does Ralph believe that Mary Ann Evans was a man?’

Jane  

‘No, he doesn't.’

Socrates  

‘Does Ralph believe that George Eliot was a man?’

Jane  

‘Yes.’

Socrates  

‘So George Eliot is someone Ralph believes was a man?’

Jane  

‘Yes.’

Socrates  

‘What about Mary Ann Evans, then? Does Ralph also believe she was a man?’

Jane  

‘Ralph doesn't believe that Mary Ann Evans was a man. But you're now asking about Mary Ann Evans herself. Mary Ann Evans and George Eliot are the same person, don't you know? And Ralph does indeed believe she was a man.’

Socrates  

‘Very well. Is Mary Ann Evans someone Ralph also doesn't believe was a man?’

Jane  

‘Of course not; that would be logically impossible. I just told you: Mary Ann Evans is someone Ralph does believe was a man.’

Socrates  

‘Is George Eliot someone Ralph doesn't believe was a man?’

Jane  

‘You're not listening to me: George Eliot and Mary Ann Evans are the same person. Ralph does believe she was a man.’

Jane's position is rational, sophisticated, even subtle. It is perfectly coherent (even if it is inconsistent, at least by Millian lights). It is part of a neo-Fregean theory that purports to analyze or explain de re constructions solely in terms of Fregean thoughts. Putting ‘Jane’ for 0x0003b1, ‘George Eliot’ for 0x0003b2, ‘believe’ for V, and ‘Ralph believes she was a man’ for 0x0003d5it , the resulting instance of (S) is true, the resulting instance of (S′) false. Schiffer's reductio derivation fallaciously infers the latter from the former on its way to deriving a contradiction.

Schiffer's objection can make do without this fallacious inference if (FC) can be extended into the following:

FC′:  

(Necessarily) if 0x0003b1rationally believes of 0x0003b2that 0x0003d5it while also disbelieving (or merely withholding believing) of 0x0003b2that 0x0003d5it , then in so doing 0x0003b1takes 0x0003b2in differing ways.

(Schiffer proposes a related generalization.) But as remarked earlier, there are complex singular propositions about y that one can rationally believe without attributing the corresponding property to y. Someone can rationally believe and disbelieve one of these propositions without taking y to be distinct things. Given the existence of such cases, there is no obvious rationale for (FC′). Indeed, the very situation (a) arguably yields a counter-instance. I maintain that in (a), Jane rationally both believes and disbelieves of George Eliot, de re, that Ralph believes she was a man—even though in so doing, Jane does not take Eliot to be two separate people. It is unclear how, or even whether, a neo-Fregean can plausibly avoid this conclusion.6

There remains a bit of a mystery: How can someone both believe and disbelieve a singular proposition about y without thereby taking y to be distinct things?

The solution is not far to find. There is a potentially sound substitute for Schiffer's fallacious reductio, an alternative derivation that relies on (FC) and (S) without fatally detouring through dubious generalizations. This time, putting for 0x0003b2the ‘that’-clause ‘that George Eliot was a man’ and putting for 0x0003d5it the open sentence ‘It is something Ralph believes’, the relevant half of the resulting instance of (S) states that necessarily, if Jane believes that (the proposition) that Eliot was a man is something Ralph believes, then Jane believes of (the proposition) that George Eliot was a man, de re, that it is something Ralph believes. In situation (a), it may be supposed, so Jane does. One similarly obtains the result that necessarily, if Jane believes that (the proposition) that Mary Ann Evans was a man is something Ralph does not believe, then Jane believes of (the proposition) that Mary Ann Evans was a man, de re, that it is something Ralph does not believe. In situation (a), it may be supposed, so Jane does. According to Millianism, the propositions to which Jane in (a) de re attributes complementary properties (being believed by Ralph and not) are one and the same. Reasoning from (FC), it follows that Jane, insofar as she is rational in (a), must take this proposition in differing ways.

In situation (a), it may be supposed, so Jane does. She evidently mistakes this singular proposition for two independent thoughts (or at least is committed to doing so), one that Ralph believes, the other (according to Jane) not. No contradiction is derived and no problem for Millianism generated. On the contrary, our conclusion solves the riddle of how, without mistaking Eliot for two distinct people, one can rationally both believe and disbelieve of Eliot, de re, that Ralph believes she was a man. Though Jane does not mistake Eliot for distinct people, she may nevertheless mistake the singular proposition that Eliot was a man for distinct thoughts.7 With this new derivation, Jane has been outed as a proto- or closet neo-Fregean. With a little further Socratic questioning, she might be induced to embrace her neo-Fregeanism with pride.

Schiffer defends his objection to Millianism, asserting, ‘. . . the only reasonable construal of propositional modes of presentation is that they are structured entities whose basic components are modes of presentation of the basic components of the Russellian propositions of which the propositional modes of presentation are modes of presentation.’ Since Jane does not have the requisite differing modes of presentation of Eliot (nor of the property or concept of having been a man), she also does not have differing modes of presentation of the (putatively singular) proposition that Eliot was a man, as would be required by (FC).

With all due respect, it is unreasonable to suppose that the only proposition guises are such composite constructions as Schiffer envisions. The rational neo-Fregean who takes the proposition that George Eliot was a man to be believed by Ralph and also

takes the proposition that Mary Ann Evans was a man not to be believed by Ralph takes a single proposition to be two thoughts, and thereby takes it differently. The proposition might be taken as invoking Ralph's concept of who George Eliot is, and alternatively, as not doing so. The former is a misconception, to be sure, but misconceiving is a way of taking.

13 Being of Two Minds: Belief with Doubt (1995) *

Nathan Salmon

I Belief is systematically connected with a variety of psychological attitudes. Disbelief is, in a certain sense, the opposite of belief. But one may fail to believe something—say, that Ortcutt is a spy—without going so far as to disbelieve it. One may suspend judgment on the issue. For the purposes of the present discussion, let us agree to stipulate the following definition for the word ‘doubt’:


A doubts p = def (A disbelieves p) V (A suspends judgment concerning p).

Notice that according to this definition, in order for Ralph to count as doubting whether Ortcutt is a spy, Ralph need not even believe it unlikely that Ortcutt is a spy. It is enough that Ralph have no opinion on the matter. This constitutes a departure from standard usage, but it is merely a stipulation concerning how the word ‘doubt’ will be used here.1

What, now, is the relationship among these five: belief, disbelief, failure to believe, failure to disbelieve, and suspension of judgment?

Here is one plausible way to make out the connections. Let us tentatively lay down the following additional definitions, treating the English verb ‘believes’ together with the standard truth-functional connectives as primitive:


A disbelieves p = def A believes 0x00223cp.


A fails to believe p = def 0x00223c(A believes p).


A fails to disbelieve p = def 0x00223c(A disbelieves p).


A suspends judgment concerning p = def (A fails to believe p) 0x002227(A fails to disbelieve p).


Notice that disbelief is (unlike failure to believe, failure to disbelieve, and suspension of judgment) a form of belief: it is belief of the denial. Suspension of judgment is defined as the joint failure of both belief and its opposite, disbelief. This definition is objectionable on the ground that genuine suspension of judgment requires in addition, for example, that one have a grasp—some apprehension, perhaps even if imperfect—of the proposition in question. One might suppose furthermore that suspension of judgment, in Russell's words, ‘represents the result of an attempt to decide between the two’—i.e. that in order to count as suspending judgment on some matter one must have at least consciously considered the question at issue.2 The points I shall make below are not greatly affected if one adds such restrictions as these to the proposed definition. For the most part, the discussion will require only minor modification to take account of the further conditions (for example by restricting the range of the propositional variable ‘p’ to propositions that A apprehends). As we did for doubt, let us simply stipulate that as we use the phrase here, suspension of judgment does not require that one have consciously considered the question.

Some immediate consequences of the definitions should be noted. We have made doubt definitionally equivalent to the disjunction of disbelief with suspension of judgment, thereby making for two distinct ways of doubting something. The definitions, as given, yield an alternative equivalent disjunction: To doubt something is to disbelieve it, or alternatively, simply to fail to believe it. It is not that failure to believe is equivalent to suspending judgment, suspending judgment, as defined above, entails failing to believe, but not vice versa. In failing to believe something one either disbelieves it, thereby doubting by disbelieving, or failing that, one suspends judgment (by definition), which is the second way of doubting. But the definitions allow for at least the possibility of someone believing something while also disbelieving, and hence doubting, it. Having contradictory beliefs is depicted here as at least a logical possibility, even if it is an irrational possibility and even if, as some have argued, it is a psychological impossibility. With this in mind, one can see that doubt is not simply identified with failure to believe. It is logically possible for one to doubt something while still believing it, but only by believing it and disbelieving it at the same time. The only way to fail to doubt something is to believe it but without also disbelieving it, i.e. to believe it in the normal way.

Such consequences as these are more easily seen if our definitions are symbolized in a standard logical notation. Let upper-case ‘P’ symbolize ‘Ralph believes that Ortcutt is a spy’, and let upper-case ‘Q’ symbolize ‘Ralph disbelieves that Ortcutt is a spy’. The following symbolizations for the notions of failure to believe, failure to disbelieve, suspension of judgment, and doubt are thereby generated:


Ralph fails to believe that Ortcutt is a spy: 0x00223cP.


Ralph fails to disbelieve that Ortcutt is a spy: 0x00223cQ.


Ralph suspends judgment concerning whether Ortcutt is a spy: 0x00223cP 0x0022270x00223cQ.


Ralph doubts whether Ortcutt is a spy: Q V (0x00223c P 0x0022270x00223cQ).

The decision to symbolize in this manner presupposes the logical independence of belief and disbelief. One may compensate for this, if one wishes, by laying it down as a special postulate that Ralph does not both believe and disbelieve that Ortcutt is a spy, 0x00223c(P 0x002227Q). In the general case, let us call the following postulate ‘A's Consistency’:


0x00223c(A believes p 0x002227A disbelieves p).

Here now are several theorems, each of which is easily derived from the definitions in standard propositional logic:

T1

A believes p V A doubts p.

T2

0x00223c(A believes p 0x002227A suspends judgment concerning p).

T3

0x00223c(A disbelieves p 0x002227A suspends judgment concerning p).

T4

A doubts p0x00223c(A disbelieves pA suspends judgment concerning p).

T5

A doubts p ≡ (A believes p 0x002283A disbelieves p).

T6

(A believes p 0x002227A doubts p) 0x002283A disbelieves p.

Theorem T1 tells us of every proposition within the range of ‘p’, that A either believes it or doubts it, where A can be anyone at all. Theorem T2 tells us that no one both believes and suspends judgment concerning the very same proposition, and theorem T3 tells us that no one both disbelieves and suspends judgment concerning the very same proposition. Theorem T4 indicates that doubting—which was defined as the inclusive disjunction of disbelief with suspension of judgment—is equivalent to the exclusive disjunction. This equivalence is an immediate corollary of T3. Theorem T5 indicates an alternative equivalent of doubting p: if one believes p, then one also disbelieves p. This was foreshadowed in our observation that doubt is definitionally equivalent to the disjunction of disbelief with mere failure to believe. Theorem T5 immediately yields the result, given in T6, that believing while at the same time doubting the same thing inevitably requires one also to disbelieve that same thing—a corollary that resonates with T2.

Taking A's Consistency as a postulate yields the following addenda to T1 and T2:

C1

0x00223c(A believes p 0x002227A doubts p).

C2

0x00223c(A believes pA doubts p).

A's Consistency thus tells us of every proposition within the range of ‘p’, that A either believes it or doubts it, but never both. We noted above that the logical possibility of believing while also disbelieving is all that prevents the identification of doubt with simple failure to believe. Consequence C2 immediately yields the following additional consequence, as a strengthened replacement for T5:

C3

A doubts pA fails to believe p.

It is easily shown that each of C1, C2, and C3 is in fact equivalent to A's Consistency.

II

All of these theorems and consequences are questionable results. In effect, they exclude various combinations of doxastic attitudes and/or the lack of doxastic attitudes as logically impossible—or in the case of A's Consistency, as perhaps impossible in some other manner (e.g. psychologically). In particular, T2 through T6 and A's Consistency and its equivalents exclude as impossible various ways of being of two minds, combining belief with doubt. What shall we make of these results?

Whatever oddity there may be in T1 results entirely from our decision to understand suspension of judgment in a passive way. If we bear in mind that, so understood, merely failing to believe something while also failing to disbelieve it qualifies as suspending judgment concerning it, and hence as doubting it, T1 should not strike us as unacceptable—or at least it should not strike us as being unacceptable in some further way. The case is very different, however, with T2 through T6, and with A's Consistency and its equivalents. For the combinations of conflicting attitudes that they rule out are evidently combinations that one may nevertheless exhibit.

Is it possible, in a real sense, to have genuinely conflicting doxastic attitudes? One immediately thinks of the subconscious and of self-conscious ambivalence. It is arguable that such cases provide genuine counterexamples to T2 through T6 and/or to A's Consistency and its equivalents. It is equally arguable that they do not. Let us set such cases aside. The philosophy of language has provided an altogether different kind of example of conflicting attitudes.

Nearly four decades ago in his classic ‘Quantifiers and Propositional Attitudes’, Quine made a significant case against A's Consistency.3 He there provided a now famous example in which it would be clearly correct to say that, because he has failed to recognize Ortcutt in his different personae, Ralph believes Ortcutt to be a spy while simultaneously believing Ortcutt not to be a spy. Being a Millian with respect to proper names, I accept Quine's example as a case of Ralph both believing that Ortcutt is a spy, and at the same time also disbelieving, and hence doubting, that Ortcutt is a spy. Quine himself evidently does not so construe the case, insisting instead on Ralph's Consistency and on the inaccuracy of characterizing Ralph as believing of Ortcutt that he is a spy. But his argument for this is confused and, in my judgment, very much mistaken.4

Even setting Quine's example alongside cases from the subconscious and ambivalence, similar sorts of examples are driving an increasing number of philosophers to the same conclusion that failure to recognize someone or something typically results in contradictory beliefs about that one or that thing. Nothing has done more to lend credence to this conclusion, and to foster its widespread acceptance, than Kripke's recent classic ‘A Puzzle about Belief’.5 Kripke himself concludes his trenchant essay by cautioning against drawing any significant theoretical conclusions from his arguments and examples.6 And indeed, several remarks seem to indicate that he adamantly opposes this conclusion in particular.7 In hindsight, however, his examples and arguments are today very often seen—perhaps even usually seen—as making an extremely strong case (however inadvertent) against A's Consistency. Those examples and arguments also make an extremely strong case against claims like those made in T2 through T6, when taken in their usual senses, or something close to it (as opposed to the nonstandard senses imposed on them by the proposed definitions). The case against the ‘theorems’ is in many respects quite similar to, even though significantly stronger than, Quine's (equally inadvertent) case against A's Consistency and its equivalents.

Kripke's examples refute A's Consistency by providing cases in which a rational believer, Pierre, is unknowingly of two minds concerning whether London is pretty. Although frequently overlooked, one of the most significant aspects of Kripke's examples is that the difficulties they raise for A's Consistency and its equivalents are quite independent of the on-going debate between Millianism (or neo-Russellianism) and Fregeanism. Millians and Fregeans alike have concluded that Pierre is of two minds, harboring conflicting attitudes toward the single proposition that London is pretty. In the central example, Pierre both believes and disbelieves that London is pretty. Kripke also briefly considers a modified example in which Pierre instead both believes and suspends judgment without disbelieving (op. cit., pp. 122–123). Although Kripke does not do so, one might also consider an alternative modified example in which Pierre disbelieves and suspends judgment without believing. In

fact, it is a simple matter to extend the original example into one in which Pierre is of three minds. Imagine that Pierre has learned not only English but also Italian by direct assimilation (not by translation into either French or English). He comes to believe that the city named ‘Londra’ is a third city, distinct from both the pretty city named ‘Londres’ and the ugly city named ‘London’. When queried in Italian, ‘Londra è graziosa?’, he neither assents nor dissents, explaining that he has no opinion on the matter. In this example, he believes, disbelieves, and also suspends judgment with respect to the same proposition that London is pretty! This and the other permutations on Kripke's original example, I contend, invalidate each of T2 through T6, when taken in something like their standard senses, as well as A's Consistency.8

Since each of these theorems follow logically from the proposed definitions, the examples thereby discredit those definitions. Our conclusion, then, is that, however plausible they seemed at first sight, at least one of our definitions has missed its intended target. Which one, or ones?

It is under the pressure applied by examples of someone being of two minds—combining belief with doubt—that I have suggested alternative accounts of belief and doubt.9 Many commentators have thought that my alternative account is proposed as an ad hoc supplement to my advocacy of a Millian theory of names, in order to make the theory more palatable. Let me emphasize that the pressure to adopt some such alternative account does not come from my Millianism, except perhaps by a very circuitous route. If I were a Fregean, I would still advocate my alternative account of the doxastic attitudes, and for very much the same reasons. Even looking at the situation through Fregean lenses, one is drawn to the conclusion that someone in Pierre's state of confusion is, or at least can be, of two minds (or of three or more minds) with respect to one and the same proposition—or in Frege's preferred terminology, with respect to one and the same ‘thought’ (Gedanke).10 To account for this anomaly, the Fregean need only turn to his/her notion of indirect sense (ungerade Sinn). The indirect sense of an expression is the sense that the expression allegedly takes on in positions in which it has indirect reference (ungerade Bedeutung), referring not to its customary referent but to its indirect referent, which is the sense customarily expressed. Indeed, although I do not know of anyone who has explicitly responded to Kripke's arguments by invoking the orthodox Fregean notion of indirect sense, that notion is tailor-made to explain predicaments like Pierre's.11 The English ‘London is pretty’, the French ‘Londres est jolie’, and the Italian ‘Londra è graziosa’ all express the same proposition. Pierre fully understands each of the three sentences. Each of those sentences therefore expresses the very same thing even for Pierre. But he does not realize that. The sentences present their shared proposition content to Pierre in different ways. Though exactly alike in customary sense, the three sentences thus differ in indirect sense, at least for Pierre, as he understands them.12

Although I am not a Fregean, I have helped myself, enthusiastically, to certain aspects of Frege's notion of sense—or more specifically, to certain aspects of his notion of indirect sense.13 I have done so not because my Millianism imposes a special requirement to do so, but because Pierre's predicament does. Pierre is of two (or more) minds concerning the proposition that London is pretty because he takes the proposition in different ways, mistaking it for two (or more) independent propositions—just as he mistakes London for two (or more) different cities. If a believer A treats a pair of propositions p and q as being distinct, then he or she takes p and q in different ways—even if, in fact, p = q. Thus if A mistakes p for two independent propositions, then he or she takes p in two different ways. I have proposed that we recognize a ternary relation, BEL, underlying the binary relation between believer and proposition believed. The BEL relation obtains among a believer A, a proposition p, and a way x of taking p, when A is disposed to cognitive assent to p, taking it in way x. Or something along those lines. The important point is that A may stand in BEL to p and one third relatum x (one way in which A takes p), yet fail to stand in BEL to p and some other third relatum x′≠x (some other way in which A takes p). When one fails to recognize something or someone, one's attitude toward that thing or that one may depend on how one takes it, on which thing or which one it is taken to be.

The simple claim ‘A believes p’ is analyzable as A's standing in BEL to p and some way or other in which A takes p:


(0x002203x)[A takes p in way x 0x002227BEL(A, p, x)].

A point that has escaped many of my commentators is that this analysis makes belief a binary, rather than a ternary, relation. One might view my reliance on the BEL relation as making for a relative notion of belief, one that obtains relative to ways of taking propositions. If one does, then ordinary belief is nothing other than the absolute notion naturally corresponding to this relative one. The English verb ‘believes’ may be regarded as a dyadic predicate for the relation between individuals and propositions defined by the expression displayed above (more accurately, for the relation defined by prefixing ‘(0x0003bbA, p)’ to the expression displayed above).

Combining this analysis for belief with our earlier definitions, we arrive at the following analyses for ‘A disbelieves p’, ‘A fails to believe p’, and ‘A fails to disbelieve p’, respectively:


(0x002203x)[A takes 0x00223cp in way x 0x002227BEL(A, 0x00223cp, x)];


0x00223c(0x002203x)[A takes p in way x 0x002227BEL(A, p, x)];


0x00223c(0x002203x)[A takes 0x00223cp in way x 0x002227BEL(A, 0x00223cp, x)].

These constructions simply insert a negation sign at one place or another in the analysis for ‘A believes p’. There is at least one other position in which the negation sign might be sensibly placed. To account for situations like Pierre's, I offered an analysis of a supplementary notion, which is modeled in a certain sense after the notion of failure to believe, and which I called ‘withheld belief’. ‘A withholds belief from p’ is analyzed as:


(0x002203x)[A takes p in way x 0x0022270x00223cBEL(A, p, x)].14

Notice that this notion is logically compatible not only with failure to believe and with disbelief, as analyzed above, but also with belief of the very same proposition p. Taken together with our analysis of belief it immediately yields the following theorem:

T7:  

(0x002203x)(A takes p in way x) 0x002283(A believes p V A withholds belief from p).


This tells us that anyone who apprehends a given proposition without believing it withholds belief from it. But refraining from believing an apprehended proposition is not the only way to withhold belief. One can both believe and withhold belief from the same proposition.

In place of the earlier definition for suspension of judgment, we now have the following analysis for ‘A suspends judgments concerning p’:


(0x002203x)[A takes p in way x 0x0022270x00223cBEL(A,p,x) 0x002227A takes 0x00223cp in way Neg(x) 0x0022270x00223cBEL(A, 0x00223cp, Neg(x))],

where Neg(x) is the corresponding way of taking the denial of the proposition that x is a way of taking.15 This immediately yields the following theorems:

T8

A suspends judgment concerning p 0x002283A withholds belief from p.

T9

A suspends judgment concerning p 0x002283A withholds belief from 0x00223cp.

These theorems, taken together with our new analysis of suspension of judgment, tell us that to suspend judgment concerning a proposition is to withhold belief both from that proposition and from its denial, but to do so in a special manner via a single way of taking the matter.

III

We have seen that failure to believe an apprehended proposition entails withholding belief from it, but not vice versa. What is the relationship among disbelief, withheld belief, suspension of judgment, and doubt?

To answer this question, I propose assuming three special postulates.16 The first I shall call ‘A's Comprehension’:


A takes p in way xA takes 0x00223cp in way Neg(x).

This tells us that if A apprehends a certain proposition p, then A also apprehends its denial 0x00223cp in the appropriate way corresponding to the way in which A takes p, i.e. as the denial of p. It also tells us that if A apprehends a certain negative proposition 0x00223cp in an appropriate manner (i.e. as a negative proposition), then A also apprehends the proposition p that 0x00223cp negates in the appropriate way corresponding to the way in which A takes 0x00223cp, i.e. as the proposition negated by 0x00223cp. A's Comprehension (in the left–right direction), taken alone, yields the following consequence:

C4

A withholds belief from p 0x002283(A disbelieves p V A suspends judgment concerning p).

The second postulate I shall call ‘the Negativity Principle’:


A takes 0x00223cp in way x 0x002283(0x002203y)(x = Neg(y)).

This tells us, in effect, that to any way of taking a negative proposition 0x00223cp there corresponds an appropriate way of taking the proposition p negated by 0x00223cp. The third postulate, which I shall call ‘A's Rationality’, replaces the now discarded A's Consistency:


0x00223c[BEL(A, p, x) 0x002227BEL(A, 0x00223cp, Neg(x))].17

Recall that A's Consistency, in its consequence C3, rendered doubt equivalent to failure to believe. Using the Negativity Principle and A's Comprehension (in the right–left direction only) in combination with A's Rationality, we may derive:


A disbelieves p 0x002283A withholds belief from p.

Combining this consequence with T8 and C4 we have the following:

C5:  

A withholds belief from pA doubts p.

Consequence C5 is our replacement for C3. Although the definition for ‘doubt’ has not been altered, the notion so defined has changed significantly. This is because doubt is defined in terms of suspension of judgment, and our new notion of suspension of judgment is significantly different from our old one. Consequence C4 yields a near entailment between the old notion and the new one:


(0x002203x)(A takes p in way x) 0x002283[(A fails to believe p 0x002227A fails to disbelieve p) 0x002283A suspends judgments concerning p].

This tells us that if A apprehends p but neither believes it nor disbelieves it, then A suspends judgment. But we no longer have that if A apprehends p and suspends judgment concerning it, then A fails to believe it, and likewise we no longer have that if A apprehends p and suspends judgment concerning it, then A fails to disbelieve it. In short, the new notion of suspension of judgment is, in a sense, weaker than the old one. Most significantly, ‘A suspends judgment concerning p’ is now consistent both with ‘A believes p’ and with ‘A disbelieves p’. In fact, even A's Rationality (with or without the other two postulates) does not exclude the joint truth of all three. This is all for the good, since on the amended example, Pierre believes, disbelieves, and suspends judgment with respect to a single proposition. The new, weaker notion of suspension of judgment yields a notion of doubt that is likewise weaker than the old one.

We have already seen our replacements for the discarded A's Consistency and its equivalents. But what has become of the previous theorems T1 through T6? In place of T1, as a direct consequence of T7 and C5 we now have:

C6:  

(0x002203x)(A takes p in way x) 0x002283(A believes p V A doubts p).


Thus failing to believe an apprehended proposition remains one way of doubting it.

By contrast with T1, all of T2 through T6 simply go by the wayside.18

IV

I have stressed that my postulation of a ternary relation underlying the binary relation between a believer and the proposition believed is motivated primarily by considerations that are largely independent of the controversy between Millians and Fregeans. Recognition of the BEL relation allows for the natural definition of a relation of suspension of judgment that is compatible with both belief and disbelief of the same proposition, and with belief-with-disbelief. It also allows for a straightforward understanding of such notions as that of believing the same thing in two different ways or believing the same thing twice over, of doubting the same thing twice over, etc. Examples like Kripke's compel one to recognize these various doxastic notions, and the examples do so largely independently of one's theory of meaning. I have also relied on the presence of the BEL relation in the underlying structure of the belief relation to explain the prevailing intuitions against some of the consequences of Millianism concerning substitution.19

Other philosophers have looked to the BEL relation to do independent duty as part of a device that can rescue Millianism altogether from its untoward consequences. One strategy is to treat the grammatical complement clause in a belief attribution as specifying at one and the same time both the proposition, belief of which is being attributed, and with it also a specific third relatum for the BEL relation. For example, an English belief attribution of the form


0x0003b1believes that 0x0003d5,

where 0x0003b1is a singular term and 0x0003d5is a declarative sentence, might be regarded as expressing a proposition about the referent of 0x0003b1, to the effect that he/she stands in BEL to p and w (or that he/she believes p ‘relative to’ w), where p is the proposition content of 0x0003d5and w is a particular third relatum for the BEL relation carried by the very sentence 0x0003d5for the referent of 0x0003b1. The complement clause 0x0003d5is thus pressed to perform two separate roles, determining distinct relata in separate argument places of the BEL relation. Indeed, on this theory, the belief attribution may be regarded as a shorthand for something like the following:


BEL(0x0003b1, that 0x0003d5, W[0x0003b1, 0x0003d5]),

where ‘W’ is special operator, not appearing explicitly in the surface structure, such that the result of attaching it to a singular term 0x0003b1and a sentence 0x0003d5in brackets refers to the way the referent of 0x0003b1takes the content of 0x0003d5when that proposition is presented

to him/her by means of (his/her version of) the very sentence 0x0003d5. Let us call this the double-dipper theory.20

Assuming that pairs of co-contentful sentences like ‘Hesperus appears at dusk’ and ‘Phosphorus appears at dusk’ provide speakers with distinct ways of taking their shared proposition content, the double-dipper theory offers a ready explanation for the appearance of a failure of substitution in problematic attributions like ‘Jones believes that Hesperus appears at dusk’: Whereas substituting ‘Phosphorus’ for ‘Hesperus’ preserves the attributed proposition, doing so does not also preserve the specified way of taking that proposition, and hence need not preserve truth value for the whole attribution. The double-dipper theory is in fact reminiscent of Fregeanism. One of the principal characteristics that distinguish the double-dipper theory from a mere notational variant of Fregeanism is that the thing said to be believed in ‘Jones believes that Hesperus appears at dusk’ (or the thing said to be doubted in ‘Jones doubts whether Hesperus appears at dusk’, etc.) is not supposed to be the proposition-cum-way-of-taking-it provided by the complement clause, but merely the proposition, in this case a singular proposition. As will become clear in due course, this feature of the double-dipper theory is significant. Another feature of the double-dipper theory that differentiates it from Fregeanism is that it is refuted by Alonzo Church's famous translation argument.21

Stephen Schiffer has proposed a close relative of the double-dipper theory, which he calls the hidden-indexical theory.22 The hidden-indexical theory, or something extremely similar, has been defended by Mark Crimmins and John Perry.23 The central idea is that an English belief attribution of the form


0x0003b1believes 0x0003b8,

with 0x0003b1a singular term and 0x0003b8a term referring to a proposition, is indexical, expressing different propositions with respect to different contexts of utterance. With respect to

a given context c, it expresses (or at least commonly expresses) a proposition about the referent of 0x0003b1with respect to c and the referent of 0x0003b8with respect to c, to the effect that the former stands in BEL to the latter and w, where w is a particular third relatum for the BEL relation, one that is implicitly or tacitly referred to (‘unarticulated’, to use Perry's term) in, and determined only relative to, the context c. It is as if the attribution were shorthand for something like the following:


BEL(0x0003b1, 0x0003b8, that way of taking 0x0003b8).

Here the third argument is a demonstrative phrase which is ‘hidden’ in the surface structure, and by means of which (or as if by means of which) the speaker refers, in his/her context, to a particular way of taking a proposition.24

Both the double-dipper and the hidden-indexical theories, as well as my own theory, are compatible with, and even strongly suggest, the thesis that a ‘that’-clause 0x00231cthat 0x0003d50x00231d, with 0x0003d5a declarative sentence, is a singular term (or at least a term much like a singular term) referring to the proposition content of 0x0003d5. As I have noted elsewhere, independently of the rivalry among these theories, this thesis regarding ‘that’-clauses is both natural and plausible.25 It provides the best explanation, for example, for the validity of inferences like the following:

(I):  

Pierre believes everything Jean-Paul says about London.


Jean-Paul says (about London) that London is pretty.


Therefore, Pierre believes that London is pretty.

Indeed, Schiffer cites this observation as yielding a very important consideration in favor of the hidden-indexical theory over alternative theories that preclude treating ‘that’-clauses as singular terms for propositions.26 Notice furthermore that the hidden-indexical theory provides an analysis for belief attributions of the form ‘A believes 0x0003b8’ even when the proposition term 0x0003b8does not take the form ‘that 0x0003d5’, with 0x0003d5a declarative sentence, and instead takes the form of a definite description (‘the proposition to which our nation is dedicated’, ‘what Jean-Paul said’) or a name (‘Church's Thesis’, ‘functionalism’). It is questionable whether the double-dipper theory can be plausibly extended to cover attributions of the more general form. The hidden-indexical theory may thus afford significantly greater flexibility in this regard.

There is considerable intuitive evidence, however, that typical belief attributions do not semantically specify (or even constrain) particular third relata for the BEL relation—whether explicitly or implicitly, whether contextually or noncontextually. The point at issue parallels in many respects the much-debated question of whether so-called indefinite descriptions, like ‘a man’, are singular terms or instead nonspecific existential-quantificational constructions.27 For example, suppose Peter utters the attribution,

𝒫:  

Pierre believes that London is pretty

based on the erroneous assumption that Pierre, on reflection, is disposed to assent sincerely to the sentence ‘London is pretty’. To press the case even further, suppose that the background for Peter's utterance of 𝒫 includes special attention to the matter of what sort of impression one forms of London based primarily on an exposure to its slums. There is some temptation to judge that 𝒫 is false, as uttered by Peter under these circumstances. And this is exactly the verdict delivered by the hidden-indexical theory.28 Yet (as Kripke forcefully demonstrates), on reflection there is a solid intuitive basis for the contrary judgment that 𝒫 is literally true in English, with respect to Peter's context, even though Peter's basis for it is seriously flawed. For Pierre does indeed assent to the proposition that London is pretty when it is presented to him by means of the French sentence ‘Londres est jolie’; he thus believes the proposition in at least one way (‘relative to’ some way or other). One might rightfully say that Peter spoke incorrectly; perhaps one may even say that Peter said something false about Pierre. But none of this overturns the thesis that the sentence Peter used is literally true.29 The situation here is exactly analogous to the debate concerning whether ‘I met a man this afternoon’ is true in English even if the man the speaker has in mind was in fact met that morning—the speaker's watch was mistakenly set an hour ahead—when the speaker also met some man or other that afternoon, even though the speaker has forgotten all about it. A sentence that is true by sheer accident or dumb luck is no less true than one whose iron-clad support is still fresh in one's mind.

If there is a genuine clash of reflective intuitions here, then it is no defect in the hidden-indexical theory (or indeed in any other theory) that it fails to accommodate all of the relevant intuitions. However, a much more serious problem arises from the fact that the hidden-indexical theory makes the additional, distinctly counterintuitive claim that 𝒫 is literally true with respect to some contexts, while also being not merely misleading or otherwise infelicitous but literally false with respect to others (like the one described above)—this even though Pierre's relevant opinions remain unshakably firm.30

Perhaps the most compelling intuitive evidence against the hidden-indexical theory is provided by valid inferences that the theory declares invalid. Crimmins and Perry discuss a special version of Leibniz's Law:


0x0003b1believes 0x0003b8


0x0003b1= 0x0003b2


Therefore, 0x0003b2believes 0x0003b8.


Crimmins and Perry argue that this inference is logically invalid, in the sense that there are instances for which there is a single context with respect to which the premisses are true and the conclusion false.31

The claim that this inference is invalid on the hidden-indexical theory is, at best, misleading. The issue is complicated. Inspection of the case discussed by Crimmins and Perry reveals that, on their view of the matter, the substitution performed on the first premiss necessarily alters the context, thereby shifting the reference of the hidden indexical between the relevant (minor) premiss and the conclusion, providing a different ‘unarticulated constituent’. If this were indeed the case, we would not have a situation in which truth fails to be preserved when the premisses and conclusion are all evaluated with respect to a single context. Rather, what Crimmins and Perry seem to be claiming is that truth fails to be preserved when the premisses are evaluated with respect to a single context and the conclusion is evaluated with respect to a different context, one just like the context of the premisses except for the presence of different words being uttered. It is precisely this shift in context that is supposed to explain the difference in ‘unarticulated constituents’ between premiss and conclusion.32 Compare: Giorgione was called by that name because of his size. Giorgione = Barbarelli. Therefore Barbarelli was called by that name because of his size.

Where indexicals are involved, the classical notion of logical validity must be adjusted to take account of context. But truth preservation under shifting contexts does not constitute the proper notion of validity. Rather, what is at issue is truth

preservation under fixed contextual parameters (in every model).33 This notice accommodates the classically valid inference form ‘0x0003d50x0022340x0003d5’. It also validates the above inference involving Barbarelli. Furthermore it declares logically inconsistent the illusionist's trademark slogan ‘Now you see it; now you don't’. To accommodate the slogan and lose the inference involving Barbarelli, one may define a complementary notion for the assessment of arguments, one that looks at such phenomena as the shifting of contexts that occurs, or may occur, in the actual utterance of an argument. One might then reject even repetition inference of the form ‘0x0003d50x0022340x0003d5’—for example, replacing ‘I am seeing a flash now; therefore I am seeing a flash now’ with ‘I am seeing a flash now; therefore, I was seeing a flash then.’ (Notice that the latter is semantically invalid.) Let us call this speech-act centered notion pragmatic cogency, to distinguish it from semantic validity.34 It is not the proper notion of logical validity, but it is not a useless notion. With it one can see a genuine aberration in the hidden-indexical theory: Whereas, pace Crimmins and Perry, the theory in fact accommodates the semantic validity of Leibniz's Law when applied to belief attributions, it fails to accommodate its pragmatic cogency. The willingness of the theory's adherents to embrace this consequence, or their possible willingness to do so, does not alter the fact that the consequence is decidedly counterintuitive.35

Perhaps the most compelling evidence that belief attributions do not semantically specify (or constrain) any way of taking a proposition in addition to the proposition itself is provided by the validity of inference (I) displayed above. Ironically, in the proper sense of ‘valid’, the hidden-indexical theory fails to accommodate inferences of the very sort that Schiffer cites in defense of that theory. According to the theory, the conclusion of inference (I), 𝒫, will (typically) specify, with respect to any given context c, the same way of taking the proposition that London is pretty that is specified with respect to c in the minor premiss ‘Jean-Paul says that London is pretty’. Indeed, if either the double-dipper theory or the hidden-indexical theory were correct, the conclusion of (I) would contain more information than one would be warranted in inferring on the basis of the premisses. Far from supporting the hidden-indexical theory as Schiffer argues, the evident validity of such inferences thus intuitively refutes both the double-dipper theory and the hidden-indexical theory.

end p.248


14 Relational Belief (1995) *

Nathan Salmon

I

When faced with a philosophically problematic locution, Quine has proposed replacing the offending construction with one better suited to his philosophical temperament and point of view. At first sight this replacement strategy seems a profitable move. But on closer scrutiny the strategy can be somewhat puzzling. If the replacement means the same thing as the original construction, then surely nothing is to be gained in the substitution of the one by the other. But even if the replacement construction does not mean the same thing as the original, what is to be gained in the substitution—other than obfuscation? The problematic locution has merely been replaced with something less problematic; it has not been obliterated. It still exists; it just does not occur where it used to. Philosophical problems are not solved by diverting attention from them.

Part of the answer sometimes lies in the fact that the original locution is not only replaced, but also repudiated. It is deemed ill-formed nonsense. The replacement is made to fill the void left by the expulsion of the meaningless.

Such is the case with part of Quine's proposed solution to his famous puzzle concerning Bernard J. Ortcutt from his classic article ‘Quantifiers and Propositional Attitudes’ (Quine, 1956). Quine imagines a character, Ralph, who believes someone is a spy. Ralph believes this in both of two very different senses. Like all of us, Ralph believes that someone or other is a spy, i.e., that there are spies. This is the notional sense of believing someone is a spy. But more than this, Ralph believes someone in particular to be a spy. This is the relational sense of believing someone is a spy. Ralph believes that a certain man he saw under suspicious circumstances, wearing a brown hat, is a spy. Ralph also happens to believe that a certain pillar of the community named ‘Bernard J. Ortcutt’, whom he remembers having seen once at the beach, is not a spy. What Ralph does not realize is that the man at the beach and the man in the brown hat are one and the same. Consider this man Bernard Ortcutt. Does Ralph believe that he is a spy? One may be inclined to say that Ralph does, since he believes that the man in the brown hat is a spy, and that man is Ortcutt. But Ralph does not believe that the man at the beach is a spy, and that man is also Ortcutt.

The problem concerns the sentence

0a  

Ralph believes of Ortcutt that he is a spy.

To bring the problem into its sharpest focus, consider the following quasiformal sentence, which seems to assert the same thing as 0a:


(0x0003bbx) [Ralph believes that x is a spy] (Ortcutt).

By the conventional semantic rules governing Alonzo Church's ‘0x0003bb’-abstraction operator, this sentence is true if and only if the open sentence

1  

Ralph believes that x is a spy

is itself true under the assignment of Ortcutt as value for the variable ‘x’. Is 1 true under this assignment or is it false? To pose the same question in the terminology of Tarski, does Ortcutt satisfy 1? There does not seem to be a satisfactory answer. When the variable is replaced by the phrase ‘the man seen wearing the brown hat’, the resulting sentence is true. When the variable is replaced by the phrase ‘the man seen at the beach’, however, the resulting sentence is false. Whether Ralph believes Ortcutt to be a spy or not depends crucially on how Ralph is conceiving of Ortcutt. It seems impossible to evaluate 1 under the assignment of Ortcutt himself, as opposed to various ways of specifying him, to the variable. Quantification (or any other sort of variable binding) into a nonextensional context like ‘Ralph believes that . . .’ is thus senseless. These considerations seem to bar us from saying anything along the lines of

2  

Ralph believes that he is a spy

with reference to Ortcutt (so that the pronoun ‘he’ in 2 plays the same role as the variable ‘x’ in 1)—as, for example, in the context ‘As regards Ortcutt, . . .’. And this bars us from 0a. How, then, shall we express the obvious fact that Ralph believes someone is a spy in the relational sense?

It is important to notice that this problem, unlike Kripke's famous puzzle about belief (Kripke, 1979), primarily concerns the object that the belief is about, i.e., Ortcutt. Ralph and his notional beliefs (as represented by the sentences he accepts), considered in abstraction from Ralph's fellows, present no special difficulties. He is simply in a state of partial ignorance. He does not realize that the suspicious looking man wearing the brown hat is the man at the beach; he erroneously believes that the man in the brown hat is someone other than Ortcutt. The crucial philosophical question is whether Ortcutt, independently of any particular specification of him, satisfies a certain relational condition: Is he believed by Ralph to be a spy? The grounds for an affirmative answer—that Ralph does indeed believe that the man in the brown hat is a spy—seem perfectly counterbalanced by equally good (or equally bad) grounds for the opposite answer. One is invited to conclude that the question of whether Ortcutt himself, in abstraction from any particular conception of him, is believed by Ralph to be a spy makes no sense—or at least that it has no sensible answer.1

The puzzle can be made out especially forcefully from the perspective of a Fregean philosophy of semantics. As Frege would have noted, although the expressions ‘the man seen wearing the brown hat’ and ‘the man seen at the beach’ both refer to Ortcutt, they differ in sense. They present Ortcutt by means of different individual concepts. In any belief attribution, such as

3a  

Ralph believes that the man in the brown hat is a spy

every expression following the phrase ‘believes that’ occurs in an indirect or oblique context, and refers in that position not to the expression's customary referent but to its customary sense. In this theoretical framework, quantification into an oblique context poses a special difficulty. The ‘x’ in 1, taken under the assignment of Ortcutt as value, is supposed to refer in that position to its customary sense. But ‘x’, under the assignment of a particular value, has no sense. (Alternatively, it ambiguously expresses infinitely many different senses, viz., every sense that determines its value as referent.) It would seem that 1, under the assignment of Ortcutt to ‘x’, must therefore also lack sense. Once again, we seem driven to the conclusion that the question of whether Ortcutt himself satisfies 1 has no sensible answer—or at best, that Ortcutt satisfies neither 1 nor its negation, so that no one can ever believe of anyone that he or she is either spy or nonspy. How, then, do we express the fact that Ralph believes someone is a spy in the relational sense?

Quine proposed as a way out of this puzzle that, corresponding to the distinction between two senses of believing someone is a spy, we recognize a lexical ambiguity in ‘believes’ (and ‘wishes’, ‘hopes’, ‘fears’, etc.). There is the ordinary notion of belief expressed in a sentence like 3a. We may call this n-belief (for notional belief), so that 3a may be rewritten as:

3b  

Ralph n-believes that the man in the brown hat is a spy.

Quine urged that we also recognize an alternative kind of belief, which we might call r-belief (for relational belief). Grammatically, whereas one n-believes (or fails to n-believe) that such-and-such, one r-believes someone (or something) to be thus-and-so.2 Ralph does not n-believe that Ortcutt is a spy, but he does n-believe that the man in the brown hat is a spy, and he thereby r-believes Ortcutt to be a spy. The sentence

Ob

Ralph r-believes Ortcutt to be a spy

does not present the same difficulties as 0a, since 0b remains true whether the name ‘Ortcutt’ is replaced by either ‘the man at the beach’ or ‘the man in the brown hat’—or by any expression that refers to Ortcutt. By contrast, the true sentence 3b is transformed into a falsehood when ‘the man at the beach’ is substituted for ‘the man in the brown hat’. Consequently, replacement of the latter by a variable in the style of 1 is to be disallowed as ill-formed nonsense. Presumably, the same would hold for 2, and hence for 0a.

Quine did not rest content, however, with the distinction between n-belief and r-belief. For sentence 3b entails the existence not only of Ralph but of an additional entity, that the man in the brown hat is a spy, and 0b likewise entails the existence of being a spy. The former entity is a proposition, the latter a property. Quine devoutly disbelieves in such ‘intensions’ (for reasons that are largely independent of the issues concerning relational belief). Quine proposed replacing 3b with

3c  

Ralph believes-true ‘The man in the brown hat is a spy’

and likewise replacing 0b—which was itself a replacement for 0a—with

0c  

Ralph believes-true ‘is a spy’ of Ortcutt.3

Whereas the former constructions employing ‘n-believes’ and ‘r-believes’ involve a commitment to the existence of intensions, these new, wholly artificial constructions involve a commitment merely to the existence of sentences and predicates. This is a meager commitment that Quine is prepared to accept (however reluctantly). Thus, these replacements portend ontological dividends. They portend conceptual dividends as well. For the substitutes apparently replace unclear notions like that of belief of a proposition with far less dubious notions like that of truth (which might even be mathematically definable in the style of Tarski).

Quine's solution thus consists in a chain of replacements. An ‘unregimented’ belief attribution

Ia

0x0003b2believes that 0x0003d5

where 0x0003d5is a closed sentence, may be perspicuously formalized as

Ib

B n (0x0003b2, that 0x0003d5)

where ‘B n ’ is a dyadic predicate for notional belief and ‘that’ is a nonextensional operator that forms a term for the proposition expressed by the attached sentence. This construction is replaced directly with

Ic

Believes-true(0x0003b2, ‘0x0003d5’)

in which the sentence that forms the ‘that’ clause of Ia is taken out of the scope of ‘that’ and placed within quotation marks instead. By contrast, an unregimented sentence of the form

IIa

0x0003b2believes of 0x0003b1that 0x0003d5it

where the pronoun ‘it’ (‘he’, ‘she’) occurs anaphorically in 0x0003d5it , undergoes a two-stage modification. In the first stage it is replaced with

0x0003b2 

r-believes 0x0003b1to be such that 0x0003d5it

This may be formalized as:

IIb

B r (0x0003b2,0x0003b1,(0x0003bc0x0003b3) [0x0003d5 0x0003b3])

where 0x0003d50x0003b3is the same expression as 0x0003d5it except for containing free occurrences of a variable 0x0003b3where 0x0003d5it contains ‘free’ occurrences of the pronoun ‘it’. Here ‘B r ’ is a triadic predicate for relational belief, and the ‘0x0003bc’ in its third argument is a nonextensional variable-binding operator that allows for the abstraction of an attribute name from an open sentence. (See note 2 regarding Quine's alternative notation.) This formalization makes it obvious why the relevant notion is called ‘relational’; 0x0003b1occurs all alone in a ‘purely referential’ argument position, where it is open to substitution and to quantification from without.4 In the second stage, IIb is replaced further by

IIc

Believes-true-of (0x0003b2, ‘(0x0003bb0x0003b3)[0x0003d5 0x0003b3]’, 0x0003b1).

In the more recent discussion of ‘Intensions Revisited’ (Quine, 1981: 115, 119), the move between IIa and its final replacement is described as a ‘translation’, one by means of which relational belief is explained in terms of ‘believes-true’.

II

Owing largely to Quine's impressive rhetorical gift and persuasive skill, a great many philosophers of language today—perhaps most—are under the impression that quantification into a nonextensional context is dubious business, and that such innocent looking constructions as 0a are, from the point of view of philosophical logic, deeply problematic. This is ironic.

A few critics (Kaplan, 1986: 264–266; Kazmi, 1987: 95–98; Forbes, 1985: 52) have objected to Quine's argument by noting that an analogous situation arises out of certain temporal constructions, where the corresponding claim analogous to Quine's

in connection with 1 would be completely unwarranted. For example, the open sentence

S

In 1978, x was a Republican

is true when the variable is replaced by the name ‘George Bush’ but false when the variable is replaced by the phrase ‘the United States President’, despite the fact that these two expressions refer to the same individual. (That is, they refer to the same individual with respect to the present time.) It hardly follows that S cannot be evaluated under the assignment of Bush as value for ‘x’—let alone that we are forced to acknowledge a distinction between a notional and a relational concept of being the case in 1978 (whatever that would mean). The open sentence S, as it stands, is straightforwardly true under the assignment of Bush to ‘x’, since he (independent of any particular specification of him) was indeed a Republican in 1978. Quine's argument in connection with 1 is fallacious.

One may respond by rejecting the treatment of the phrase ‘in 1978’ as a sentential operator attachable to open sentences, insisting instead that S ultimately involves a dyadic predicate ‘is a Republican at’, which expresses a binary relation between individuals and times. (Very well. Suppose we invent an artificial, temporally neutral monadic predicate ‘Republicanize’ for the property of being a Republican—which applies with respect to any time t to exactly those individuals who are Republicans at t—and a sentential temporal operator ‘During 1978’ + past tense. What of that?) Fortunately, there is an alternative way of showing that Quine's argument against the logical intelligibility of 1 is fallacious, one that does not depend on any allegedly nonextensional context other than ‘Ralph believes that . . .’.

A half century before Quine's influential discussion, Russell was able to draw a very general distinction, of which Quine's distinction between the notional and relational sense of believing (or wishing, etc.) some F is G is merely a special case.5 Russell's distinction between primary occurrence and secondary occurrence applies to constructions involving any ‘denoting phrase’, i.e., any definite or indefinite description, in place of Quine's ‘some F’—for example, ‘Ralph believes every foreigner he meets is a spy’, ‘Ralph believes no friend of his is a spy’, ‘Ralph believes the union president is a spy’, ‘Ralph believes most Russians are spies’, and so on. In fact, Russell's more general distinction is not merely twofold, but (n+1)-fold where n is the number of operator occurrences in which the description (‘denoting phrase’) is embedded. For example, in addition to predicting its straightforwardly relational reading, Russell distinguished two notional readings for the complex attribution

Quine said that Ralph believes someone is a spy

Whereas the small-scope reading correctly reports the content of Quine's assertion when he attributes to Ralph a notional belief that someone is a spy (e.g., were Quine to utter the sentence ‘Ralph believes that there are spies’), the intermediate-scope reading correctly reports the content of Quine's assertion when he instead attributes relational belief (‘There is someone whom Ralph believes to be a spy’).

More significantly, Russell was able to explain his more general distinction as itself a special case of an even more general phenomenon: scope ambiguity On the theory of ‘On Denoting’, it is not in the least problematic that 1 is true when ‘x’ is replaced by ‘the man in the brown hat’ and false when ‘x’ is replaced by ‘the man at the beach’. The resulting ‘that’ clauses ‘denote’, i.e. refer to, different propositions, one of which Ralph believes and the other one of which he does not. By contrast, the original ‘that’ clause

that x is a spy

refers, under the assignment of Ortcutt to ‘x’, to yet a third proposition, one in which Ortcutt himself ‘occurs as a constituent’. This is the singular proposition about Ortcutt that he is a spy. Logically, the question of whether Ralph believes this singular proposition is quite independent of whether he believes either, both, or neither of the other two.

Quine's philosophical bias precluded him from endorsing Russell's elegant account of the notional/relational distinction. The evidence suggests that, even while entertaining the theory of propositions as objects of belief, Quine dismissed out of hand the Russellian idea of a singular proposition as an object of belief.6 Where Russell saw syntactic ambiguity Quine posited semantic ambiguity. One may quarrel over the


relative merits of a theory that posits lexical ambiguity over one that posits singular propositional belief. Still, there is nothing in the logic (as opposed to the psychology) of the situation that precludes the theory of singular propositions. One may reject singular-proposition theory as false, as implausible, even as outrageously so. My own view is that one would be dead wrong in doing so, but there is room for debate. One may not similarly reject singular-proposition theory as logically incoherent. Indeed, Russell's theory is virtually inevitable. Wherever there is quantification into a propositional-attitude context, the idea of a singular proposition cannot be very far behind.7 The mere coherence of Russell's 1905 theory was already sufficient to demonstrate that any argument for the thesis that quantification into the context ‘Ralph believes that . . .’ is logically or semantically incoherent is itself mistaken.8 Given Russell's theory, it is puzzling that Quine and his many followers could have thought that quantification into this context creates any logical difficulty.

Although Quine's critics are correct to point out that his (apparent) argument against the legitimacy of quantification into notional belief contexts is fallacious, pointing this out does not constitute a demonstration that Quine's solution to his puzzle is not a viable alternative to Russell's. It can be shown, however, that insofar as one is prepared to accept Russellian singular propositions, Quine's proposal to translate sentences of form IIa into sentences of form IIb does not work. In fact, whether or not singular propositions are countenanced, Quine's proposal fails.

III

One immediate difficulty for Quine's account is that, as it stands, it does not accommodate such evidently valid inferences as the following:


Everything Ralph believes is true (doubted by Quine, plausible, etc.).


Ralph believes Ortcutt to be a spy.


Therefore, Ortcutt is truly (doubted by Quine to be, etc.) a spy.

The problem is that, on Quine's account, the major premiss involves the notion of notional belief and the minor premiss instead involves the distinct notion of relational belief. One might hope to accommodate this inference within Quine's framework by adopting an analysis of the relational in terms of the notional, perhaps along the lines of David Kaplan's earlier commentary in ‘Quantifying In’. Recent results in the theory of meaning and reference, however, leave little promise for the success of this type of an analysis, and Kaplan himself has abandoned the project. (The matter remains highly controversial.) In any event, Kaplan's original scheme does not validate all inferences of this type, and it is none too clear how to give an analysis within the spirit of Quine's philosophical views that does. (Indeed, Quine would probably reject such inferences, or at least many of them.)

Another serious flaw in Quine's proposal was uncovered by Kaplan in ‘Opacity’ (268–272). Following Quine, Kaplan proposes a distinction among propositional attributions (whether attributions of propositional attitude, of modality, or whatever), between what Kaplan calls the syntactically de dicto and the syntactically de re. The syntactically de dicto is illustrated by such attributions as 1, 2, and 3a—each of which involves the ‘believes that’ construction. Syntactically de dicto belief attributions would be formalized along the lines of Ib, where 0x0003d5may be either open or closed. The syntactically de re is illustrated by 0b, which involves the ‘believes . . . to be’ construction. Syntactically de re belief attributions would be formalized along the lines of IIb. Kaplan sees Quine as proposing a method for translating an (apparently) de re (relational) belief attribution that is syntactically de dicto (such as 0a) into a pure de re form, i.e., something that is both semantically and syntactically de re. Kaplan pointed out, however, that Quine's method of translation is insensitive to subtle distinctions in content involving the phenomenon that I call ‘reflexivity’.9 The problem arises in the case of sentences of the form IIa where there are multiple (two or more) free occurrences of the pronoun ‘it’ in 0x0003d5it . Thus suppose Ralph is under the illusion that the man in the brown hat is taller than the man at the beach. It would seem then that the following sentence is true:


Ralph believes of Ortcutt that he is taller than he.

Quine's procedure translates this sentence into


B r (Ralph, Ortcutt, (0x0003bcx)[x is taller than x])

which may be read: Ralph r-believes Ortcutt to be a thing that is taller than itself. Unless Ralph is insane this is false. Kaplan improved upon Quine's scheme by employing a procedure that Kaplan calls ‘articulation’. Kaplan translates the problem sentence instead into something along the lines of:


B r (Ralph, , (0x0003bcxy) [x is taller than y]).

This may be read: Ralph r-believes Ortcutt and himself to be so related that the former is taller than the latter.10

Unlike Quine, Kaplan sees no logical difficulty with 0a as it stands. Nevertheless, in ‘Opacity’ he apparently accepts Quine's contention that all such mixed (syntactically de dicto semantically de re) belief attributions can be paraphrased into the pure de re form using the syntactically de re ‘believes . . . to be’ construction—as long as articulation is employed wherever possible. On this view, Quine's proposal to replace 0a with 0b (when stripped of the proposal's philosophical underpinnings) is neither superior nor inferior to Russell's account of quantifying in. In the long run, Quine's translation, modified to incorporate articulation, is simply a rephrasing of Russell's account.

More recently, in ‘Afterthoughts’ (605–606), Kaplan suggests instead that the pure de re construction is significantly stronger than the mixed (syntactically de dicto semantically de re). On his more recent view, the mixed 0a does not say that Ralph believes Ortcutt to be a spy (although this may well be what we generally mean when we utter 0a). The difference, according to Kaplan, is that if Ralph were to introduce a new name by means of some definite description that, unknown to Ralph, happens to refer to Ortcutt (say ‘the world's shortest spy’), then Ralph could believe of Ortcutt that he is a spy even if Ralph has had no epistemic contact with Ortcutt and, to use Russell's phrase, knows him only by description.11 By contrast, according to Kaplan, in order for Ralph to believe Ortcutt to be a spy, Ralph must be, in a certain epistemological and perhaps interest-relative sense, en rapport with Ortcutt.12 On this view, Quine's proposal (even when modified to incorporate articulation) fails, since 0b is significantly stronger than 0a.

This view does not reject all translation between the mixed form and the pure de re. It is just that the translation will have to be complicated. Presumably, the epistemologically stronger IIb would analyze into something like the following:

0x0003b2is en rapport with 0x0003b1and 0x0003b2believes of 0x0003b1that 0x0003d5it , grasping the proposition about 0x0003b1that 0x0003d5it in such-and-such a manner by means of 0x0003b2's acquaintance with 0x0003b1,

where ‘it’ has only one free occurrence in 0x0003d5it . (If the pronoun has multiple occurrences, IIb must be replaced by an articulated expansion.) In this way, the pure de re form is equivalent to a complex mixed form that entails the simple mixed form.

The problem is to specify that special ‘manner’ in which the belief is held. Kaplan says that this particular problem with translating between the mixed form and the pure

involves understanding the conditions under which we correctly ascribe to [Sherlock] Holmes, for example, the de re attitude that there is someone whom he believes to have committed the murder [as opposed to asserting merely that there is someone such that Holmes believes that he committed the murder]. It seems clear that the mere fact that the murderer has given himself a nom de crime and leaves a message using this name should not suffice. (In fact, I suspect that there are no fixed conditions, only conditions relative to the topic, interests, aims, and presuppositions of a particular discourse.) (605–606n)

Here Kaplan is surely mistaken. Quite the contrary, it seems clear that the mere fact that Holmes has drawn inferences from clues gathered at the scene of the crime suffices in order for Holmes to form relational beliefs concerning the murderer—even without a nom de crime to facilitate Holmes's expression of those beliefs. (‘Elementary, Watson. On the basis of my preliminary investigation, I believe our quarry to be

an elderly bachelor who is fond of pasta and owns a sheep dog.’) Kaplan has evidently confused two potential states of Holmes: (i) r-believing someone to be the murderer; and (ii) having an opinion as to who the murderer is. The second notion is far more plausibly regarded as interest-relative. Whereas obtaining the murderer's nom de crime does not suffice (in most ordinary contexts) to place Holmes in the second state, it is overkill for the first. Of course, in the special case of Holmes, the first state is invariably followed by the second, but this is a matter of Holmes's powers of deduction, not of ours.13

Whether Kaplan has confused (i) and (ii) or not, I have to confess to not knowing exactly what he means by a sentence like 0a. As I use 0a, it is straightforwardly equivalent to ‘Ralph believes Ortcutt to be a spy’. Each requires that Ralph have some (albeit perhaps minimal) epistemic connection to Ortcutt—and neither requires that Ralph know, or even have any opinion about, who Ortcutt is (in any nonvacuous sense).14 Perhaps Kaplan means instead that there is some sentence S satisfying the conditions that: S's content is the singular proposition about Ortcutt that he is a spy; Ralph knows what S's content is, though perhaps only by description; and Ralph believes S to be true. To be sure, this does not require Ralph to be epistemically connected to Ortcutt in any manner beyond knowledge by description, but it also has nothing to do with relational belief concerning Ortcutt. It involves only relational belief concerning S.15

Beware of wanting too much to have one's cake and eat it too. Kaplan offers little or no evidence on behalf of the nonequivalence of 0a and 0b. In my view, the contrary claim that the latter is indeed equivalent to, and even definable by means of, the former is so intuitive, and so theoretically smooth, that a great deal of evidence indeed should be required to warrant its rejection. The definition I have in mind is captured neither by Quine's schema nor by Kaplan's. It is the following:


B r (0x0003b2, 0x0003b1, (0x0003bc0x0003b3)[0x0003d5 0x0003b3]) = def. (0x0003bb0x0003b4)[B n (0x0003b2, that (0x0003bb0x0003b3)[0x0003d5 0x0003b3](0x0003b4))](0x0003b1).

Notice that this definition does not provide for a translation of an arbitrary mixed belief attribution into one that is pure de re. In some sense, what it provides is precisely the opposite.16

In any event, there are examples that simultaneously refute Quine's original proposed translation, Kaplan's improved method invoking articulation, and Kaplan's more recent view that 0b is stronger than 0a in the manner suggested. One such example is obtained by a natural extension of Quine's story concerning Ralph and Ortcutt. Perhaps the most straightforward version of the argument assumes the theory of Russellian singular propositions—a theory that Kaplan accepts, even if

Quine does not—but this assumption can be weakened considerably, to an extent evidently acceptable even to Quine.

IV

My aim is first to show, by example, that a sentence of the form IIa will often (typically) attribute a different belief from that attributed in the corresponding sentence of the form IIb. Suppose Ralph has a reflective but commonsensical friend, Kevin, who realizes what Ralph does not: that the suspicious-looking man that Ralph saw wearing the brown hat is none other than Bernard Ortcutt, the pillar of the community whom Ralph saw that time at the beach. (Like Ralph, Kevin knows fully well who Ortcutt is.) When asked whether Ralph believes that Ortcutt is a spy, Kevin responds as follows:

No, Ralph does not believe that Ortcutt, the man he saw at the beach, is a spy. In fact, he believes that Ortcutt is not a spy. But he also believes that the man he saw wearing the brown hat is a spy, and although Ralph does not know it, the man in the brown hat is Ortcutt.

So far, so good. Now we press Quine's puzzle question: ‘Very well, consider this man Ortcutt. Does Ralph believe that he is a spy?’ Suppose Kevin replies, cautiously and philosophically, as follows:

Well, as I said, Ralph doesn't believe that the man seen at the beach is a spy. But if you are asking about Ortcutt himself—as opposed to various ways of conceiving of him—yes, Ralph believes that he is a spy. Ralph believes that the man he saw wearing the brown hat is a spy. Thus Ralph believes of Ortcutt that he is a spy, without believing that Ortcutt is a spy. Of course, Ralph also believes that the man he saw at the beach is not a spy. He therefore also believes of Ortcutt that he is not a spy. So if you're asking about Ortcutt himself, Ralph believes that he is a spy, but Ralph also disbelieves that he is a spy. It all depends on how Ralph is conceiving of him.

Well spoken. Kevin's position is coherent, rational, well considered, and very plausible. Although the matter remains controversial, no doubt many readers (and many more nonreaders)—perhaps even Quine—are in perfect agreement with Kevin.17

We consider the following complex sentence:

4a  

Kevin believes of Ortcutt that Ralph does not believe that he is a spy

Is this sentence true? Support for an affirmative response begins with the truth of the following sentence:

5  

Kevin believes that Ralph does not believe that Ortcutt is a spy


One argument for the truth of 4a comes by way of the theory of singular propositions. Assuming that the contribution made by the name ‘Ortcutt’ to the propositional content of sentences containing the name is Ortcutt—the man himself—sentence 5 says that Kevin believes that Ralph does not believe the singular proposition about Ortcutt that he is a spy. On this same assumption, the proposition (which is believed by Kevin) that Ralph does not believe the singular proposition about Ortcutt that he is a spy is itself a complex singular proposition about Ortcutt, to wit, the proposition about Ortcutt that Ralph does not believe the proposition that he is a spy. Thus, since 5 is true, Kevin believes the singular proposition about Ortcutt that Ralph does not believe that he is a spy. Therefore, Ortcutt himself is such that Kevin believes that Ralph does not believe that he is a spy.

Not everyone subscribes to the theory of singular propositions. But it should be clear that even without singular propositions, a similar line of reasoning will quickly lead to the same conclusion that 4a is true.

Consider in particular the theory advanced in ‘Intensions Revisited’ (Quine, 1981: 120–121). There Quine declares that the following form of exportation is valid:

0x0003b2believes that 0x0003d50x0003b1

(0x0022030x0003b3)[0x0003b2 believes of 0x0003b3that it = 0x0003b1]

Therefore, 0x0003b2believes of 0x0003b1that 0x0003d5it

Quine also suggests that the second premiss might be taken instead as


0x0003b2knows who 0x0003b1is18

In the case at hand, there is indeed someone whom Kevin believes, and even knows, to be Ortcutt—and Kevin knows who Ortcutt is. Given 5, it follows by either of Quine's suggested forms of exportation that 4a is true.

In its simplest terms, the argument for the truth of 4a is this: If 5 is true, then Kevin stands in a certain relation to Ortcutt, by virtue of Kevin's believing that Ralph does not believe that Ortcutt is a spy. That relation is the relation that a bears to b when a believes that Ralph does not believe that b is a spy. Thus if 5 is true, then Kevin has a certain belief about Ortcutt: that Ralph does not believe that he is a spy. And 5 is true.

If there is a more direct argument for Kevin believing of Ortcutt that Ralph does not believe that he is a spy, it can only be this: So what else does it take if not 5?

Applying Quine's proposal to the present case, in the first stage, 4a is to be replaced with (or ‘translated’ into):

4b  

Kevin believes Ortcutt to be such that Ralph does not believe him to be a spy

The rub is that 4b, unlike 4a, is false. When asked whether Ortcutt himself was such that Ralph believed that he was a spy, Kevin answered that Ortcutt was indeed. Kevin thus believes Ortcutt to be such that Ralph does believe him to be a spy. This evidently precludes the truth of 4b.

One might respond by pointing out that, as we have seen, it is possible for Kevin to believe Ortcutt to be thus-and-so even while disbelieving Ortcutt to be thus-and-so (that is, even while believing Ortcutt not to be thus-and-so)—just as Ralph does—so that the fact that Kevin believes Ortcutt to be believed by Ralph to be a spy does not prove that Kevin does not also believe Ortcutt not to be such.

Quite so. But assuming Kevin is sane and rational, he will not believe Ortcutt to be thus-and-so while also disbelieving Ortcutt to be thus-and-so unless he somehow mistakes Ortcutt to be two different people—just as Ralph does. In order for Kevin to form a belief about Ortcutt that he is not believed by Ralph to be a spy, without altering his opinion that Ortcutt is believed by Ralph to be a spy, Kevin must encounter Ortcutt under different circumstances, and failing to recognize him, come to believe that he is someone Ralph does not believe is a spy. Kevin does no such thing. It is because Kevin is not thus confused that his believing Ortcutt to be someone Ralph believes is a spy precludes the truth of 4b.19

There is an interesting complication: Kevin does indeed have inconsistent beliefs about Ortcutt. For it is part of Kevin's view that Ralph believes of Ortcutt that he is a spy. This belief of Kevin's concerning Ralph is also a belief concerning Ortcutt, to the effect that Ralph believes that he is a spy. Thus, even though Kevin has not mistaken him for two different men, Ortcutt is such that Kevin both believes and disbelieves that Ralph believes that he is a spy. How is this possible if Kevin is rational?

The matter is controversial. My own answer (see note 17 ) is that Kevin has indeed mistaken a single thing for two different things—or is at least committed to doing so. That thing is not Ortcutt himself but the singular proposition that he is a spy. Kevin's incompatible beliefs concern this proposition; he believes it to be something that Ralph believes, but he also believes it to be something that Ralph does not believe. In judging that Ralph does not believe that Ortcutt is a spy, Kevin does not recognize the proposition in question, the belief of which he thereby denies to Ralph, as the very same proposition the belief of which he ascribes to Ralph in maintaining that Ralph believes of Ortcutt that he is a spy. Kevin does not have similarly inconsistent beliefs concerning Ortcutt, to the effect that he is thus-and-so and he is not thus-and-so. In particular, Kevin is in no position to see that it would follow from his (mistaken) belief that Ralph does not believe that Ortcutt is a spy, that Ortcutt is not believed by Ralph to be a spy. Kevin does not recognize that in dissenting from the attribution ‘Ralph believes that Ortcutt is a spy’, he commits himself to something he explicitly rejects, Ortcutt's being someone Ralph does not believe is a spy.20

The example also demonstrates that Kaplan's more recent view (as I have reconstructed it) concerning the import of the pure de re form must also be incorrect. Consider the following variant of 4b (replacing the pure de re ‘Ralph does not believe him to be a spy’ with the allegedly stronger ‘Ralph does not believe that he is a spy’):

6  

Kevin believes Ortcutt to be such that Ralph does not believe that he is a spy

On Kaplan's view, 6 says something like the following: Kevin is acquainted with Ortcutt and believes the singular proposition about Ortcutt that Ralph does not believe that he is a spy, when grasping that proposition in a special [such-and-such] manner by means of Kevin's aforementioned acquaintance with Ortcutt. If that were what 6 meant, it evidently would be true (as the entirety of facts underlying the truth of 4a would seem to attest) instead of false.

What has gone wrong? The defect in Quine's original scheme that Kaplan's articulation was introduced to correct stems from the fact that in moving from the syntactically de dicto semantically de re

0x0003b2believes of Ortcutt that 0x0003d5he

to the pure de re

0x0003b2believes Ortcutt to be an individual such that 0x0003d5it

(formalized by IIb with 0x0003b1= ‘Ortcutt’), one reparses the attributed belief into two components—an objectual component and a qualitative component—by simultaneously isolating the individual the belief is about and abstracting a property from the complement ‘open sentence’ 0x0003d5he . That is, one consolidates the internal propositional structure of the complement clause into a single property. One then depicts the referent of 0x0003b2as ascribing this property to Ortcutt. Thus Ralph's complex belief of Ortcutt that he is taller than he is erroneously rendered as the absurd belief about Ortcutt that he is a thing-that-is-taller-than-itself. The reparsing into objectual and qualitative components alters the nature of the belief attributed to Ralph, and Quine's translation fails to capture any relational belief of Ralph's. Articulation more discriminantly consolidates the propositional structure into a relation, in a manner that is sensitive to beliefs that (unknown to the believer) involve a reflexive structure. But articulation remains a method of reparsing and abstraction, whereby the structure of the belief attributed in the untranslated construction is fundamentally altered in the course of translation. The general problem remains: One's relational belief may have the propositional structure indicated by the sentence 0x0003d5he without the believer also ascribing to Ortcutt the corresponding attribute (property or relation), as the proposed translation requires. Kevin's belief about Ortcutt reported in 4a has a complex structure; it is the denial of an attribution to Ralph of a particular belief involving Ortcutt. The belief attributed to Kevin in 4b has a very different structure; it is the

attribution of a certain property to Ortcutt. Kevin has the first belief and not the second.21

The example demonstrates that no such attempt to reduce the allegedly problematic mixed form to the pure form can succeed, since reparsing into an objectual and a qualitative component is required by the very form of the syntactically de re—to fill the second and third argument places of ‘B r ’ in IIb.

V

Quine's ultimate goal is to replace the ‘that’ clauses of belief attributions with quotations, thereby replacing a field of unruly weeds with neatly arranged fruit trees. Since the problem we have noted with the attempt to reduce the syntactically de dicto semantically de re form to the pure de re arises from the abstraction on the open sentence occurring in the ‘that’ clause of the former, Quine's ultimate goal might be attained by simply bypassing the intermediate stage and moving directly from 4a to

4d  

Kevin believes ‘Ralph does not believe that x is a spy’ satisfied by Ortcutt

In general, the allegedly problematic IIa may now be replaced with

IId

Believes-satisfied-by(0x0003b2, ‘0x0003d5 0x0003b3’, 0x0003b1)

in which the open sentence that forms the ‘that’ clause of IIa is quoted directly without first abstracting a predicate from it.22

At first sight, the replacement of 4a by 4d does not seem an improvement over the earlier replacement by 4b. Kevin does not believe Ortcutt to be someone that satisfies the open sentence ‘Ralph does not believe that x is a spy’, any more than he believes Ortcutt to be someone Ralph does not believe is a spy. Indeed, the new replacement

seems even worse than the old. Even if Kevin were to come to believe of Ortcutt (say, by failing to recognize him in his new black hat) that he is someone Ralph does not believe is a spy, Kevin need not conclude that Ortcutt satisfies the open sentence in question. Kevin may know nothing of formal semantics. A similar concern arises in connection with Quine's proposed replacement of 3a by 3c. Ralph may believe that the man in the brown hat is a spy without believing ‘The man in the brown hat is a spy’ to be true—for example, if Ralph speaks no English.

In a revealing passage, Quine acknowledges (in effect) that his terminology is misleading:

This semantical reformulation [of Ia into Ic] is not, of course, intended to suggest that the subject of the propositional attitude speaks the language of the quotation, or any language. We may treat a mouse's fear of a cat as his fearing true a certain English sentence. This is unnatural without being therefore wrong. . . . [If] anyone does approve of speaking of belief of a proposition at all and of speaking of a proposition in turn as meant [i.e., expressed] by a sentence, then certainly he cannot object to our semantical reformulation . . .; for [Ic] is explicitly definable in his terms as [‘0x0003b2 believes the proposition expressed by “0x0003d5” ’]. Similarly for the semantical reformulation [of IIb into IIc]. (Quine, 1966: 192–193)23

Despite appearances, believing-true 0x0003d5is something very different from believing 0x0003d5to be true (which is something the mouse cannot do). Truth is not involved in any way in Quine's concept of ‘believing-true’. Indeed, the concept would be more perspicuously written ‘believes-the-content-of’. For the propositionalist (such as myself), this concept involves not truth, but the relation, usually called ‘expressing’, between a sentence and its propositional content. For Quine, it involves neither.24

Quine's terminology in the passage quoted remains misleading. For Quine, the ‘semantical reformulations’ are more pragmatic than semantic. The supposed point of writing 3c in place of 3a is precisely that the former allegedly avoids the latter's commitment to Ralph's belief of a proposition. Believing-true, for Quine, is evidently a relation that a subject bears to a sentence by virtue of a certain kind of match between the subject's psychological state and some ontologically thrifty feature of the sentence—perhaps its associated assent-producing and dissent-producing stimuli (in Quine's jargon, its stimulus meaning) or its conventional use in communication, where this is taken as not involving the assignment of a proposition as semantic content. If this thin notion is deemed semantical, our concern is with ‘semantics’ in a very loose sense. In its more restrictive sense as a term for the formal study of the symbolic nature of language—a subject that essentially involves the assignment of semantic values (truth values, or ‘intensions’, etc.)—believing-true, for Quine, is about as semantical as True Value Hardware Stores or The Plain Truth magazine. It is semantical in name only. Any comfort or security derived from the use of the words ‘true’ or ‘satisfy’ in Quine's proposal is based on illusion.

Since it is an attempt to eliminate propositions and the like from propositional-attitude attributions in favor of expressions, Quine's proposal faces Alonzo Church's powerful objection from Church, 1950. Church points out that typical purported analyses that seek to do away with propositions in favor of such things as sentences ‘must be rejected on the grounds that [the analysans] does not convey the same information as [the analysandum]’ (97–98). In the present case, 3a conveys the content of Ralph's belief—specifying that it is a belief whose content is that the man in the brown hat is a spy—whereas 3c specifies certain words that express that content ‘without saying what meaning is attached to them’. Adapting Church's objection to the present case, he argues that

(3c) is unacceptable as an analysis of (3a). For it is not even possible to infer (3a) as a consequence of (3c), on logical grounds alone—but only by making use of the item of factual information, not contained in (3c), that ‘The man in the brown hat is a spy’ means in English that the man in the brown hat is a spy.

Following a suggestion of Langford [in Journal of Symbolic Logic, 2, 1937: 53] we may bring out more sharply the inadequacy of (3c) as an analysis of (3a) by translating into another language, say German, and observing that the two translated statements would obviously convey different meanings to a German (whom we may suppose to have no knowledge of English). (Church, 1950: 98)25

Quine, by way of response, concedes Church's point but dismisses the objection as inapplicable to his proposed replacements, since 3c and 1c are offered as materially equivalent substitutes, and not as meaning-preserving analyses, for the constructions they replace. He writes:

a systematic agreement in truth value [between Ic and Ia] can be claimed, and no more. This limitation will prove of little moment to persons who share my skepticism about analyticity. (194)

This response makes it extremely difficult to understand just what is going on in the last seven paragraphs of Quine, 1956. Church (1950) begins with the following observation:

For statements such as Seneca said that man is a rational animal and Columbus believed the world to be round, the most obvious analysis makes them statements about certain abstract entities which we shall call ‘propositions’ . . ., namely the proposition that man is a rational animal and the proposition that the world is round; and these propositions are taken as having been respectively the object of an assertion by Seneca and the object of a belief by Columbus. . . . [Our] purpose is to point out what we believe may be an insuperable objection against alternative analyses that undertake to do away with propositions in favor of such more concrete things as sentences.

Church may thus be seen as issuing a challenge: A true propositional-attitude attribution like 3a expresses a fact that appears to require not only a believer but also a

proposition for the believer to believe. (Consider, for example, the intuitively valid inference from 3a to ‘That the man in the brown hat is a spy is something Ralph believes’ or to ‘There is something that Ralph believes, which is that the man in the brown hat is a spy’.) If you reject propositions, then propose an analysis of 3a that avoids them (and that explains, or otherwise accommodates, such phenomena as the intuitive validity of the two inferences just mentioned), while also avoiding the apparently insuperable objection noted above. In admitting that 3c is put forward only as a substitute and not as an analysis, Quine fails to address—let alone to meet—this serious challenge.

Perhaps Quine rejects any notion of analysis that such a challenge might presuppose, and therefore respectfully declines. He motivates his proposal to substitute 3c for 3a on the ground that this is sufficient to avoid the latter's commitment to Ralph's belief of a proposition. He admits 3a's commitment to a proposition; it is for that very reason that he proposes replacing it with something less extravagant.

At this juncture the question posed at the start of this essay arises with overwhelming force. Given Quine's admission that Ia and Ic are alike in truth value, how can the replacement of the former by the latter serve his purpose? Specifically, what can be the point of writing 3c ‘instead of’ 3a if it is granted that the latter, though not equivalent to its proposed replacement, is literally true and entails the existence of a proposition? One cannot avoid the ontological commitments of a theory merely by refraining from asserting the theory, if at the same time one concedes the theory's truth. If Quine's proposal to replace 3a with 3c is not simply an attempt at subterfuge, it can only be a confusion. In making the substitution one may camouflage the commitment to an ‘intension’, but the commitment remains. Indeed, given Quine's admission of 3a's truth as well as its commitment to a proposition, his own commitment to that proposition remains quite visible.

This is a curious inconsistency. The only viable remedies are three. Quine could recant his concession that 3a involves a commitment to an ‘intension’. Alternatively, he could recant his concession that 3a is true, and renounce 3a along with 1a. Similarly for 1b, and indeed for all attributions of either the syntactically de dicto form Ia or the syntactically de re form IIb.

The second alternative must be regarded as extremist; as Quine himself has insisted, both the theory and practice of psychology—not to mention our ordinary conceptions of everyday human affairs and of what it is to have a cognitive life—depend heavily on just such attributions. The first alternative is perhaps even less attractive. For it would obligate Quine to rise to Church's challenge; it remains highly doubtful whether that challenge will ever be met in a completely satisfactory way.

The third alternative is to admit propositions. There are problems here as well, but it seems likely that their solution lies within our grasp. To make the conversion to intensionalism as painless as possible, one might begin with Russellian singular propositions. Admitting singular propositions has the additional feature that Quine's proposed replacements, one and all, may be discarded in favor of an extremely resilient and satisfying account of relational belief, the essentials of which have been with us since 1905.

References

Burge, T., 1977. ‘Belief De Re’, The Journal of Philosophy, 74, June: 338–362.  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them

Chisholm, R., 1981. The First Person, Minneapolis: University of Minnesota Press.

Church, A., 1950. ‘On Carnap's Analysis of Statements of Assertion and Belief’, Analysis, 10, 5: 97–99.  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them

—— 1989. ‘Intensionality and the Paradox of the Name Relation’, in Themes from Kaplan, J. Almog, J. Perry, and H. Wettstein, eds, Oxford: Oxford University Press, pp. 151–165.

Donnellan, K., 1979. ‘The Contingent A Priori and Rigid Designators’, in Contemporary Perspectives in the Philosophy of Language, P. French, T. Uehling, and H. Wettstein, eds, Minneapolis: University of Minnesota Press, pp. 45–60.

Fine, K., 1990. ‘Quine on Quantifying In’, in Propositional Attitudes: The Role of Content in Logic, Language, and Mind, C. Anthony Anderson and J. Owens, eds, Stanford: Center for the Study of Language and Information, pp. 1–25.

Forbes, G., 1985. The Metaphysics of Modality, Oxford: Oxford University Press.

Kaplan, D., 1969. ‘Quantifying In’, in Words and Objections: Essays on the Work of W. V. Quine, D. Davidson and J. Hintikka, eds, Dordrecht: Reidel, pp. 206–242.

—— 1986. ‘Opacity’, in The Philosophy of W. V. Quine, L. E. Hahn and P. A. Schilpp, eds, La Salle: Open Court, pp. 229–289.

—— 1989. ‘Demonstratives’, in Themes from Kaplan, J. Almog, H. Wettstein, and J. Perry, eds, Oxford: Oxford University Press, pp. 481–565.

—— 1989. ‘Afterthoughts’, in Themes from Kaplan, J. Almog, H. Wettstein, and J. Perry, eds., Oxford: Oxford University Press, pp. 565–614.

Kazmi, A., 1987. ‘Quantification and Opacity’, Linguistics and Philosophy, 10: 77–100.  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them

Kripke, S., 1979. ‘A Puzzle About Belief’, in Meaning and Use, A. Margalit, ed., Dordrecht: Reidel, pp. 239–283; also in Propositions and Attitudes, N. Salmon and S. Soames, eds, Oxford: Oxford University Press, 1988, pp. 102–248.

Lewis, D., 1979. ‘Attitudes De Dicto and De Se’, The Philosophical Review, 88: 513–543.  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them

Quine, W. V., 1956. ‘Quantifiers and Propositional Attitudes’, The Journal of Philosophy, 53: 177–187, reprinted in Quine (1966: 183–194).  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them

—— 1960. Word and Object, Cambridge, Mass.: MIT Press.

—— 1966. The Ways of Paradox, New York: Random House.

—— 1969. ‘Reply to Kaplan’, in Words and Objections: Essays on the Work of W. V. Quine, D. Davidson and J. Hintikka, eds, Dordrecht: Reidel, pp. 341–345.

—— 1979. ‘Intension Revisited’, in Contemporary Perspectives in the Philosophy of Language, P. French, T. Uehling, and H. Wettstein, eds., Minneapolis: University of Minnesota Press, pp. 268–274; also in Quine (1981: 113–123).

—— 1981. Theories and Things, Cambridge, Mass.: Harvard University Press.

—— 1986. ‘Reply to David Kaplan’, in The Philosophy of W. V. Quine, L. E. Hahn and P. A. Schlipp, eds, La Salle: Open Court, pp. 290–294.

Richard, M., 1987. ‘Quantification and Leibniz's Law’, The Philosophical Review, 96, 4: 555–578.  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them

Russell, B., 1956, Logic and Knowledge, Robert C. Marsh, ed., London: George Allen and Unwin.

Salmon, N., 1986a. Frege's Puzzle, Cambridge, Mass.: MIT Press (a Bradford Book).

—— 1986b. ‘Reflexivity’, Notre Dame Journal of Formal Logic, 27, 3: 401–429; also in Salmon and Soames (1988: 240–274).  The following link may allow you to access a non-Oxford website. Oxford University Press has no control over external websites and is not liable for any material on such websites or your use of them

—— 1987/1988. ‘How to Measure the Standard Meter’, Proceedings of the Aristotelian Society, 88: 193–217.

end p.268


—— 1989a. ‘How to Become a Millian Heir’, Nous, 23, 2: 211–220.

—— 1989b. ‘Illogical Belief’, in Philosophical Perspectives, 3: Philosophy of Mind and Action Theory, J. Tomberlin, ed., Atascadero, Calif.: Ridgeview, pp. 243–285.

—— 1990. ‘A Millian Heir Rejects the Wages of Sinn’, in Propositional Attitudes, C. A. Anderson and J. Owens, eds, Stanford, Calif.: Center for the Study of Language and Information, pp. 215–247.

Salmon, N., and Soames, S., eds, 1988. Propositions and Attitudes, Oxford: Oxford University Press.

15 Is De Re Belief Reducible to De Dicto? (1998)*

I

Yes and no. It depends on the meaning of the question. Traditionally, those on the affirmative side—predominantly neo-Fregeans—hold that Ralph's believing about Ortcutt, de re, that he is a spy is identical with, or otherwise reducible to, Ralph's believing some proposition or other of the form The such-and-such is a spy, for some concept the such-and-such that is thoroughly conceptual or qualitative (or perhaps thoroughly qualitative but for the involvement of constituents of Ralph's consciousness or of other mental particulars), and that uniquely determines, or is uniquely a concept of, Ortcutt (in Alonzo Church's sense of ‘determines’ and ‘concept of’).1 Concerns over Ralph's believing that whoever is shortest among spies is a spy while not suspecting anyone in particular have led some neo-Fregeans (not all) to qualify their affirmative response by requiring that the concept the such-and-such and its object bear some connection that is epistemologically more substantial than that between the shortest spy and the shortest spy. For example, in his classic ‘Quantifying In’, David Kaplan required that the concept be (among other things) vivid in a certain sense.2 If the question is whether a de re belief attribution like

(1)  

Ralph believes of Ortcutt that he is a spy,

logically entails in English, and is logically entailed by, the claim that for some thoroughly conceptual or qualitative concept such-and-such that uniquely determines Ortcutt in an epistemologically special manner, Ralph believes that the such-and-such is a spy, I believe the answer is unequivocally ‘No’. (Kaplan also no longer endorses this theory.) If the question is instead whether it is in the nature of human cognition, rather than by logic, that (1) is true iff for some epistemologically special, thoroughly qualitative concept such-and such of Ortcutt, Ralph believes that the such-and-such

is a spy, the answer is still ‘No’. If there is a Twin Earth in the great beyond, and my Dopplegänger there believes his wife to be beautiful, I nevertheless have no de re judgment concerning her pulchritude (how could I?), even though he and I share all the same thoroughly qualitative beliefs of the form The such-and-such is beautiful, and neither of us possesses any thoroughly qualitative concept that uniquely determines his wife.3

There is a significantly weaker sense in which de re belief may correctly be said to be reducible to de dicto. It is that Ralph's belief about Ortcutt (a res) that he is a spy is identical with, or otherwise reducible to, Ralph's belief of some proposition (a dictum) to the effect that Ortcutt is a spy—though not necessarily a proposition of the form The such-and-such is a spy where such-and-such is a special, thoroughly qualitative concept of Ortcutt. This weaker thesis is fairly modest as far as reducibility claims go. Nevertheless, it too has been challenged. Indeed, philosophers who make one or another of the more full-blooded reducibility claims typically reject my claim that de re belief is analyzable into belief of a proposition, as I intend the analysis.

The classic case against reducibility of de re belief to de dicto was made in Quine's ‘Quantifiers and Propositional Attitudes’.4 He described a scenario, which I shall call ‘Act I’, in which Ralph has witnessed a man, his face hidden from view by a brown hat, engaged in clandestine activity that prompted Ralph to conclude that he was a foreign spy. What Ralph does not realize is that the man wearing the hat is Ortcutt, whom Ralph remembers having seen once at the beach and whom Ralph regards as a patriotic pillar of the community, hence no spy. Ralph has conflicting views concerning Ortcutt, separately believing and disbelieving him to be a spy. On the basis of Act I, Quine argued that true de re belief attributions like (1) and

(2)  

Ralph believes of the man seen at the beach that he is a spy,

stand in need of regimentation. Clearly (2) should not be viewed as imputing to Ralph a de dicto belief that the man seen at the beach is a spy. Using ‘B dd ’ as a symbol for belief of a proposition, the sentence

(3)  

Ralph B dd that the man seen at the beach is a spy,

says something very different from (2), indeed something that is false with respect to Quine's example.5 A crucial feature of a de re construction like (2), distinguishing it sharply from (3), is that the occurrence of ‘the man seen at the beach’ is open

to substitution of ‘the man in the brown hat’. It is tempting to provide (2) a quasi-formalization in:

(4)  

(0x002203x)[x = the man seen at the beach & Ralph B dd that x is a spy ],

thus removing ‘the man seen at the beach’ from the scope of ‘Ralph believes that’. This is equivalent to something familiar to readers of Russell:

(4′)  

(0x002203x)[(y)(y is a man seen at the beach ↔ x = y) & Ralph B dd that x is a spy ].

Either way, it would seem therefore that (2) is true if and only if the component open sentence,

(5)  

Ralph B dd that x is a spy,

is true under the assignment to the variable ‘x’ of the individual who uniquely satisfies ‘y is a man seen at the beach’, i.e. of Ortcutt. The meaning of ‘B dd ’ is such that a sentence of the form 0x00231c0x0003b1B dd that 0x0003d50x00231dis true if and only if the referent of the subject term 0x0003b1believes the proposition expressed by 0x0003d5(the proposition referred to by the argument 0x00231cthat 0x0003d50x00231d). But, Quine reasoned, this yields a truth condition for (2) that is essentially incomplete. Whether it is fulfilled depends not only on what the value of the variable in (5) is but also on how that value was assigned, since Ralph believes that the man in the brown hat is a spy but does not believe that the man at the beach is. If the variable receives its value by means of the particular description ‘the man seen at the beach’ rather than ‘the man in the brown hat’—as it seems to have done—then under that assignment, performed that way, (2) should simply recapitulate (3), and consequently should be false rather than true.

Quine concluded that (2) should not be seen as attributing de dicto belief at all. Instead Quine counseled that (4) and (4′) be scrapped, and that (2) be seen as ascribing to Ralph a different relation—that of de re (‘relational’) belief—to the beach man and the property of being a spy:

(6)  

Ralph B dr (the man seen at the beach, to be a spy).

In Quine's words, (6) ‘is to be viewed not as dyadic belief between Ralph and the proposition that Ortcutt has [the attribute of being a spy], but rather as an irreducibly triadic relation among the three things’ (op. cit., p. 106). The proposal thus echoes Russell's ‘multiple-relation’ theory of belief.6 Also true with respect to Act I is the following:

(7)  

Ralph B dr (the man seen at the beach, 0x00223c[to be a spy]).

Quine emphasized that the joint truth of (6) and (7) does not indicate an inconsistency on Ralph's part.

I have argued against Quine that any sweeping proposal to parse 0x00231cRalph believes of 0x0003b1that 0x0003d5he/she/it 0x00231dinto a ternary-relational assertion is doomed.7 My objection focused on specific instances involving a complicated substituend for 0x0003d5(specifically, a belief ascription). This leaves open the question of whether a less ambitious proposal might fare better, at least when restricted to gentler 0x0003d5like ‘He is a spy’. Is there anything problematic about regimenting (2) and its ilk, rewriting it in the style of (6) as ‘Ralph believes the man seen at the beach to be a spy’?

There is. Quine conjectured that (6) should be seen as a logical consequence of (3).8 Kaplan labeled the inference pattern ‘exportation’, and argued against it through his example of the shortest spy. Quine recanted, and later recanted his recant.9 Still, it would appear that the predicates for de dicto and de re belief are not logically independent. Whatever the final decision with regard to exportation, the logical validity of the following inference is difficult to resist:

(I) Every proposition Ralph believes, Kevin disbelieves. Ralph believes the man seen at the beach to be a spy. Therefore, Kevin believes the man seen at the beach not to be a spy.

But if the first premiss is symbolized by means of ‘B dd ’ and the second by means of ‘B dr ,’ then a middle term is missing and the validity remains unexplained.

II

In ‘Quantifying In’, Kaplan proposed a full-blooded reducibility thesis for modality as well as belief and other propositional attitudes. He proposed first (p. 130) that


N dr (the number of planets, to be odd),

i.e., ‘The number of planets is such that it is necessary for it to be odd’, be analyzed into:


(0x0022030x0003b1)[0x000394 N (0x0003b1, the number of planets) & N dd 0x00231c0x0003b1is odd0x00231d].10

The variable ‘0x0003b1’ may be taken as a first approximation as ranging over singular terms, but should ultimately be regarded as ranging over thoroughly conceptual or qualitative individual concepts, with the quasi-quotation marks accordingly

interpreted either standardly or as quasi-sense-quotation marks.11 The first conjunct ‘0x000394 N (0x0003b1,the number of planets)’ says that 0x0003b1necessarily determines the object that actually numbers the planets—in effect, that 0x0003b1rigidly designates that number, in the sense of Kripke. Analogously, Kaplan proposed (p. 138) that (6) be analyzed thus:

(K6)  

(0x0022030x0003b1)[R(0x0003b1,the man seen at the beach, Ralph) & Ralph B dd 0x00231c0x0003b1is a spy0x00231d].

The first conjunct says that 0x0003b1provides a de re connection for Ralph to the man seen at the beach. In Kaplan's terminology, 0x0003b1‘represents’ the man seen at the beach for Ralph. Kaplan provides an analysis for his epistemologically special notion of representation, whereby ‘R(0x0003b1, the man seen at the beach, Ralph)’ entails, but is strictly stronger than, ‘0x000394(0x0003b1,the man seen at the beach)’ (i.e., 0x0003b1determines the man seen at the beach). It has not been established, however, that this further step is properly a matter of philosophical logic—rather than, for example, of philosophical psychology.12 Beyond the mentioned entailment, the exact analysis of Kaplan's ‘R’ will not concern me here.

Kaplan's ingenious reductive analysis of de re propositional attribution might be interpreted as a proposal for dealing with any propositional attribution that involves an open sentence. One might regard an open ‘that’-clause, like ‘that x is a spy’, as having no meaning in isolation, but as contributing indirectly to the meanings of sentences in which it occurs. A contextual definition for ‘that x is a spy’ is provided as follows: First, analyses are provided for atomic formulae 0x00231c0x0003a0n(0x0003b2 1 , 0x0003b22 , . . . , that x is a spy, . . ., 0x0003b2n − 1 )0x00231d containing the ‘that’-clause among its argument expressions. The most common cases are: those where n = 1 and 0x0003a01 is a predicate for a de dicto modality, i.e. a modal predicate of propositions (‘necessarily true’, ‘probably true’, etc.); and those where n = 2 and 0x0003a02 is a predicate for a de dicto propositional attitude (‘believes’, ‘doubts’, ‘hopes’, ‘fears’, ‘wishes’, etc.). In the latter case,


0x0003b20x0003a0dd that x is a spy

is analyzed as:


(0x0022030x0003b1)[R(0x0003b1, x, 0x0003b2) 0x0003b20x0003a0dd 0x00231c0x0003b1is a spy0x00231d].

Plugging this contextual definition of ‘that x is a spy’ into (4) yields (K6), or rather, something classically equivalent to it. More complicated constructions involving the analysandum are then subject to scope ambiguities exactly analogous to those found in Russell's Theory of Descriptions. The negation 0x00231c0x00223c(0x0003b2 0x0003a0dd that x is a spy )0x00231d, for example, may be analyzed as involving a ‘primary occurrence’ of the ‘that’-clause, or alternatively as involving a ‘secondary occurrence’, where the latter corresponds to the genuine negation of the original, un-negated analysandum:


(0x0022030x0003b1)[R(0x0003b1,x,0x0003b2) 0x00223c(0x0003b2 0x0003a0dd 0x00231c0x0003b1is a spy0x00231d)]


0x00223c(0x0022030x0003b1)[R(0x0003b1,x,0x0003b2) 0x0003b20x0003a0dd 0x00231c0x0003b1is a spy0x00231d].13

One virtue of Kaplan's analysis is that it may reduce the inference (I) to a valid argument of first-order logic. Declining any analysis of de re belief into de dicto leaves few alternatives. One may take ‘B dd ’ and ‘B dr ’ as primitives, for example, and propose Carnapian ‘meaning postulates’ for them that would enable one to derive (I). Perhaps one may save the inference instead through an analysis of the former predicate in terms of the latter.14 Or one may reject inferences like (I) as invalid.

Kaplan argued on somewhat different grounds that leaving the de re form unanalyzed into the de dicto is inadequate (pp. 140–143). His argument invokes a later development in Quine's example:

In Quine's story, [(7) holds]. But we can continue the story to a later time at which Ralph's suspicions regarding even the man at the beach have begun to grow. Not that Ralph now proclaims that respected citizen to be a spy, but Ralph now suspends judgment as to the man's spyhood. At this time (7) is false. (pp. 141–142)

In Act II, Ralph has not changed his mind concerning whether the man in the brown hat is a spy. Thus (1), (2), and (6) are all still true. While (3) is still false—Ralph still does not believe that the man seen at the beach is a spy—Ralph no longer believes that the man seen at the beach is not a spy.

The important feature of Act II is that Ralph's suspension of judgment is not only de dicto but de re. Ralph's attitudes towards Ortcutt still conflict, but not in the straightforward manner of believing him to be a spy while also believing him not to be a spy. Concerning Ortcutt, Ralph believes him to be a spy while also actively suspending judgment. Using ‘SJ’ as a predicate for suspension of judgment, both of the following are true in Act II:

Ralph B dd that the man in the brown hat is a spy

Ralph SJ dd that the man seen at the beach is a spy.

The consequences of the latter regarding belief are given by the following conjunction, which provides a kind of analysis of at the least the core meaning:

0x00223c[Ralph B dd that the man seen at the beach is a spy] 0x00223c[Ralph B dd that 0x00223c(the man seen at the beach is a spy)].

Indeed, the truth of this conjunction with respect to Act II may simply be taken as stipulated.15 Also true, partly in virtue of the foregoing, are the following:

(6)  

Ralph B dr (the man seen at the beach, to be a spy)

(8)  

Ralph SJ dr (the man seen at the beach, to be a spy).

Without analyzing de re belief in terms of de dicto, rendering (8) in terms of withheld belief poses a special difficulty. One is tempted to write:

0x00223c[Ralph B dr (the man seen at the beach, to be a spy)] 0x00223c[Ralph B dr (the man seen at the beach, 0x00223c[to be a spy])].

But the first conjunct flies in the face of the continued truth of (6) in Act II. Not to mention that the second conjunct (which is the negation of (7)) is unjustified. We have no guarantee that Ralph is not acquainted with Ortcutt in some third way. The problem is to express the withheld belief of Ralph's new doxastic situation indicated by (8) consistently with (6).

The difficulty, according to Kaplan, is that the left conjunct above—the apparent negation of (6)—is ambiguous. He writes:

Cases of the foregoing kind, which agree with Quine's intuitions, argue an inadequacy in his regimentation of language. For in the same sense in which (7) and (6) do not express an inconsistency on Ralph's part, neither should (6) and 0x00231c0x00223c(6)0x00231d express an inconsistency on ours. Indeed it seems natural to claim that 0x00231c0x00223c(6)0x00231d is a consequence of (7). But the temptation to look upon (6) and 0x00231c0x00223c(6)0x00231d as contradictory is extremely difficult to resist. The problem is that since Quine's ‘B dr ’ suppresses mention of the specific name [or concept] being exported, he cannot distinguish between


(0x0022030x0003b1)[R(0x0003b1,the seen man at the beach, Ralph) 0x00223c(Ralph B dd 0x00231c0x0003b1is a spy0x00231d)]

and


0x00223c(0x0022030x0003b1)[R(0x0003b1,the man seen at the beach, Ralph) & Ralph B dd 0x00231c0x0003b1is a spy0x00231d].

If 0x00231c0x00223c(6)0x00231d is read as [the former], there is no inconsistency with (7); in fact on this interpretation 0x00231c0x00223c(6)0x00231d is a consequence of (7) (at least on the assumption that Ralph does not have contradictory beliefs). But if 0x00231c0x00223c(6)0x00231d is read as [the latter] (Quine's intention, I suppose) it is inconsistent with (6) and independent of (7).

So long as Ralph can believe of one person that he is two, as in Quine's story, we should be loath to make either [reading of 0x00231c0x00223c(6)0x00231d] inexpressible.16

Analyzing de re suspension of judgment in terms of de dicto in the style of (K6) yields the following Kaplanesque analysis of (8):


(0x0022030x0003b1)[R(0x0003b1,the man seen at the beach, Ralph) & Ralph SJ dd 0x00231c0x0003b1is a spy0x00231d].

The principal consequences of this regarding belief are summed up by:

(K8)  

(0x0022030x0003b1)[R(0x0003b1,the man seen at the beach, Ralph) 0x00223c(Ralph B dd 0x00231c0x0003b1is a spy0x00231d) 0x00223c(Ralph B dd 0x00231c0x00223c(0x0003b1 is a spy)0x00231d)].

This represents Kaplan's way of laying bare the withholding of belief expressed in (8). It is perfectly compatible with (K6). Both may be true so long as the two 0x0003b1's are different, as are the man in the brown hat and the man seen at the beach.

The ambiguity that Kaplan sees in 0x00231c0x00223c(6)0x00231d is precisely the Russellian primary-occurrence/secondary-occurrence ambiguity that arises in 0x00231c0x00223c(5)0x00231d on the contextual-definition interpretation of his project. The important point is not whether the reader (or the current writer) agrees that the alleged primary-occurrence reading is legitimate. Kaplan's principal point is that if 0x00231c0x00223c(6)0x00231d is interpreted so that it is the genuine negation of (6), then without analyzing de re suspension of judgment ultimately in terms of de dicto belief the withheld belief in (8) becomes inexpressible.

III