Philosophy and the Vision of Language (routledge Studies in Twentieth-century Philosophy)

I. EARLY ANALYTIC PHILOSOPHY

2. Frege on the Context Principle and Psychologism ==================================================

The “context principle” articulated by Gottlob Frege, holding that a word has significance only in the context of the sentences in which it appears, has played a determinative role in the projects of analytic philosophy’s investigation of language and sense. It was in theGrundlagen der Arithmetik of 1884 that Gottlob Frege first formulated it; there, he describes it as crucial to his groundbreaking analysis of the logical articulation of the contents of thought. Such contents, Frege thought, must beobjective in the sense of being independent of subjective mental states and acts of individual thinkers or subjects of experience. It was particularly important to him, therefore, that the context principle could be used to help demonstrate the inadequacy of existingpsychologistic theories of content that accounted for it in terms of subjective states or events. In this chapter, I shall examine this connection between the context principle and Frege’s argument against psychologism in order to better understand its significance for the most characteristic methods and results of the analytic tradition as a whole. As is well known, the critique of psychologism that Frege began would also prove decisive for the projects of the philosophers that followed him in defining this tradition; for the young Wittgenstein as well as for Carnap, for instance, it was essential to the success of analysis that it adumbrate purelylogical relations owing nothing to psychological associations or connections. Later on, as has also sometimes been noted, the context principle would figure centrally within projects of analyzing or reflecting on theuse orpractice of a language as a whole.

I

Frege twice asserts in theGrundlagen that observing the context principle as a methodological guideline is practically necessary if we are to avoid falling into apsychologistic theory of meaning or content, according to which content is dependent on mental or psychological states or events. Thus formulated, the principle tells us that, rather than looking for the meaning of individualwords in isolation, we should begin by considering words only in the context of thesentences in which they figure. The first suggestion of a connection between it and antipsychologism comes near the beginning of theGrundlagen , where Frege lays out the “fundamental principles” of his investigation:

In this investigation I have adhered to the following fundamental principles:

There must be a sharp separation of the psychological from the logical, the subjective from the objective;

The meaning of a word must be asked for in the context of a proposition, not in isolation;

The distinction between concept and object must be kept in mind.

To comply with the first, I have used the word ‘idea’ [‘Vorstellung’] always in the psychological sense, and have distinguished ideas from both concepts and objects. If the second principle is not observed, then one is almost forced to take as the meaning of words mental images or acts of an individual mind, and thereby to offend against the first as well.[^70]

At this point, the suggestion of a connection between the observance of the context principle and the avoidance of psychologism is only programmatic. Frege does not say, here,how the two are connected, orwhy we must think that seeking the meaning of words in isolation will “almost” force us into subjectivist psychologism. Frege’s second mention of the context principle in theGrundlagen provides more detail. It comes in the course of his attempt to define the concept of number, after he has already argued that numbers are independent, self-standing objects, and that each judgment about a number contains an assertion about a concept. Frege considers an objector who challenges the mind-independence and objecthood of numbers on psychological grounds. Such an objector may hold that the conception of numbers as objects cannot be sustained, since we have no idea or image of many numbers; numbers expressing very small or large quantities or magnitudes, for instance, routinely outstrip our ability to provide intuitive images in thought or imagination to represent them. Frege’s response does not dispute the truth of the psychological claim, but instead suggests the replacement of the psychologistic procedure with a logical one:

We are quite often led by our thought beyond the imaginable, without thereby losing the support for our inferences. Even if, as it seems to be, it is impossible for us as human beings to think without ideas, it may still be that their connection with thought is entirely inessential, arbitrary and conventional.

That no idea can be formed of the content of a word is therefore no reason for denying it any meaning or for excluding it from use. The appearance to the contrary doubtless arises because we consider the words in isolation and in asking for their meaning look only for an idea. A word for which we lack a corresponding mental picture thus appears to have no content. But one must always keep in mind a complete proposition. Only in a proposition do the words really have a meaning. The mental pictures that may pass before us need not correspond to the logical components of the judgment. It is enough if the proposition as a whole has a sense; its parts thereby also obtain their content.[^71]

Our quantitative judgments about great distances, or about the size of objects, like the Earth, that are vastly larger or smaller than us, do not rest on our ability to form a mental image of anything accurately representative of the magnitudes involved. But this does not deprive our judgments of warrant or show that they do not concern genuine objects. Indeed, Frege avers, our temptation to think that these judgmentsmust be contentless arises from our temptation to identify the meanings of their constituent terms with the intuitive images or mental pictures that occur to us as we hear or consider them in succession. When, because of the inherent limitations of our intuitive faculties, we cannot supply a mental image for a particular term, for instance “the size of the Earth,” we may then be tempted to conclude that the term has no meaning. But we can, after all, make judgments about magnitudes even when they far exceed our intuitive grasp; and although we attach no intuitive content to the idea of there being 0 of any particular type of object, nevertheless our quantitative judgments involving 0 are unimpaired.

The possibility of making such judgments meaningfully, Frege suggests, itself suffices to defend the objecthood of numbers against the envisaged objection. That they can be made at all shows that these judgments concern entities that do not depend on our particular intuitive abilities. Frege’s defense of the objecthood of numbers therefore rests, in this case, on a notion of content according to which judgments may have particular, well-defined contents even if some or all of their key terms cannot be supplied with representativeintuitive images. Given this notion of content, it will be possible to construe the possibility of content-bearing judgments as demonstrating the existence of the objects to which their terms refer. But this conclusion will itself, Frege claims, depend on our considering the contents of sentences as logically prior to the meanings of their individual terms. Beginning with sentence-level contents, we are to identify their real “logical components,” components which may not correspond to anything identifiable as the meanings of the sentence’s constituent words. It will be these true components of the judgment, rather than the mental accompaniments of individual words, that determine the actual existential commitments of the judgment as a whole.

Two sections later, Frege further specifies the sort of judgments we should begin with in order to determine the actual logical content and existential commitments of judgments involving numbers:

How, then, is a number to be given to us, if we cannot have any idea or intuition of it? Only in the context of a proposition do words mean something. It will therefore depend on defining the sense of a proposition in which a number word occurs. As it stands, this still leaves much undetermined. But we have already established that number words are to be understood as standing for independent objects. This gives us a class of propositions that must have a sense - propositions that express recognition [of a number as the same again]. If the symbola is to designate an object for us, then we must have a criterion that decides in all cases whetherb is the same asa , even if it is not always in our power to apply this criterion. In our case we must define the sense of the proposition

‘The number that belongs to the conceptF is the same as the number that belongs to the conceptG ”;

that is, we must represent the content of this proposition in another way, without using the expression

‘the Number that belongs to the conceptF .’

In doing so, we shall be giving a general criterion for the equality of numbers. When we have thus acquired a means of grasping a definite number and recognizing it as the same again, we can give it a number word as its proper name.[^72]

Having already argued that numbers are objects and that judgments about number are judgments about concepts, Frege realizes that judgments of the equinumerosity of concepts are at the same time judgments that “express recognition” of particular numbers, that identify a number as the same again in a new case. Given this, the possibility of judgments of equinumerosity suffices to defend the objecthood of numbers against any objection based on the possible failure of intuition to provide images corresponding to them. The possibility of judging that the number belonging to one concept is the same as the number belonging to another provides what an intuitive image cannot: the identification of a particular number as an object, self-identical and re-identifiable in ever-new situations in our judgments of equinumerosity.

Frege’s general reason for requiring a distinctive kind of logically defined content that arises primarily at the level of sentences, then, seems clear. Only by recognizing such a level of content, he claims, will it be possible to underwrite the objectivity of judgment and the existence and mind-independence of its objects. This recognition moreover depends on our according priority in the practice of logical analysis to sentence-level contents. For considering words in isolation will debar us from recognizing their real logical contents and force us to construe their contents as consisting in their idiosyncratic psychological accompaniments. The application of the context principle in theGrundlagen thus requires that contents on the sentential level play a role not only in determining the meaning or content of sentences, but also the possibility of their terms making objective reference.[^73] For Frege’s argument moves, as we have seen, from the recognition of the significance of judgments of equinumerosity to the ontological conclusion that number-terms refer to self-standing, independent objects. The general ontological conclusion would not follow if determinations of the meaning of sentences did not also provide general conclusions about the references of the terms which make them up.[^74] The sort of content that shows up in the analytic practice that Frege suggests will belogical content, moreover, in that it is at least partly determined by inferential and deductive relationships between sentences in the language. Only this sort of content, because of its determination by logical relations, rather than intuitive or psychological ones, can legitimately participate in logically relevant judgments about the identity of referents. Accordingly, only this sort of content is qualified to ground thepossibility of objective reference.

One might wonder, however, what it is about the role of this kind of content in judgment that entitles it to enjoy this special claim to ground objective reference. Part of the answer lies in Frege’s conception of intuition not only as subjective but also as essentiallyprivate . In “The Thought,” for instance, he argues that intuitive images are not only subjective but also, because of the impossibility ofknowing the contents of another’s mind, strictly private and incommunicable.[^75] If this is right, then reference to an intuitive image by itself will clearly be of no use in an argument attempting to establish the objectivity of what it represents. But even if this is the case, we may still wonder whylogical content, simply because it is related to and determined by logical relations of deduction and inference among sentences, should fare any better. For one thing, it is not at all obvious why intuitive contents, even if themselves private, could not at least provide abasis for the public, potentially objective judgments of equinumerosity to which Frege appeals. When Frege wrote, he was well aware that empiricists like Locke and Hume had provided detailed theories of abstraction to account for the possibility of meaningful judgments about mathematics and numbers even when these judgments exceed direct, intuitive support. And Frege’s conversant, Husserl, would soon provide a complex anti-psychologistic theory of abstraction that portrayed particular acts of numerical judgment asgrounded in individual intuitive acts.[^76] On any of these theories, the judgments that Frege appeals to as lacking intuitive support, and so exemplifying an alternative sense of content that does not rely on intuition, are construed instead as arising from concrete, intuitive contents by way of a process of abstraction. If these theories of abstraction are at all plausible, Frege’s examples of judgments lacking in immediate intuitive support are not decisive. Moreover, it is difficult to see how the context principle could make the important difference that Frege says it does, if what is at issue is simply theprivacy of intuitive contents. For it is not initially clear why the contents of sentences should be anyless dependent on intuition than are the contents of words, taken alone; and if they are just as dependent on intuition, they must, on Frege’s view, be just as private, and hence just as incapable of grounding objective reference. Alternatively, if there is a distinctive, logically robust kind of content in virtue of which judgments are both public and potentially objective, it is far from obvious why single words, even “considered in isolation,” could not have content in this logically robust sense as well.

II

What is needed to make Frege’s claims for the importance of the context principle intelligible is a notion of a kind of non-intuitive, logically defined content defined primarily at the level of sentences rather than words and capable of demonstrating the objectivity of the referents of their terms. Such a notion of content can indeed be found, at least implicitly, in Frege’s conception of logical analysis. It results from his view of the relationship of the comprehension of a sentence to the determination of itstruth-conditions . Whatever kind of meaning an individual word might be thought to have, individual words do not possess truth-conditions of their own; the possibility of making a claim that is true or false emerges only at the level of sentences. Frege will consistently connect this feature of sentences - that they alone are apt for truth or falsehood - to his conception of the content of sentences as determined by their inferential relations. This notion of content indeed provides an alternative to any intuitionist or psychologistic account. As Dummett has argued, it also suggests that Frege’s doctrine of thought is inseparably entwined with a general consideration of theuse orpractice of a language, a consideration that Frege himself did not explicitly undertake, but can be seen to be all but explicit in his account.

Throughout his career, Frege understood “thoughts” as, definitively, contentscapable of truth or falsity. As early as theBegriffsschrift he gave this conception a prominent role in his practice of logical analysis. Here, he linked the logical content of a sentence with its inferential role, understanding two sentences to express the same thought if and only if they have the same set of inferential consequences and antecedents.[^77] Thisinferentialism about content provides substantial justification for extracting from Frege’s method of logical analysis a conception of the role of sentences that accords them a special status. For if logical contents are determined by inferential roles, it will evidently only be sentences that can have logical contents of this sort. Foronly sentences have their own, identifiable roles in the process of inference.[^78] But f Frege’s appeal to the context principle is to establish the anti-psychologistic conclusion, it must draw a further nexus between the truth-aptness of a sentence-level content and its ability to establish both the potentialobjectivity of its claim and theobjecthood of its referents. Following Dummett, we can bring out this nexus, in a way sympathetic to Frege’s project of analysis, by situating that project within a broader consideration of linguisticuse . In the context of this reflection, the special aptness of sentence-level contents for truth or falsity is just one aspect of a broader privilege of sentences in thepractice of a language. We can express this privilege by noting that a sentence is the smallest unit by which a speaker can effect the linguisticact of asserting a judgment. Thus Dummett reconstructs the basis of the context principle as the recognition that any characterization of the senses and references of individual words must be dependent upon a characterization of the possibleuses to which they may be put in sentences:

To assign a reference to a name or a set of names … could only have a significance as a preparation for their use in sentences …. More generally, the assignment of a sense to a word, whether a name or an expression of any other logical type, only has significance in relation to the subsequent occurrence of that word in sentences. A sentence is … the smallest unit of language with which a linguistic act can be accomplished, with which a ‘move can be made in the language-game’: so you cannot do anything with a word - cannot effect any conventional (linguistic) act by uttering it - save by uttering some sentence containing that word …[^79]

As Dummett says, any ascription of content to individual words will be, in general, unintelligible unless specified in terms of the difference it makes to the acts that can be effected by the sentences in which they figure. The intelligibility of the particular contents of particular words thus rests on a prior appreciation of the particular semantic tasks of claiming and asserting that they can contribute to accomplishing. But because they can only accomplish these tasks when combined with other words in sentences, our logical understanding of the contents of individual words must apparently rest on a prior appreciation of the contents of the sentences in which they can appear.

This way of reconstructing Frege’s views indeed provides a natural way of understanding the basis of his claims for the objectivity of thought. Throughout his career, as Dummett points out, Frege held as well that successful linguisticcommunication of a thought requires that hearer and speaker agree in attaching the same sense to a sentence. Of course it is possible for this agreement, in particular cases, not to obtain. But when it does not, the divergence in sense must, according to Dummett, at least be objectively discoverable; it must be possible, in other words, to find rational grounds for clarifying the sense of a sentence that do not depend essentially on any fact of psychology or inner mental processes.[^80] And, as Dummett also points out, Frege had at least the outlines of a powerful and general account of what such agreement on sense consists in. On the account, what speaker and hearer agree on in agreeing on the sense of an assertoric sentence is itstruth-conditions . Understanding a sentence means knowing which facts or circumstances will make it true and which will make it false, and successful communication requires agreement in this understanding. For this agreement, private items or accompaniments are irrelevant; all that matters is that we associate with a sentence the same, objective and factual, truth-conditions. Indeed, on Frege’s view as Dummett reconstructs it, the special role of sentential-level contents in underlying objective reference is naturally explained as a result of the possibility of our coming to agree on the truth-conditions of sentences. Objective reference is possible only insofar as it is possible to agree on criteria for the judgment of identity of reference; and such agreement is itself a matter of agreement on the truth-conditions of sentences expressing the requisite judgments.

A significant effect of Dummett’s reading is to yield grounds for resisting, in a way that coheres with the spirit of Frege’s thought if not the letter of his commitments, his Platonistic claims about the existence of a “third realm” of thoughts and the problematic metaphor of the “grasping” of senses residing in it. For if Dummett is right, to grasp the sense of a sentence is just to know its truth-conditions.[^81] Such knowledge can reasonably be held to be wholly manifest in ordinary, observable usage. In any case, we have no reason to suspect that it will escape intersubjective verifiability in the way that private mental events or intuitive images could. Even though Frege did not himself have any developed account of the intersubjective practice of a language, construing him, as Dummett does, as at least implicitly something like a “use-theorist” of meaning thus allows us to endorse Frege’s claim for the objectivity of thought without requiring that we concur with what has often seemed the most problematic aspect of this claim, namely commitment to a Platonic third realm. The potential objectivity of contents of thought is itself explicable, on this line, as the direct outcome intersubjective agreement on truth-conditions. And this agreement is evident, and verifiable, in ordinary practices of assertion and justification, of giving and asking for reasons for claims entertained and evaluated.

III

If this account of Frege’s appeal to the context principle is correct, its application in Frege’s method of analysis already inaugurates a comprehensive inquiry into the systematic functioning of sentences in a language as a whole. In Frege’s own case, as we have seen, this commitment can also reasonably be taken to be the methodological basis for the criticism of psychologism that Wittgenstein himself would later take up and extend. Following Dummett, we may indeed take Frege’s application of the context principle against psychologism as the first significant application, within the analytic tradition, of reasoning about the systematic logical structure of language to the question of the nature of linguistic meaning and reference. Its most direct purpose, as we have seen, is to guarantee the possibility of objective reference by demonstrating its grounding in regular criteria for the identification and re-identification of objects. Such criteria, Frege’s line of thinking suggests, are perspicuous only in the context of judgments of identity and non-identity. And the possibility of such judgments depends on the existence of sentential senses that fix the truth-conditions of the sentences whose senses they are.

Nevertheless, there are deep, essential, and determinative problems, both of an internal and external kind, with the view that Dummett attributes to Frege, and indeed with the pervasive and general commitment it expresses. To begin with, there are good reasons to doubt that Frege himself could actually have held anything like a “use-theory of meaning” given his clear desire to resist, not only psychologistic, but also historicist or socially based theories of meaning. As Green (1999) has argued, Frege’s attempt to secure the objectivity of judgments was explicitly directed as much against accounts that would explain content in terms of sharedpublic practices as those that would explain it in terms of private mental facts or accompaniments. The point of introducing the third realm was to secure a conception of the contents of thoughts as independent of whatanybody might actually think, not simply as independent of particular individuals within a larger community. Frege’s appeals to the objectivity of sense most directly support his goal of establishing or securing the objectivity of scientific investigation, a goal that theories of meaning in terms of communal linguistic use, tied as they are to the vicissitudes of actual social practice, have difficulty in satisfying. It may be the case, indeed, that something like Frege’s Platonistic appeal to objectively existing senses is necessary in order to satisfy this goal. We may detect in this appeal the persistence of a mythology that Frege gives us little independent reason to accept; we may even locate in its obscure metaphor of “grasping” the undischarged remnant of the very psychologism that Frege is concerned to dispute. But it may also be impossible to accomplish Frege’s goal of securing the objectivity of sense without it. In particular, it is not at all obvious that anything like adescription of intersubjective social practices gives us the ability to do so.

Beyond this, it is not clear that the view that Dummett attributes to Frege is coherent, even on its own terms. We can see this by reflecting on what the context principle requires, according to Dummett, of the relationship between the senses of sentences and the senses of words in intersubjective practice. In the article “Nominalism” Dummett expresses the context principle as embodying the claim that “When I know the sense of all the sentences in which a word is used, then I know the sense of that word…”[^82] Elsewhere, he construes Frege’s argument for the objecthood of numbers as depending upon our having “provided a sense” for each identity-statement involving numerical terms.[^83] On Dummett’s view, then, the context principle asserts that the sense and reference of each word in a sentence depends systematically on the senses ofall of the sentences in which that word can appear. Dummett furthermore interprets the sense of a word asrule systematically dependent on sentential senses, holding that:

…The sense of a word consists in a rule which, taken together with the rules constitutive of the senses of the other words, determines the condition for the truth of a sentence in which the word occurs. The sense of a word thus consists - wholly consists - in something which has a relation to the truth-value of sentences containing the word.[^84]

According to Dummett, then, the context principle implies in part that fixing the senses of the range of sentences in which a word can appear is at least sufficient (and perhaps necessary) to determine the sense of the word. The sense of a word is itself a rule which, together with the rules for other words, determines the truth-value of each of the sentences in which it appears.

This helps to explain how, given the context principle, we can nevertheless understand (viz., determine the truth-conditions of) new sentences that we have not previously heard. On Dummett’s account, we do so by comprehending the rules that govern the combination of individual words to provide determinate sentential senses. But these rules governing individual words are themselves first determined by abstraction from the interrelations of the senses of the sentences in which the words figure. Dummett recognizes that, construed as a theory of understanding, this threatens to place an impossible demand upon the competence shown by ordinary speakers. For it is evident that no ordinary speaker can ever be construed as having explicitly consideredall (or even very many) of the infinite number of sentences in which a particular word can appear.[^85] As Dummett realizes and admits, this threatens to make a person’s understanding of a word unverifiable in principle; for we can only test her understanding of a finite number of sentences, whereas on the view her linguistic competence with a word would have to consist in her capability of grasping each of the infinite number of sentences in which it can occur.

The epistemological side of this objection can be answered by construing our ordinary ability to understand new sentences as manifestations of a cognitivecapacity whose actual performance need not exactly match its idealized, infinitary performance. We can, then, take ordinary performances of understanding as good (though imperfect) evidence for the requisite capacities. There might still be some indeterminacy about exactly what these capacities are, or what further performances they might underlie, but the indeterminacy will be no greater than what is normally involved, in any case, in induction from a finite set of examples.

If theorizing about language amounts to the formulation of empirical theories of linguistic competence to systematize and explain actual performance, we might well, therefore, take the objection in stride as a necessary, though not fatal, limitation on our ability to systematize the relevant capacities completely. But behind the epistemological objection that the context principle, as Dummett applies it to the social practice of a language, threatens to make our knowledge of the sense of a word unverifiable in principle, there lurks a different, non-epistemological line of objection that cuts much deeper. For Dummett’s suggestion that Frege’s conception of sense be treated as explicable in terms of socially inculcatedrules for use, understanding, or comprehension exposes this conception to the open question of theground andforce of such rules. This is, at the same time, the question of the possibility of describing “meaning as use” at all; the question is whether there is an intelligible concept of “use” at all by means of which we can indeed characterizeknowing the sense of a term asknowing “how it is used.” [^86] Here (to anticipate results that would, admittedly, only be articulated much later), Wittgenstein’s consideration of rule-following and the “paradox” ofPI 201 come directly to bear. On Dummett’s conception of Frege’s view, to determine the sense of a word is to determine a rule that allows us, for any sentence in which the word occurs, together with the rules that determine the senses of the other words in the sentence, to determine the truth-conditions of the sentence. Of course, the sentential contexts in which any particular word may appear, and the combinations into which it may enter, are infinite and widely varied. We might, with some justice, therefore be reluctant to attempt tospecify any such rules, at least before we are in a position to specifyall of the rules for the language as a whole. Wittgenstein’s point, however, is that (even if we have worked it out as part of a total specification of all the rules for the language) any such specification isitself a symbolic expression, and as such is open to various possible interpretations in practice. That is, if understanding the sense of a word means comprehending the rule that connects it to the truth-conditions of the sentences in which it occurs, then (as Wittgenstein argues in a more general context) any expression of such a rule canalso be taken to connect the same word, in some contexts, todifferent truth-conditions.

The objection, put this way, is not adequately met simply by drawing a distinction between competence and performance in the practice of a language overall.[^87] For even if we draw such a distinction, distinguishing linguistic capacities or dispositions from the performances that issue from them, the force of Wittgenstein’s paradox is that we have no ability even toidentify these capacities, even where we take them to exist.[^88] We might speak ordinarily, for instance, of a capability to use the word “red,” and take someone’s finite set of (ordinary and non-deviant) occurant sentential performances with the word to license our ascription to them of this capability. The person can, in all the cases we have yet observed, associate with sentences involving the word “red” the “right” truth-conditions, in any case the ones that we ourselves expect to be associated with those sentences. But according to the context principle, as Dummett reconstructs it, we can have no understanding of what the relevant capacity is - nor even any assurance that it is indeed a capacity relating to thesame sense that we take our own sentences involving “red” to invoke - without knowing how it contributes to fixing the senses, and truth-conditions, of an infinite number of sentences. It follows that, prior to gaining knowledge of how a speaker would perform in an infinite number of cases, we can have no legitimate basis even for guessing that a speaker’s new performance with what appears to be a familiar word will conform with her prior usage. Nor can we intelligibly criticize a new performance as incorrect owing to its failure to comport with the speaker’s or the community’s existing standard.

The Wittgensteinian paradox poses a problem for the very possibility of a systematic understanding of a language in terms of the “rules for its use.” This problem has, indeed, influenced and inflected many of the various projects that have taken up Frege’s conception of sense along the lines of something like Dummett’s interpretation. Since Tarski wrote in the 1930s, it has been known that it is possible to gain access to some portion of the systematic structure of truth and reference for a language by stating and systematizing the truth-conditions of its sentences. Donald Davidson, drawing on Quine’s project of “radical translation,” was the first to envision the project of giving a completetheory of meaning for a natural language.[^89] Such a theory would, Davidson supposed, necessarily be an empirical one, grounded in the observable behavior and reactions of the language’s speakers. It would have as deductiveconsequences all of the (true) Tarski sentences for the language, that is, all true sentences of the form:

“Snow is white” is true in English if and only if snow is white.[^90]

By capturing the totality of Tarski sentences for the language, the envisaged theory of meaning would capture the systematic dependence of sentential sense on truth-conditions. But it would derive the Tarski sentences, Davidson supposed, from some finite number of recursive principles specifying the dependence of the senses of sentences on the words from which they are composed. The total corpus of such rules, recursively specified, would, Davidson supposed, embody what is involved in knowing a language and what is accordingly attributed to an ordinary speaker of it.[^91] Within the envisaged theory of meaning, sentential senses would thereby be regularly connected to the determination of truth conditions and the senses of terms to their systematizable role in determining sentential senses. If it could be worked out completely and without begging any questions, such a theory would therefore vindicate Frege’s conception of sense as Dummett reconstructs it, showing how the regular practice of a language follows from a distinct and particular set of specifiable rules of use.

For a time after Davidson wrote, the pursuit of such theories of meaning for natural languages became a widely pursued project.[^92] Nevertheless, forty years later, there is still no general consensus on whether even one such theory is possible. Intensional contexts such as direct and indirect quotation, indexical terms, tense, and metaphor have all been cited as posing problems for its development.[^93] The recalcitrance of these phenomena to a straightforward Tarski-style analysis gives grounds for thinking that the connection between meaning and truth that Davidsonian theories take as essential does not exhaust, and so does not suffice to explain, the intuitively graspable possibilities of meaning in any natural language. More significantly in relation to Wittgenstein’s paradox about rules, it is not clear what would be accomplished, even if a complete Davidsonian theory of meaning for a natural language such as English were, one day, successfully worked out. As McDowell (1983) has recently argued, there is good reason to think that a completed theory of meaning would indeed capture schematically what is involved in the grasping of the various concepts of a language, but in such a way that the schematization couldonly be understood by speakers already in possession of a grasp of those concepts. But to construe a theory of meaning, in this way, as incapable of conferring a grasp of the concepts whose use in the language it sets out to explain (in terminology also used by Dummett in his interpretation of Davidson, to construe it as “modest”) is to construe it as having this explanatory role only against the backdrop of the ordinary practice of the language itself.[^94] Nothing about Wittgenstein’s paradox threatens the claim that we can count on an explicit schematization of the rules of use of a language to capture the senses of wordsif we can already appeal to our knowledge that our interlocutor’s behavior is correctly describable in terms of her performing some familiar, general type of action.[^95] For instance, nothing about Wittgenstein’s paradox prevents us from taking a description of the rules for use of the word “red” to capture its sense,if we may already presuppose that our interlocutor already shares our way of using the term and so attaches to it the same sense that we do. The force of Wittgenstein’s paradox, however, is that nothing completely describable on the level of rules of use can groundthis additional presupposition. Nothing that we can capture in a symbolic description of rules can, by itself, require of our interlocutor (even if he accepts this symbolic description) that he indeed attach the same sense to a term that we do, or demonstrate that he indeed will go on, in each of an infinite number of cases, to understand its role in determining the truth-conditions of sentences in the same way that we do.

The Wittgensteinian paradox threatens any theory that, like Dummett’s, attempts toexplain the senses of words wholly by reference to (what are supposed to be) rules characterizing the regular use of words and sentences in a language. It thereby raises a challenge to the coherence of the notion of regular use that Dummett sees as underlying senses, and thereby (if Dummett’s interpretation is actually true to the motivations of Frege’s own project) to the coherence of Frege’s notion of sense itself. There are various ways to finesse the objection; for instance, Dummett himself often admits that the senses of expressions are, in general, indescribable, sometimes relying on Wittgenstein’s own showing/saying distinction to hold that, in associating a term with its regular referent, wesay (by stipulating) what its reference is to be, but onlyshow its sense (namely, its way of contributing to the sense and reference of the sentences in which it figures).[^96] Wittgenstein himself, in theTractatus , held something similar about sentential senses: they were to be the way ofusing orapplying sentences (for instance to determine truth-conditions in particular cases).[^97] In general, as Dummett says, the only way to specify the sense of a sentence is to provide another sentence with the same sense, and there is no reason to suppose that this will always be possible. But to hold that the conditions for the identity or difference of senses in the shared use of a language are only to be shown, and never said, is to hold that determinations of such identity and difference have no basis in anything like adescription of this use itself. There is, in other words, no basis to be found, in the description of the rules underlying anyone’s use of a word, for holding that they will go on using the word in the same way that they have before, or will use it the same way that I do in a new case.

IV

The problem that Frege’s application of the context principle brings out is first perspicuous as the problem of the possible bearing of language onobjective referents, as opposed to the merely subjective ones that would apparently be all that language could support, if psychologism were correct. But set in a larger critical context, it is actually a problem about how linguistic expressions have anapplication at all. That is, it is the problem of how a linguistic expression cando anything at all, how its utterance can amount, for instance, to an assertion, or how it can be evaluated, in a way regularly determined by its constituent terms, for truth or falsity. The problem, even in its more general form, was indeed already clear to Frege, as is shown by his critical discussion inGrundgesetze of the formalist mathematicians Heine and Thomae.[^98] These mathematicians thought of mathematics as a purely formal game involving the rule-bound manipulation of symbols, themselves conceived as lacking any intrinsic meaning. In the course of his exhaustive and biting criticism, Frege shows that the formalists themselves constantly renege on their own commitments, repeatedly presupposing the properties of the objects that the symbols of mathematics are supposed to represent, rather than (as would have been more consistent with their own methodological principles) confining themselves simply to discussing the symbols themselves. But the core of Frege’s objection to the formalist project is that any purely formal description of the rules for combining mathematical symbols would still leave open the question of the basis of theapplication of these symbols to real facts, statements, and events:

Why can no application be made of a configuration of chess pieces? Obviously, because it expresses no proposition. If it did so and every chess move conforming to the rules corresponded to a transition from one proposition to another, applications of chess would also be conceivable. Why can arithmetical equations be applied? Only because they express propositions. How could we possibly apply an equation which expressed nothing and was nothing more than a group of figures, to be transformed into another group of figures in accordance with certain rules? Now, it is applicability alone which elevates arithmetic from a game to the rank of a science. So applicability necessarily belongs to it. Is it good, then, to exclude from arithmetic what it needs in order to be a science?[^99]

Without their applicability to real-world situations, Frege suggests, the symbols of mathematics would be as inherently empty of content or meaning as are configurations of chess pieces. As things are, however, according to Frege, the capacity of mathematical expressions to be applied is a result of their expressingpropositions , that is, as a result of their capacity to capturecontents evaluable as true or false. As we have already seen in connection with the context principle, this capacity also implies, according to Frege, the ability of the constituent terms of mathematical sentences (for instance number-symbols) to refer to actually existing objects. The ultimate basis for this capacity of reference, and so for the applicability of mathematical propositions in real-world contexts is the possibility of objective judgment, for instance of those judgments of equinumerosity that Frege makes the basis of the reference of number-terms.

In his discussion of the formalists in theGrundgesetze , Frege therefore already situates his question of the objective reference of terms within the context of the larger and more general question of theapplication of linguistic symbols. And this question is decisive, not only for the success or failure of Frege’s own account of sense, but for all of the subsequent projects of analytic philosophy that take up and develop the critical impulse implicit in it. The connection is evident, for instance, in theBlue Book passage where Wittgenstein comments most directly on the methodological character of Frege’s thought.[^100] In the passage, Wittgenstein effectively endorses the methodology of Frege’s criticism of psychologism, while at the same time suggesting that Frege’sown Platonistic theory of senses itself tends to fall afoul of this criticism. His method, like Frege’s in applying the context principle against psychologism, is to consider the relationship between symbols and their application, what Wittgenstein here calls the “use” of the sign.

Reflection on this relationship of use to meaning is here, as it was in Frege’s application of the context principle, to underwrite the conclusion that psychological items or mental accompaniments of speaking and understanding cannot provide the basis for an explanation of meaning. Such items or accompaniments are, in relation to the systematic functioning of language as a whole, only further symbols, and so cannot provide the basis for an explanation of howany symbolic meaning is possible. But by putting the objection against psychologism this way, Wittgenstein also expands the criticism initially suggested by Frege to a more general form. In this more general form, it bears not only against the thought that psychological items or accompaniments can be the basis for an account of meaning, but against the thought thatanything graspable as an object can be such a basis.[^101] The conclusion holds equally for “thoughts”, understood as “distinct from all signs” but nevertheless grasped in understanding them and responsible for their capacity to carry meaning. Decisively for Wittgenstein’s own later consideration of rule-following in thePhilosophical Investigations , it holds equally, as well, for “rules of use,” wherever the grasping of such rules is taken to be essential to the understanding of a language and responsible for the meaningfulness of its terms.

Commentators, including Dummett, have missed the significance of this broader application of the critical methods originally developed by Frege because they have misunderstood Wittgenstein’s injunction to “look for the use” (rather than the meaning) in just the way Wittgenstein warns against in theBlue Book passage. That is, taking Wittgenstein to have been committed to the “slogan” that “meaning is use,” they have understood his reflection on the relationship between symbols and their application to contribute to a theoretical project ofdescribing ordisplaying the “rules of use” for a language as a whole. This project is supposed to bear against psychologism in that it makes it clear that no mental items or subjective phenomena can by themselves determine how a word is to be used; any such determination, it is further supposed, depends on the intelligible regularities of a public, socially learned and inculcated, practice. But in substituting a search for public conditions of meaningfulness for the earlier search for private ones, it misses the broader critical significance of the reflective methods originally brought to bear against that earlier search. For as Wittgenstein says, to “look for the use” is no better than to look for psychological accompaniments, if we thereby treat the “use” as an object potentially present to mind and thereby explanatory of the possibility of meaning. Any such object, anything capturable as adescription of the right or normal use of a word or anexpression of the “rule” determining it, is itself simply another sign or set of signs, still open to various interpretations. In the course of the attempt to understand whatdetermines a sign’s (right or normal) application, such descriptions and expressions in fact do no better than the description of psychological acts or accompaniments. In both cases, the gulf between symbols and their application, what Wittgenstein calls the difference between the symbols themselves and their “life” in the practice of a language[^102] , remains unbridged and unbridgeable by any item, rule, or principle introducible in the course of theoretical reflection.

V

Frege’s application of the context principle, as we have seen, already suggested the more general thought that terms have meaning only in the context of the system of their roles in alanguage as a whole. His way of putting this was to say that terms have their meaning only in the context of sentences that express thoughts, or contents evaluable as true or false. In interpreting the point, he relied on considerations about the possibility of intersubjective communication, or of the possibility of agreement on the sense of a sentence. The question that is most decisive for the critical legacy of the reflection that Frege began is: what underlies the possibility of this agreement on what wemust share, if we can mutually understand a sentence at all? Frege himself could answer this question with his theory of sentential senses, his Platonist account of them as strongly objective and ideal, and his metaphorical description of our knowledge of them as the intellectual act of “grasping”. But if we find this account unsatisfying, or if we suspect, with Wittgenstein, that the obscurity of its metaphors is essential to its purported ability to explain, we will have to seek further for ground for the notion of identity of sense that plays such a decisive role in Frege’s account.

The assumption that one and the same word (or, in any case, successive tokens of the same word-type) can be used again and again, in various contexts and sentential connections, with the “same” meaning, figures so deeply in our ordinary thinking about meaning that this thinking would probably be rendered impossible without it. But the broadest implication of Wittgenstein’s reflection on symbols and their uses, and the paradox it leads to, is that there isnothing accessible to systematic reflection on the structure of language that supports this ordinary and pervasive assumption. Wecan , and regularlydo , assume that we use words in the same ways that we always have before, that others will do so as well, that it will be more or less clear when someone has used a word differently than we do or has not explained her way of using it, that such explanations, when offered, will be readily intelligible and will lead to a reform in our own practices or a criticism of their deviant application. But it is one thing to say that we make this assumption (and even that our making it is essential to the intelligibility of what we say and do), and quite another to hold that we can, within a theory of language or its systematic structure, find grounds for justifying it.

In our ordinary language, the assumption of the identity of the sense of a word across its manifold different contexts of application is indeed systematicallyinterwoven with the assumption of the existence of a rule underlying its use.[^103] Inquiries after the justification of claims of sameness of sense will, in the ordinary practice of the language, regularly advert to rules of use, and vice-versa. But this regular interweaving does not imply that the introduction or description of rules can provide anything like a generaljustification for the assumption of identities of sense across the heterogeneity of contexts of employment that regularly pervades our discourse. Indeed, one way of putting the force of Wittgenstein’s paradox, in relation to the principle of identity that Frege constantly presupposes, would be to say that:if we needed criteria of identity to apply terms significantly, then the criteria of identity would themselves stand in need of criteria of application. Any description or formula we could introduce as accounting for our ability to use a term, in the wide variety of contexts, with the same sense, or even as determining what “the same sense” consists in, would itself still stand in need of criteria for itsown application to the heterogeneity of cases. On the level of the systematic description of symbols or reflection on their application,nothing explains the assumption of the identity of senses that constantly pervades our practice. Its justification is nothing other than itself, or the actuality of our ways of using of language to which we can, finally, only gesture mutely toward, without further explanation.[^104]

In retrospect, then, Frege’s appeal to the context principle can be seen as inaugurating the systematic reflection on the structure of signs and the use of language that has been decisive for much of the analytic tradition. The logically based reflection he developed was sufficient to allow the statement, though not the resolution, of the paradox of signs and their application that Wittgenstein’sPhilosophical Investigations brought to its fullest expression. Frege’s own Platonistic theory of the identity of sense is perspicuous, in retrospect, as an unsatisfactory attempt to resolve the paradox. Bringing it out in its general form shows, as well, the unsatisfactoriness of “use-theories” of meaning in resolving it by means of a description of (what are supposed to be) the “rules of use” for terms in a language. For Frege (or anyone else) to have found grounds on the level of such a theory to support his assumption of the identity of sense, he would have needed, in addition to his description of the systematic logical structure of a language, a theory of the pragmaticforce of terms in application to the various acts and accomplishments of which language is capable.[^105] He would have needed such a theory not only, as Dummett says, because his account of senses tied their truth-conditions to the special act of judgment, and so required an account of the pragmatic force ofassertion (as distinct from, for instance, consideration, questioning, negating, and so forth), but more generally because the underlying assumption of an identity of sense across different contexts of a term’s use implies the distinction between terms and their meanings, one the one hand, and the effects of their employment, on the other. But Wittgenstein’s paradox of rule-following is just the most perspicuous and clearly stated of the wide variety of results of the analytic tradition that tend to suggest that grounds for drawing such a distinction between “semantics,” and “pragmatics,” on the level of a systematic explanation of linguistic practice, are essentially lacking.

More than a hundred years after Frege’sBegriffsschrift, we know as little as Frege himself did about what, in the systematic structure of a language, underlies the regular and pervasive assumption of the unity of the sense of a word across the heterogeneity of its contexts and applications. We know as little (or as much), indeed, as Plato did when he invoked the supersensible idea as that which all of the items rightly called by a term have in common, in virtue of which theyare all rightly called by that term.[^106] But the logico-linguistic reflection on symbols and their use that Frege began inaugurated the inquiry that, in its subsequent development within the analytic tradition, would evince the metaphysics of the identity of sense on the level of its ordinary presupposition, and so, in a radical and unprecedented way, expose language to the deeper effects of its immanent self-critique.