Alhassanain(p) Network for Heritage and Islamic Thought

3. ‘Meaning is Use’ in the Tractatus

It has long been standard to attribute to the later Wittgenstein a “use theory” of meaning, a theory which is supposed to have replaced the “metaphysically realist” meaning-theory of theTractatus . Having become skeptical of theTractatus account of meaning as mirroring between language and the world, so the standard story goes, Wittgenstein replaced it, in theInvestigations , with a pragmatic description ofintersubjective communicative practice, a description he partially developed through the suggestive but puzzling concepts of “language games” and “forms of life.” I shall argue in this chapter that this interpretation of Wittgenstein’s development is misleading, and that we misunderstand his role in the history of the analytic tradition if we accept it. For the early Wittgenstein was actually more closely an adherent of the doctrine expressed by the slogan “meaning is use” than was the later Wittgenstein; and an understanding of the central role of this doctrine in the theory of theTractatus is essential, as well, to understanding Wittgenstein’s decisivecritical reaction to it in thePhilosophical Investigations . The central notion of the Tractarian theory ofmeaning , the notion of “logical form” shared between meaningful propositions and the states of affairs they describe, itself depends on theTractatus ’ theory of themeaningfulness of signs as arising from their syntactical application according to logical rules of use. In seeing linguistic criticism as grounded in reflection on the use of expressions, the theory already captures one of the most pervasive themes of the analytic tradition’s consideration of language overall. But after 1929, Wittgenstein would also come to see it also as a characteristic expression of themythological picture of language as a regular calculus that the “rule-following considerations” of thePhilosophical Investigations directly aims to dispel.

I

TheTractatus has long been seen as articulating a jointly semantic and metaphysical “picture” theory of meaning that treats the meaning of a sentence as a function of its specific “logical form.” But just as important to Wittgenstein’s concerns in theTractatus is an account of themeaningfulness of signs, an account of the possibility that otherwise inert written or spoken signs have meaning at all. He provided this account by appealing to the concept of theuse - or, as he put it in theTractatus , the “logico-syntactical employment” - of a sign in accordance with logical rules. By examining the set of remarks in section 3 of theTractatus in which Wittgenstein articulates the first version of a “meaning is use” doctrine explicitly formulated within the analytic tradition, we can understand the relationship of this central strand in Wittgenstein’s philosophical method to the reflection on meaning from which it arose, and thereby begin to understand its decisive relationship to some of the most important critical and interpretive practices of analytic philosophy.

It is well known that theTractatus articulates a “picture” theory of meaning, according to which a proposition has the meaning that it does in virtue of sharing an abstractstructure orform with a possible state of affairs.[107] Just as a visual picture, in order to depict a situation, must share itsspatial form, any proposition whatsoever, in order to depict, must share with the possible or actual state of affairs for which it stands its “logico-pictoral” or “logical” form.[108] A proposition is said to share the logical form of a state of affairs when there is an isomorphism between the relational structure of the proposition and the relational structure of the state of affairs; thefact that the elements of the proposition are related in a particular way represents thefact that things are related, in the state of affairs, in the same way.[109] Wittgenstein emphasized that the logical structure of a proposition can be shown clearly in the arrangement of its constituent signs; we can imagine using physical objects, rather than written signs, in various spatial arrangements to depict possible situations.[110] But propositions as they are written in ordinary language do not always show clearly the relational structure of their logically simple elements.[111] One task of philosophical criticism or analysis, accordingly, is to articulate these elements by rewriting ordinary-language propositions in a perspicuous notation thatshows through its symbolism the logical relations that propositions express.

Many commentaries on theTractatus are content to leave matters here, with the Tractarian picture theory of meaning explained as a metaphysical theory of the meaning of propositions in terms of their articulation as relational structures of signs.[112] In so doing, although they often appeal to the analogy that Wittgenstein suggests between the spatial form of an ordinary picture and the logical form of a proposition, they typically leave the metaphysical underpinnings of the central notion of logical form somewhat obscure. A proposition’s meaning is said to consist in an “abstract” or “formal” correspondence between the relational structure of signs in a proposition (once these are logically articulated by analysis) and the relational structure of simple objects in a state of affairs. But it is not said what this correspondence amounts to, or how to recognize when a proposition has been articulated, through analysis, enough to make it perspicuous.

It is in this connection that Wittgenstein’s theory of themeaningfulness of signs , generally missed by standard interpretations, proves to be an especially important part of the Tractatus theory of meaning. The theory unfolds in a series of remarks at the thematic center of the Tractatus , in the immediate context of the development of the picture theory and the introduction of the idea of a perspicuous notation capable of clarifying the logical structure of ordinary propositions. It begins with a distinction that Wittgenstein draws between signs - mere perceptible spoken sounds or (token) written marks [113] - and symbols , which are signs taken together with the ways in which they signify:

3.32 A sign is what can be perceived of a symbol

3.321 So one and the same sign (written or spoken, etc.) can be common to two different symbols - in which case they will signify in different ways.

3.322 Our use of the same sign to signify two different objects can never indicate a common characteristic of the two, if we use it with two different modes of signification. For the sign, of course, is arbitrary. So we could choose two different signs instead, and then what would be left in common on the signifying side?

In these remarks, Wittgenstein characterizes symbols as signs together with their “modes of signification,” their “use[s] with a sense,” or their “logico-syntactical employment.”[114] Prior to an understanding of their logico-syntactical employment, signs themselves are inert, incapable of defining by themselves a logical form in virtue of which they could correspond to possible states of affairs. For it is, of course, arbitrary that a particular orthographic or audible sign should be chosen for a particular expressive purpose within a particular language; what makes arbitrary signs capable of signifying the states of affairs that they do - what gives them meaning - are the logical possibilities of their significant use:

3.326 In order to recognize a symbol by its sign we must observe how it is used with a sense.

3.327 A sign does not determine a logical form unless it is taken together with its logico-syntactical employment.

3.328 If a sign is useless, it is meaningless. That is the point of Occam’s maxim.

(If everything behaves as if a sign had meaning, then it does have meaning).

We cannot understand the logical form of a symbol without understanding the ways in which the signs that comprise it are significantly used. Wittgenstein goes so far as to suggest that these possibilities of significant use define theessence of a symbol.[115] At the same time, the possibility of understanding the uses of symbols in a proposition, what Wittgenstein calls “recognizing the symbol in the sign,” is also one of the metaphysical preconditions for the possibility of meaning. For it is only by having significant uses that sequences of signs mean anything at all. Wittgenstein’s theory of meaningfulness - his theory of the conditions under which signs have meaning at all - therefore plays an essential role in his general picture of meaning. It is only insofar as signshave significant uses that they have logical forms at all; and it is, of course, only in virtue of their logical forms that they can embody meanings.

For Wittgenstein, then, the sense of a sentence is defined not simply by the way in which its simple signs are combined, but by the relational structure of its signsagainst the backdrop of their possible uses in the language If a sentence has a sense, it is because its constituent signs have significant uses that allow their combination to express that particular sense; we do not understand the sentence unless we grasp these possibilities of use. The correspondence at the basis of the meaning-making isomorphism between propositions and states of affairs is not a correspondence between signs and objects, but between symbols and objects. It is essential to grasping the logical form of a sentence - to understanding its meaning - that its simple signs be understood, not only in their combinatorial structure, but together with their possibilities of significant use or application. If there is a question about the sense of a sentence - if its logical form is not understood, even though all of the verbal or written signs are given - clarification of sense can only amount to clarification of the ways in which those signs are being used, in the context of the sentence, to signify.

II

The central Tractarian concept of logical form, then, cannot be understood except in conjunction with Wittgenstein’s use-doctrine of the meaningfulness of signs. But this doctrine of meaningfulness as use also immediately suggests a process of semantic clarification whereby confusions common in ordinary language are exposed and remedied through the development of a logically purified notation:

3.323 In everyday language it very frequently happens that the same word has different modes of signification - and so belongs to different symbols - or that two words that have different modes of signification are employed in propositions in what is superficially the same way.

Thus the word ‘is’ figures as the copula, as a sign for identity, and as an expression for existence; ‘exist’ figures as an intransitive verb like ‘go’, and ‘identical’ as an adjective; we speak of something, but also something’s happening.

(In the proposition ‘Green is green” - where the first word is the proper name of a person and the last an adjective - these words do not merely have different meanings: they are different symbols.).

3.324 In this way the most fundamental confusions are easily produced (the whole of philosophy is full of them).

3.325 In order to avoid such errors we must make use of a sign-language that excludes them by not using the same sign for different symbols and by not using in a superficially similar way signs that have different modes of signification: that is to say, a sign-language that is governed by logical grammar - by logical syntax.

(The conceptual notation of Frege and Russell is such a language, though, it is true, it fails to exclude all mistakes.)

Philosophical and ordinary confusions typically arise, Wittgenstein thinks, from the unrecognized use of a single sign to signify in two or more different ways; accordingly, analysis proceeds by recognizing distinctions in use that are not clear at the level of everyday language and expressing them in an improved symbolic notation. In the logically perspicuous notation that Wittgenstein envisions as the endpoint of analysis, identity of use is represented by identity of sign.[116] Each sign has exactly one use, and this use is shown, in each case, in the combinatorial rules that govern the sign’s possibilities of significant combination with other signs in the perspicuous notation. Wittgenstein calls the complete set of such rules “logical syntax” or “logical grammar;” their role in analysis is to exhibit the patterns of usage that are implicit in ordinary language, making them explicit as combinatorial rules for the significant appearance of signs. The logical notation not only renders philosophical confusions impossible, but exhibits the patterns of use that are the implicit foundation of ordinary-language meaning.

In thus describing the basis for the meaningfulness of signs in the possibilities of their significant use, Wittgenstein therefore provides a substantially new answer to the ancient question of the relationship of material or lexicographical signs to what we intuitively or pre-theoretically understand as theirmeanings or referents. [117] As it functions in the Tractatus , the new conception, and its role in philosophical criticism, depends both on the thought that meaning is intelligible only in reflection on use and the further claim that use is itself explicable through a systematic clarification of the rules governing it. Thus, while the ordinary relationship between signs and “meanings” might have been specified, in an earlier age of philosophical thought, as consisting in the capacity of repeatable signs to evoke similar ideas or images in the minds of their speakers and hearers, Wittgenstein’s conception of the systematicity of language and the origination of possibilities of error inherent in its use led him to reject any such subjectivist picture and replace it with the direct critical inquiry into the uses of terms that he suggests here. Indeed, while philosophers at least since Locke had criticized our tendency to assume that identity of sign implies identity of meaning or reference, it is only through his conception of the systematicity of the rules of use for a language as a whole that Wittgenstein is able to transform this piecemeal and opportunistic criticism of use into a wholesale doctrine of the meaningfulness of language overall. [118]

Though he is not completely explicit about the scope and character of logical syntax, Wittgenstein proceeds to work out an instructive example of how the elucidation of its rules can dissipate one important philosophical error, Russell’s mistake of supposing it necessary to augment the logical theory of propositional signs with a theory of ordered types. A perspicuous notation that exposes the logical structure of language, Wittgenstein argues, will by itself show that there is no need for the theory of types; for it will show that Russell’s paradox, to which it answered, cannot arise. Wittgenstein makes the point by considering how a case of the paradox might be symbolized:

3.333 The reason why a function cannot be its own argument is that the sign for a function already contains the prototype of its argument, and it cannot contain itself.

For let us suppose that the functionF (fx ) could be its own argument: in that case there would be a proposition ‘F (F (fx ))’, in which the outer functionF and the inner functionF must have different meanings, since the inner one has the formf (fx ) and the outer one has the formy (f (fx )). Only the letter ‘F ’ is common to the two functions, but the letter by itself signifies nothing.

This immediately becomes clear if instead of ‘F ( Fu )’ we write ‘( $ f ): F ( f u ). f u = Fu ’.

That disposes of Russell’s paradox.

This argument against Russell’s theory follows directly from the use-based theory of the meaningfulness of signs that we explored in the last section. It operates by showing that the attempt to express the paradox results in a series of signs which have not yet been given a tolerably clear sense. Our attempt to formulate the paradox necessarily uses the same sign two different ways; if we disambiguate them, giving each sign a univocal sense, the (appearance of) paradox dissolves. It is important to note that it is no part of Wittgenstein’s argument toprohibit (conventionally or stipulatively) the embedding of a propositional sign within itself; the perspicuous notation simplyshows , when we try to express such an embedding in it, that we cannot unambiguously do so. When we writeF (F (fx )), the notation shows clearly that the two occurrences ofF havedifferent forms; they are being used in different ways and according to different rules. Once we see this, we see that there is nothing in common to the two occurrences except that they use the same letter. As often happens in ordinary language, we have used the same sign in two different ways; the difference is simply that the logical notation, unlike ordinary languages, immediately shows the difference in form through its expressive syntax. The thought that a proposition can make a statement about itself, the thought that led to Russell’s paradox, is exposed as arising from a notational confusion: it is only because we use the same orthographic sign for what are in fact two different symbols that we are led to think the paradox possible. But once we see clearly that the symbol expressed by a sign is determined by its possibilities of significant use, we can also see that the attempt to state the paradox is doomed from the outset.

This criticism of Russell exemplifies the philosophical method that, Wittgenstein thought, could disarm philosophical and ordinary confusions by exposing their roots in our temptation to use the same orthographic sign in a variety of different ways. On the method, reflection about the various uses of an ordinary sign suggests its replacement with one or more distinct signs; ultimately, we develop a notation in which each sign is used in exactly one way. The form of this perspicuous symbolism then shows the logical rules that govern meaningful linguistic use. Wittgenstein insisted that these rules of logical syntax must treat only of signs themselves, and never involve reference to their meanings.[119] In other words, there ought never, in the process of analysis, be any occasion to stipulate the possible uses of signs by referring to the meanings that we want them to have; Wittgenstein objected that Russell had done just this in his theory of types, and that this alone showed the invalidity of the theory. [120] Instead, reflection on the uses that signs already have in ordinary language must suffice to develop all the distinctions expressed in the structure of the logically perspicuous symbolism. The introduction of a new sign can, accordingly, only be justified by the recognition of a previously unrecognized use; the new use will then naturally be codified in combinatorial, syntactical rules governing the possible appearances of the new sign. In this way, the logical analysis of language proceeds from ordinary observations about significant use to the notational expression of these observations, yielding clarity about the meanings of signs by exhibiting perspicuously their use .