Wittgenstein's Later Theory of Meaning

Imagination and Calculation

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• Publisher: Wiley-Blackwell
• Year: 2014
• ISBN:
  9781118642160
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

By exploring the significance of Wittgenstein's later texts relating to the philosophy of language, Wittgenstein's Later Theory of Meaning offers insights that will transform our understanding of the influential 20th-century philosopher.

• Explores the significance of Wittgenstein's later texts relating to the philosophy of language, and offers new insights that transform our understanding of the influential 20th-century philosopher
• Provides original interpretations of the systematic points about language in Wittgenstein's later writings that reveal his theory of meaning
• Engages in close readings of a variety of Wittgenstein's later texts to explore what the philosopher really had to say about 'kinds of words' and 'parts of speech'
• Frees Wittgenstein from his reputation as an unsystematic thinker with nothing to offer but 'therapy' for individual cases of philosophical confusion

1

The Fregean Perspective and Concomitant Expectations One Brings to Wittgenstein

We know from the Tractatus (Wittgenstein 1999, p. 28) that Wittgenstein was a great admirer of the work of Gottlob Frege. In this chapter we will give an overview of those of Frege’s basic contributions to a theory of meaning that are most important for an understanding of Wittgenstein’s later thought (Frege 1972, 1979, 1984).

As a starting point we can take the older idea of an “analysis” of words and sentences. When we explain the meaning of the word “bachelor,” for example, by saying that it is applied to unmarried men, it has long been common to describe the relation between the words involved by saying that the meanings of “unmarried” and “man” are contained in the meaning of the word “bachelor.” The process of bringing this to light was accordingly described as “analysis”: hidden or implicit components of meaning, not visible by just looking at the sign, are brought to light, are made explicit, in something like the way in which water is analyzed into its invisible components hydrogen and oxygen.¹ The usefulness of such an ­analysis lies in the fact that ignorance of such “meaning components” can lead our thinking astray, and in the idea that (positively) explicit knowledge of such components is necessary for a clear understanding of the meaning of the expression in ques­tion. Accordingly, complex expressions are taken to have a clear meaning if they have been “analyzed,” that is, broken up into constituent expressions the meanings of which are less apt to be unclear or controversial.

Frege also applied something like this strategy to sentences. Here too an “analysis” can bring out “hidden” meaning-components, for example when a sentence like “lions show aggressive behavior against humans” is paraphrased as meaning “all lions show this behavior”; the “all” had been hidden and has now been brought to light.² In a slightly different case it is the semantic structure of the sentence that cannot be unambiguously read from the words alone. The sentence “the lions show aggressive behavior against humans” might be paraphrased as “our group of lions here at London Zoo…” or as “all lions… .” A sentence like “you may have cookies or fruit” can be supplemented by “but not both” or by “or both”; our normal ways of speaking often leave it open whether the “exclusive” or the “inclusive” meaning of “or” is intended.

These cases of ambiguity and implicitness need not worry the speaker of everyday language, but where maximal clarity and precision is required (as for proofs in the Philosophy of Mathematics) they do matter. And it was his work on the foundations of Mathematics that inspired Frege to develop what he called a “concept script.” He envisaged it as a “language” that would, on the one hand, be quite restricted in that it would contain only sentences that can be true or false. In other words, it would treat only contents that are “judgeable” – no commands, no questions, no expressions of feeling, etc. Frege was quite aware that it would be absurd to recommend such a symbol system to be used in everyday life. He himself remarks that such a proposal would be like recommending the use of a microscope in the performance of everyday tasks (Frege 1972, 104f.) But on the other hand (on the positive side) his “concept script” would avoid what must, in Frege’s field, be seen as two shortcomings of our “ordinary” or “natural” language. First, it would make explicit all aspects of meaning that, in ordinary communication, are understood only implicitly. Nothing, Frege declared, should (in his delicate special field of inquiry) be left to guesswork. And, secondly, it should avoid all ambiguity: one form of signs should express only one kind of meaning. To use the same example again, one should be able to see, to read it off from the sign, whether an inclusive or an exclusive “or” is intended by the speaker. So “nothing implicit!” and “nothing ambiguous!” are the two ­imperatives that rule the construction of his logical notation, his “concept script.”

Is the project of such a construction realistic? It seems that it only takes a quite simple consideration to justify an affirmative answer here. As the few examples given above show, every speaker of English is able to note (to “perceive,” to “see”) implicit aspects of meaning as well as cases of ambiguity when such features occur in an utterance. Normally she can comment on them, she can easily formulate paraphrases that make explicit what has not been said (but has very often been understood). And so too in the case of ambiguity: every standard speaker of a natural language can easily formulate paraphrases and comments, can use additional or alternative expressions when the need arises to resolve an ambiguity. But if such improvements are indeed easy to provide in any given case, there seems to be nothing that would preclude a systematic approach as envisaged by Frege. In other words, it should be possible to gain an overview of all the ways in which meaning elements can be combined in order to form expressions for a complex content, that is, to form a sentence that can be true or false. Accordingly, it should also be possible to develop a notation that would (firstly) exhibit all aspects of meaning (as far as they are relevant for truth), leaving nothing to guesswork, and would (secondly) do so in an unambiguous way, so that there would be no difference in meaning that would not be apparent in the signs themselves. The reason for this seems simple: since we can detect what (from the perspective of a mathematical logician) are shortcomings in the workings of our natural languages, and since we can avoid them in any given case by choosing a more appropriate mode of expression, it seems that we should also be able to systematically exclude these shortcomings in a notation especially constructed for limited scientific and philosophical purposes, clumsy and unappealing as such a notation may be for the purposes of everyday life.

What then, in Frege’s eyes, are the “elements of meaning” and how can they be combined in order to express truth or falsehood? He was quite careful to avoid a trap that one might fall into right at the beginning. When the possibility of a “combination” of signs into a sentence is what is at stake, we have to see to it that we do not end up with just a list of words instead of a sentence (Frege 1984b, p. 193). There is a difference between a complex expression with a unified sentential character on the one hand, and a succession of a number of utterances tied together only by their proximity in time (or on a piece of paper) on the other. A shopping list, for example, is like a “list of names”: it does not show the unity that is characteristic of a sentence. So we have to ask right from the beginning: what constitutes the unity of a complex sign, whereby is it distinguished from a mere succession of simple signs?³

Frege’s answer to this question is his doctrine of “unsaturated” expressions, which is inspired by his work in Mathematics. He says: “And it is natural to suppose that, for logic in general, combination into a whole always comes about by the saturation of something unsaturated.” (Frege 1984d, p. 390; orig. pagination 37) His analytic procedure consists in starting with a consideration of a whole “thought,” a content that can be affirmed or denied, and only then breaking it up into parts. These parts are (at the level of expressions) proper names on the one hand (“Paris,” “Caesar,” “my eldest brother”) and concept terms (“city,” “person,” “family member”) on the other. So an important part of his philosophy of language is his claim that not all meaningful expressions should be understood as names. This corresponds to the fact that in Mathematics we have not only “names of numbers” like “five” or “thirteen,” but also functional expressions like “plus” or “divided by.” In a symbol system containing only names, complex expressions could be nothing but lists of such names. So one important point in Frege is that he saw that ­concept terms are not names; like functional expressions in Mathematics they can play their role only in connection with names. Speaking figuratively, Frege says that they are “unsaturated”; their expression in his concept script therefore contains an empty space (marked by a letter like “x”: “x is green”) that indicates the place where a name must be inserted so that a complete expression results. Using another figure of speech Frege says that a name can “stand alone,” like a person, whereas different kinds of unsaturated expressions (concept terms or other functional expressions) can be added to such a name like one or more coats placed over a person’s shoulders. The coats, on the other hand, cannot “stand upright by themselves.” (Frege 1984c, p. 388; orig. pagination 157)

By distinguishing kinds of expressions in this way Frege is able to give an account of the unity of the sentence. This unity arises from the “cooperation” of words of different kinds, which have quite different functions (logical roles), namely (on the most basic level) those of “naming” and of “speaking of” (predicating). Relational terms like “x is the brother of y” he treats as predicates with more than one object term (name). The relationship between object and concept, which is at the basis of all expressions that can be true or false, Frege calls the “fundamental logical relation.” (Frege 1979b, p. 118) To understand the unity of the sentence, then, we have to understand the interplay of these two (and later some more) types of words.

This interplay constitutes the “logical structure” of the sentence in question, and it is clear that the meaning of “logical” here is defined in view of the kinds of content the expressions hold. Therefore we can also speak of semantic functions or roles, to avoid a formal reading of the adjective “logical.” In the process of working out and arguing for his “concept script,” Frege uses the word “logical” always in its content related, never its formal, sense. This comprises the “conceptual” level of language (following the old understanding that logic is the theory of concepts, judgments, and deductions) so that instead of “logical” (and the much later coined term “semantic”) we can also speak of Frege as treating “conceptual” problems. Accordingly, he has chosen the term “concept script” for his newly developed symbol system.

What he then adds to the names and concept expressions are the by now familiar truth functions (“and,” “or,” etc.) that combine sentences; like concept terms, expressions for truth functions are not names. And (original to him and most revolutionary) he adds the machinery of quantification. Here his doctrine of “unsaturated” expressions brings a great advantage: in analyzing a sentence like “the lion is man’s enemy,” Frege no longer looks for a “general object” like “the species of lions” (a “platonic form”) which is taken to be named so that something is predicated of it (like his medieval predecessors did), but rather treats both “lion” and “man’s enemy” as unsaturated predicate expressions. He therefore paraphrases the sentence as: whatever name of an object will be put into the place of “x” in the expression: if x is a lion then x is man’s enemy, the result will always be true. The quantifier for him is a “second order concept,” a concept expression speaking about concepts.

For our purposes, these few hints must suffice to give an idea of the sense in which Frege’s concept script can serve as an inspiration and model for an attempt to understand the semantics of natural language. It is a proposal concerning how the “semantically relevant structure” of expressions should be viewed; it shows what it means to classify words according to their functions in the sentence. Names name a particular entity; concept- and relation-expressions classify the entities, that is, they say that a certain predicate is true of them or that they stand in a certain relation. Logical connectives enable us to combine component sentences to form a complex sentence, the truth of which depends solely on the truth of its constituents. And quantifiers express “second order concepts” in that they speak about the results of substitutions in sentences containing a space left open for a name. Accordingly, in Frege’s concept script we are offered a general understanding of the sense in which we can “infer” the meaning of a new sentence from the meanings of the constituent words and from the (semantically relevant, i.e., “logical”) structure of the sentence. This “inferring” is a kind of “calculating”: when we know the meanings of the words and the meaning of the structure-building devices (think of “Paul loves Mary” as compared to “Mary loves Paul” or of “a and b” vs. “a or b”) we can “arrive at” the meaning of a sentence we have never heard before.

It is remarkable that in this concept script we find a rather limited number of kinds of expression that seem to be able to express a huge number of (or even “all”) true thoughts. We also find that on the lowest level of the realm of “thoughts” (i.e., where we are concerned with truth and stay at the level beneath truth-functional combination and quantification) there is just one single way of building complexes: all complex expressions on this lowest level say that an object falls under a concept (or that a plurality of objects stand in a relation).

We now have to take a second look at the method Frege uses to determine the “elements of meaning” and the ways in which these can be combined in order to form an expression that can be true or false. How does he find out what the hidden elements of meaning are, and how they combine to form complexes that we do understand, but that we cannot (in natural languages) simply read off from the design of the sign? We noted above that what we normally do (and what Frege is doing in his writings) when we have to resolve an ambiguity (or are in some other way confronted with the necessity to clarify what we had expressed) is to formulate comments and paraphrases, that is, we clarify language with the help of language. Now, it is very tempting to use the following picture when we want to understand how this is possible: since we cannot detect the relevant meaning-aspects as something exhibited by the “mere sign” (for example a certain imprint of letters in a book), we look for something behind the sign (the “meaning”) and so are led to presume that the logician has to look in the realm of meaning (or, using Frege’s technical term, “sense”) in order to find out the logically relevant structures. There seems to be a structured realm of content behind any given linguistic expression. Every competent speaker seems to “see” it; she can move freely in it, for example when she tries to find helpful paraphrases. Frege here speaks of a realm of “thoughts” (in an objective, non-psychological sense) and what he is aiming to achieve when developing his “concept script” is to follow the structure of the respective “thought” in the closest ­possible way. The “logical structure of language” would then be something behind or above language, something by which a ­philosopher of language is guided when she discusses the semantic ­structure of imperfect utterances formulated in a natural language. Later, Wittgenstein (2009, § 102) would express this guiding picture in the following words:

The strict and clear rules for the logical construction of a proposition appear to us as something in the background – hidden in the medium of understanding. I already see them (even though through a medium), for I do understand the sign, I mean something by it.

Frege indeed very often speaks this way. We cannot get into the problems such a view comes up against in any detail here; just note that in the end it turns out not to be convincing.⁴ There is no reality “behind” or “above” language in the sense of a language-independent world of thought or an invisible mechanism of “meaning something” that is so construed out of elements that the combinatorial possibil...

Table of contents

• Cover
• Title page
• Copyright page
• Acknowledgments
• Foreword
• Introduction
• 1 The Fregean Perspective and Concomitant Expectations One Brings to Wittgenstein
• 2 How a Language Game Becomes Extended
• 3 Kinds of Expression
• 4 “Function” in Language Games and in Sentential Contexts
• 5 The Sound of a Sentence I: Singing from the Score
• 6 Projection: No Mere Mapping but a Creative Activity
• 7 The Sound of a Sentence II: Surface Grammar
• 8 Complexity
• 9 An Integration of Wittgenstein and Frege?
• 10 Dummett’s Doubts and Frege’s Concept of “Sense”
• 11 Wittgenstein on “Communicating Something”
• 12 “Grammatical Sense” and “Syntactic Metaphor”: A Wittgensteinian Solution
• 13 A “Theory of Meaning” – In What Sense?
• Index