Frege's Context Principle 4 (from the Chapter 9 of Hacker & Baker 2005)

Baker, Gordon P. & Hacker, P. M. S. (2005). Wittgenstein: Understanding and Meaning: Volume 1 of an Analytical Commentary on the Philosophical Investigations, Part I: Essays. Malden, MA: Wiley-Blackwell. Edited by P. M. S. Hacker, pp. 159-170, 173-175.

 

Chapter 9. Contextual dicta and contextual principles

1. The problems of a principle

The dictum ‘A word has a meaning only in the context of a sentence’ was first enunciated by Frege in The Foundations of Arithmetic. It has been said to be the most important single statement Frege ever made. But that is puzzling, since taken at face value it is patently false. For we often ask what a word means outside any sentential context, and the question can typically be answered.

① When we want to find out what a word means, we can look it up in a dictionary which tells us, for example, that the word ‘primatology’ means ‘the study of primates’.

② Formal definitions specify the meaning of a word independently of a sentential context.

③ Furthermore, there are perfectly significant uses of words (quite apart from one-word sentences such as ‘Jump!’) outside sentential contexts. We use personal names on labels (and may order a packet of 100 such labels with our own name printed on them for future use), stick names of substances on bottles, and put name-labels on drawers or files. It would be dogmatic to insist that ‘aspirin’ on a bottle was elliptical for ‘This bottle contains aspirin’, and no more than adherence to a form of representation to insist that although what is written on the label is a single word, it is really a one-word sentence the depth grammar of which is ‘This bottle con tains aspirin’. We put numerals or number-words on houses, number-plates and licences, at the heads of chapters and at the foot of pages.

We use single words or phrases as book titles (Persuasion), as greetings (‘Hello’), exclamations (‘Hurrah’) and as expletives (‘Damn’). We insert meaningful words in cross word puzzles, and we do not allow players of Scrabble to put down meaningless concatenations of letters, but only words of our language. And we distinguish between a list of meaningful words and a list of nonsense words such as ‘Juwiwalera’ or ‘Lilliburlero’.

So if the contextual dictum is the most important statement Frege ever made, it cannot, presumably, be this that he meant to exclude.

On the other hand, we may grant that in a sense there is much truth to the famous dictum. After all, we may grant that a dictionary tells us all the different meanings of a word, but that to find out what the word means in use, we must know the context of its use. ‘Coach’ may mean a person who trains sports men, a single-decker bus, or a horse-drawn vehicle. But to know what it means in a given use, we must know in what sentence it was embedded (or whether it was used as a one-word sentence), and in what situation the sentence was uttered. ‘White’ is a colour-name, but white coffee is brown, and a white Christmas is a snowy one. And so on. But it is evident that this is not what Frege meant to include in his famous dictum. Indeed, he viewed such phenomena as faults of ambiguity in natural languages that are to be remedied in a logically perfect language. So, we must find out what Frege did have in mind.

Frege’s dictum is often referred to as ‘the context principle’. It and its variants occur five times in the course of the Foundations (1884). But they seem to signify a variety of quite different things.

① In the first occurrence the dic tum signifies a heuristic principle that we are enjoined to follow in order to avoid falling into the morass of psychologism and taking words to stand for ideas in the mind (FA p. x). It is not obvious, however, that virtually the only alternative to taking words to stand for ideas in the mind is to take them to have a meaning only in the context of a sentence.

② In the second occurrence, such a principle is invoked to shed light on the question of what it is of which we assert something when we make a statement of number. Light will be shed on the matter, Frege writes, if we ‘consider number in the context of a judge ment which brings out its basic use’ (FA §46). That, he avers, suggests that a statement of number is an assertion about a concept. It is important to note here that the emphasis is not on a sentential context, but on the context of a judgement.

③ Subsequently (FA §60), the dictum specifies a necessary condition for a word to have a meaning (‘Only in the context of a sentence does a word have a meaning’).But, rather surprisingly, this is immediately and without argu ment transformed into a sufficient condition (‘It is enough if the sentence taken as a whole has a sense; it is this that confers on its parts also their content’).

④ Subsequently the dictum appears to be invoked in order to justify a proced ure akin to what we call ‘contextual definition’ of number-words (FA §62). But that is apparently repudiated and the proposed paraphrastic definition in terms of one-to-one correspondence is replaced by an explicit definition (FA §68).

⑤  The final occurrence of the dictum in §106 merely recapitulates what Frege takes himself to have established.

So, surveying the different occurrences of the dictum, is there only one principle here, or are there different ones?

To cap this, the contextual dictum is nowhere explicitly cited, let alone emphasized, in Frege’s masterwork of the 1890s, The Basic Laws of Arithmetic (Part I).

 

This has been explained by the alleged fact that it was only in the 1890s that he disastrously assimilated sen tences to proper names, and therewith abandoned the primacy he had assigned to sentences in the Foundations. But this is puzzling, since he patently treated sentences as proper names already in Begriffsschrift in 1879. Furthermore, is it plausible that he should silently and without notice repudiate what was allegedly the most important statement he ever made? [160-161]

 

Wittgenstein apparently quotes Frege’s dictum a number of times in the Tractatus. He writes that: ‘Only propositions have a sense; only in the context of a proposition does a name have a meaning’ (‘Nur der Satz hat Sinn; nur im Zusammenhange des Satzes hat ein Name Bedeutung’ (TLP 3.3)). Again, at 3.314, he writes: ‘An expression has a meaning only in a proposition,’ and at 4.23 he adds: ‘It is only in the context of an elementary proposition that a name occurs in a proposition.’ But before jumping to the conclusion that Wittgenstein is simply endorsing Frege’s dictum, we should bear in mind that although Wittgenstein uses Frege’s terminology of ‘sense’ (‘Sinn’) and ‘mean ing’ (‘Bedeutung’), he means something quite different by ‘sense’ and holds quite different principles concerning sense and meaning.

 

For Frege held the sense of a sentence to be the thought it expresses, which is an abstract entity with which we come into contact when we think (PW 137, 145, 148 (NS 149, 157, 160)). Thinking or believing is a binary relation between a person and a thought. A thought is a mode of presentation of a meaning. It presents a truth-value (‘the True’ or ‘the False’) as the value of a function for an argument, and that truth-value is the meaning (Bedeutung) of the sentence. [161]

 

But for Wittgenstein, the sense of a sentence is its agreement and disagreement with the possibilities of obtaining and non-obtaining of states of affairs (TLP 4.2). Furthermore, a state of affairs is not an abstract entity; indeed, it is not an entity of any kind, but a possibility. Thinking is not a binary relation between a thinker and a thought. It is, rather, the projection of a representation on to the state of affairs it represents, and the method of projection is meaning or intending (TLP 3.11; PTLP 3.1–3.15; MS 108 (Vol. III), 218f.; see ‘Turning the examination around: the recantation of a metaphysician’, sect. 2). What we think (mean) when we think that p is not something distinct from the state of affairs the obtaining of which makes true what we say when we say that p. And while propositions have a sense thus construed, they do not, accord ing to Wittgenstein, have a meaning. In particular, their truth-value is not their meaning. Furthermore, unlike Frege, Wittgenstein denied that simple names have a sense at all; they have only a meaning, and their meaning is the simple sempiternal object in reality for which they go proxy in the representation of a state of affairs. So we need to examine Wittgenstein’s rationale for his con textual dictum, and must not assume without more ado that he was simply endorsing whatever it was that Frege was propounding in the Foundations.

Despite their differences about sense (Sinn) and meaning (Bedeutung), both Frege and the young Wittgenstein cleaved to the conception of a language as a calculus. Irrespective of what Frege thought about the forms and operations of natural languages (a controversial matter), it is evident that the concept-script he invented and conceived to be a logically perfect language was deliberately constructed on the model of a calculus. It was not for nothing that the subtitle of Begriffsschrift was ‘a formula language of pure thought modelled upon the formula language of arithmetic’. It is also patent that Wittgenstein, when he wrote the Tractatus, held any language to be a calculus. That, he conceded, is not evident from the surface grammar of a language, but it will become clear on analysis, for it is a requirement of the possibility of representation. For elementary pro positions are composed of simple names, the meanings of which are simple objects. The sense of such propositions is a function of the meanings of the constituent names. From the fund of elementary propositions all propositions can be generated by the operation of joint-negation. For all propositions are truth-functions of elementary propositions. So, conceiving of language as a calculus, both philosophers construed understanding as a computational process.

Frege, towards the end of his life, held that the understanding of a sentence is a process of ‘calculating’ or constructing its sense from one’s knowledge of the senses of its sub-sentential components. Furthermore, he invoked this idea in order to explain how it is that we are able to understand novel sentences. ‘The possibility of our understanding sentences we have never heard before rests evidently on this, that we construct the sense of the sentence out of parts that correspond to the words’ (letter 12 to Jourdain, 1914, PMC 79).

Wittgenstein did not think that the sense of a sentence is composed of the senses of its constituents. For the simple names of which an elementary pro position consists have no sense but only a meaning. Rather, he held that the sense of a sentence is a function of the meanings of its constituent simple names. So he may well have conceived of understanding sentences, a fortiori [더 한층 강력한 이유로] of understanding new sentences, as a computational process of calculating the sense of the sentence from one’s knowledge of the meanings of the constituent words (one’s ‘interpretation’ of the speaker’s meaning) and their mode of combination. In this respect, then, Frege’s late ideas and Wittgenstein’s early ones do perhaps converge.

This alone would make Wittgenstein’s apparent endorsement of Frege’s con textual dictum in the Investigations §49 puzzling. For by the time he wrote the Investigations, Wittgenstein had come to repudiate the calculus conception of language root and branch, and with it the computational conception of under standing. In §81 he remarks that only when one is clear about the concepts of understanding, meaning (des Meinens) and thinking will it also ‘become clear what can lead us (and did lead me) to think that if anyone utters a sentence and means or understands it, he is operating a calculus according to definite rules’. So if a specific contextual principle lay at the heart of Wittgenstein’s calculus conception of language, how is it possible to repudiate the one without aban doning the other? But matters are even more puzzling. For his endorsement of Frege’s contextual dictum gives it an interpretation which has no obvious ground in anything Frege ever wrote. Wittgenstein’s remark runs as follows:

. . naming and describing do not stand on the same level: naming is a preparation for description. Naming is not so far a move in the language-game — any more than putting a piece in its place on the board is a move in chess. We may say: nothing has so far been done, when a thing has been named. It has not even got a name except in the language-game. This was what Frege meant too, when he said that a word has a mean ing only in the context of a sentence. (PI §49)

The thought that naming is not a move in the language-game but a prepara tion for such moves is important and insightful. The idea that the sentence is the minimal unit by which one ‘makes a move in the language-game’ is arguably exaggerated (the linguistic signs used in greeting, hailing people by their name, cursing, and exclaiming are not necessarily or even typically one-word sen tences), and although sometimes attributed to Wittgenstein, is not actually asserted by him. Be that as it may, detailed reflections on speech-acts (other than asser tion) are conspicuously missing from Frege’s writings. Nowhere, in his dis cussions of his contextual dicta does he mention the thought that it is only with a sentence, and not with anything less than a whole sentence, that one can perform an act of speech.

The contextual dicta, despite appearances to the contrary, are neither unequivocal nor clear. Arguably a number of different principles are at stake, some of which may well be true while others are false. A further point that requires elucidation is how these principles stand in relation to the Augustinian conception of language. It is all too easy to assume that the so-called context principle was a definitive move away from it. But, as was already noted (‘The Augustinian conception of language’, a vii and e ii), that is not obviously right. Even in the opening quotation from Augustine’s Confessions, emphasis is placed on hearing words used ‘in their proper places in various sentences’, and it is evident that Wittgenstein conceived of the Tractatus, which patently embraced some context principle or principles, as moulded by the force-field of the Augustinian conception of language and meaning. So it is not clear that the contextual dictum is a move away from the Augustinian picture. Indeed, in the following we shall see that Frege and the young Wittgenstein invoked it in order to confirm the principles that the essence of words is to name or stand for entities, that these entities are the meanings (Bedeutungen) of the words, and that sentences are combinations of words.

 

2. Frege

Locke’s Essay Concerning Human Understanding, Book III, dominated reflections on language throughout the eighteenth century. Locke unequivocally took the meanings of words to be ideas in the mind, and paid scant attention to the role of words in sentences or indeed to the roles of sentences. In this he was followed, with but marginal qualification, by Berkeley and Hume. The British empiricists (following Descartes) were remarkable for their neglect of, and contempt for, formal logic and its theoretical foundations. But it would be wholly mistaken to suppose that prior to Frege no attention whatsoever was given to sentences and their structure and to the different roles of differ ent kinds of words in sentences.

① The role of sentences in the making of state ments, and the necessary complexity of sentences was already noted by Plato, who observed that for any statement to be made, a combination of noun and verb is requisite.

② Aristotle emphasized that truth and falsity, affirmation and denial, presuppose complexity, but that a combination of noun and verb to make up a sentence does not suffice for a proposition. For it is to propositions alone (as opposed to, e.g., a prayer) that truth and falsity can be ascribed. The nouns and verbs of which propositions and other sentences are formed have a meaning, but, by themselves, lack truth or falsehood. This conception continued throughout the Middle Ages. Words were conceived to be essen tially ‘parts of speech’ ( pars orationis), potential constituents of sentences used in speech.

③ Peter of Spain held, in conformity with Antiquity, that ‘a proposition is a sentence signifying something true or false in the manner of a judgement, such as “A man is running”; or again, a proposition is the affirming or denying something of something’. The conception persisted.

④ The Port-Royal Logic claimed that Judgements are propositions expressed by sentences . . . sentences themselves are com posed of words . . . The words set apart to refer to things or modes of things are called nouns [or pronouns]. ...A verb is nothing else but a word whose principal function is to indicate assertion . . . The indicative mood of the verb is used for this principal function. . . . The product of judging is expressed by a sentence which must contain two terms — the one term is the subject, which expresses the idea of which we affirm or deny another idea; the second term is the predicate, which expresses the idea which is affirmed or denied of the idea expressed by the subject.

⑤ Standard logical textbooks began from consideration of terms or concepts (vide Kant’s Jäsche lectures on logic), proceeded to a discussion of judgements, held to be composed of terms, and finally moved on to consider inferences. This conception was still accepted wisdom, and this order of exposition was still being repeated, in the nineteenth century by almost all authors of books on logic writing before, or at the same time as, Frege wrote his great logical works. So Frege’s innovation was obviously not to draw attention for the first time to the diversity of the parts of speech, or to the significance of structure, or to the role of sentences in the expression of a judgement. What, then, was it?

Frege spelled it out quite clearly, both at the beginning of his career and at the end of it. In 1880/1 he wrote, ‘I start out from judgements and their contents, and not from concepts ...I allow the formation of concepts to proceed only from judgements. . . . Instead of putting a judgement together out of an already previously formed concept as a predicate, we do the opposite and arrive at a concept by splitting up the content of a possible judgement’ (PW 16f. (NS 17)). In his ‘Notes for Ludwig Darmstaedter’, written in 1919 and intended to give an overview of his life’s work, he wrote:

 

What is distinctive about my conception of logic is that I begin by giving pride of place to the content of the word ‘true’, and then immediately go on to introduce a thought as that to which the question ‘Is it true?’ is in principle applicable. So I do not begin with concepts and put them together to form a thought or judgement; I come by the parts of a thought by analysing the thought. This marks off my concept script from the similar inventions of Leibniz and his successors. (PW 253 (NS 273))

Obviously this is not a doctrine about the nature and order of concept acquisition by the language-learner. It concerns logical analysis for the purposes of the science of the laws of truth. Giving ‘pride of place’ to the word ‘true’ was no innovation (Aristotle had already done that); nor was there any novelty in introducing the thought (or the content of a judgement) as that which is true or false (this too was part of the traditional conception of logic). But in traditional logic, the science of terms (their classification and the determination of their various roles) precedes the science of judgements and inferences. Frege is emphasizing, in the above two passages, that in his novel function-theoretic logical system he reverses that order. In logical analysis, unjudgeable contents originate from the decomposition of the contents of a possible judgement. We start out with judgements, not with their constituents, and we decompose them in various ways by function/argument analysis into unjudge able contents. (In his mature logical system, in which content is split into sense and meaning, he starts out with thoughts and decomposes them into their con stituents, viz. the senses of proper names, the senses of concept-words and of higher-level function-names.) It should be noted that this analytical strategy is applied in the first instance to possible judgements, and only derivatively to sentences that may be used to express them. They are decomposed not into subject and predicate, but into argument and function. So, for example (PW 16f.), the judgement that 24 = 16 may, by functional abstraction, yield the concept fourth root of 16 (x4 = 16) or the concept logarithm of 16 to the base 2 (2x = 16) or the concept relation of a number to its fourth power (x4 = y). But the sentence in natural language ‘Two to the fourth equals sixteen’ cannot yield such a rich harvest by decomposition. In the Foundations we are told that the content of the judgement ‘line a is parallel to line b’ can ‘be carved up’ so as to yield the concept of identity of direction (FA §62), although, to be sure, the sentence ‘line a is parallel to line b’ contains neither an identity-sign nor the word ‘direction’.

With this analytical, decompositional strategy in mind, we can now approach Frege’s successive invocations of his context principle (or principles) in the Foundations. We must bear in mind that in this book, Frege uses the terms ‘content’, ‘meaning’ and ‘sense’ more or less interchangeably, and that the notion of content was explicitly restricted in Begriffsschrift to what is relevant to the cogency of inference (BS §3).12 The first occurrence of the dictum in the Foundations is in the Preface, where Frege declares the three methodological principles that inform the book. The first principle is an anti-psychologist one: always to separate the psychological from the logical. The second is the heuristic context principle:

‘never to ask for the meaning of a word in isolation, but only in the context of a sentence’

Frege links the two, inasmuch as the rationale for the heuristic principle is that if it ‘is not observed, one is almost forced to take as the meanings of words mental pictures or acts of the individual mind, and so to offend against the f irst principle as well’ (FA p. x). Frege resisted the idealist (psychologist) drift to which others, such as the British empiricists and the German psychologi cians, had succumbed.

 

But, in truth, there is no good reason to suppose that asking what a given word, e.g. ‘procrastinate’ or ‘million’ means outside any sentential context must incline one to suppose that it has an idea as its mean ing, and Frege gives none. Moreover, by the end of his own investigation into number, Frege himself offers us explicit definitions, i.e. definitions outside any sentential context, of number-words such as ‘nought’ and ‘one’, e.g. ‘0 is the number which belongs to the concept “not identical with itself”’ (FA §74; cf. §76). [167]

 

The second occurrence of a context principle is in §46, in which we are invited to consider number in the context of a judgement (im Zussammenhange eines Urteils) of a kind that brings out the basic use of statements of number (Zahlangabe) that make a judgement of number (Zahlurteil). For it will then become clear that statements of number, such as ‘There are four companies’, ‘There are 500 men’ or ‘Venus has 0 moons’, assign numbers to concepts (FA §48). This fits well the association of context principles with the funda mental insight of Frege’s whole philosophy: namely, the primacy of judge ments over concepts for purposes of logical analysis and the various ways of precipitating concepts out of judgements by functional abstraction.

The third occurrence of the dictum is in §60, in which Frege first presents it in the form of a restrictive condition:

‘Only in a proposition (Satz) have the words really a meaning’.

We have already noted that this principle is patently false as far as our ordin ary conception of meaning is concerned; but there is no reason for thinking that Frege had that in his sights. What he is primarily concerned with are inference-relevant features of expressions. He emphasizes here again that the presence or absence of any associated ideas is irrelevant to the question of whether a word has any meaning. That we do not associate a word with an idea as its meaning or content, Frege insists, does not mean that we ‘thereby forfeit the support we need for our inferences’ (ibid.). But he immediately moves on to a much stronger sufficiency principle, viz.

‘It is enough if the proposition (Satz) taken as a whole has a sense; it is this that confers on its parts also their content’ (ibid.).

The transformation of what appears to be a necessary condition for a word to have a meaning into a sufficient condition is striking. Again, what he has in mind is that the fact that we associate no idea with the number 0, for example, does not imply that in the sentence ‘The number of moons of Venus is 0’ the numeral has no meaning. For we can draw legitimate inferences from this pro position (e.g. that the number of moons of Venus is less than 10).

 

However, taken au pied de la lettre, the sufficiency principle is not obviously correct: ‘It is raining’ has a sense, but that does not suffice to confer content on the word ‘It’ in this sentence, in which it functions merely to satisfy a syntactical requirement. To be sure, Frege would brush this aside as irrelevant to his concerns — as indeed it is. But that is no thanks to the sufficiency principle. [168]

 

Frege proceeds to elaborate: ‘The self-subsistence which I am claiming for number is not to be taken to mean that a number word signifies something when removed from the context of a proposition (Satz), but only to preclude the use of such words as predicates or attributes, which appreciably alters their meaning’ (ibid.). In the sentence ‘The number of moons of Jupiter is four’, ‘four’, according to Frege, is the proper name of a number, i.e. of a mathem atical object. But in its adjectival occurrence, e.g. ‘Jupiter has four moons’, ‘four’ is merely part of a compound predicate14 and does not stand for an object.

 

This does shed a little more light on Frege’s invocation of contextual dicta. It seems patent that he thought that what meaning an expression has in a sentence depends on how the sentence is ‘carved up’. So ‘four’ in some sentences may have the number four as its meaning, and in others not. (So too, ‘Vienna’ in the sentence ‘Vienna is the capital of Austria’ has an object, namely the city, as its meaning; but in the sentence ‘Trieste is no Vienna’, it does not fulfil the function of a proper name at all, but is part of a function-name that has a function (concept) as its meaning (CO 200f.).) [168]

 

Frege’s reasoning is that despite the fact that number-words do not stand for ideas or intuitions that are given to us, nevertheless they do stand for objects when they occur non-attributively in sentences. The sufficiency principle is in fact invoked precisely to confirm the idea that the number-words, as they occur in sentences of the form ‘The number of Fs is n’, are names, that they have a meaning, and that their meaning is the object they stand for. So, con sidered from the point of view of the Augustine’s picture of language and the family of ideas that grow out of it, it is evident that Frege’s invocation of the contextual sufficiency principle does not distance him at all from the Augustinian conception of meaning.

In §62 Frege invokes his contextual dictum to justify giving a paraphrastic definition of number-words. Since numbers are not ‘given to us’ in the form of ideas or intuitions, we can obtain the concept of number only by fixing the sense of a numerical identity.

Since it is only in the context of a sentence that words have any meaning, our prob lem becomes this: To define the sense of a sentence in which a number-word occurs. . . . When we have . . . acquired a means of arriving at a determinate number and of recognizing it again as the same, we can assign it a number word as its proper name.

We can assign number-words a meaning only indirectly, by giving a definition of ‘the number which belongs to the concept F is the same as the number which belongs to the concept G’, which will not mention the phrase ‘the num ber which belongs to the concept F’. This does not give any argumentative support to the restrictive condition, but takes it as given.

 

It is noteworthy that the problem to be solved is to explain the sense of a sentence in which a number-word occurs, and that this is to be accomplished by picking out for each number-word a determinate object which can be assigned to it as its content (Inhalt). [169]

 

Despite this, Frege subsequently faults his initial definition in terms of one–one correspondence, and replaces it with an explicit definition of number-words in terms of extensions. The final occurrence of the dictum in §106 merely recapitulates what Frege takes himself to have established.

It is clear that contextual dicta are invoked in The Foundations of Arithmetic for different purposes, and that there are different principles involved: the generation of concepts by functional decomposition of possible judgements, a heuristic principle, a restrictive condition and a sufficiency principle. 

Contextual Dicta in the Grundlagen

The generation of concepts by functional decomposition of possible judgements

A heuristic principle

A restrictive condition

A sufficiency principle

The dictum that a word has a meaning only in the context of a proposition (signific ant sentence) is associated with a particular conception of what it is to assign a meaning to a proper name [고유명사에 의미를 부여하는 것의 특정 개념], and with a general conception that ties the meaning of a word in a given sentence to the impact of this word on the legitimacy of inferences incorporating the judgeable content of that sentence [주어진 문장에서 단어의 의미를 이 단어가 그 문장의 판단 가능한 내용을 포함하는 추론의 정당성에 미치는 영향과 결합시키는 일반적 개념]. It is also clear that Frege was not concerned here with the nature or order of language-learning and concept-acquisition; nor was he concerned with speech-acts and the idea that the sentence is the minimal unit for ‘making a move in the language-game’. Rather, it was the sentence as the vehicle of judgement that concerned him. The primacy of judgement in logical analysis was because the contents of judgement (no matter whether asserted or unasserted) are the bearers of truth, and logic is the science of the laws of truth. What marked off Frege’s procedures from the Aristotelian tradition was not this, but rather the idea of the analytic decomposition of judgeable contents into function and argument, by contrast with the traditional synthetic conception of judgeable contents as assembled out of terms (subject and predicate).

 

5. Compositional theories of meaning

It was noted above that Wittgenstein in the Tractatus raised the question of how it is possible to understand sentences we have never heard before. He implicitly offered a computational answer. The sense of a sentence is not a function of the senses of its constituent expressions (since the simple names have no sense), nor is it composed of the meanings of its constituent expres sions. For the sense of a sentence is not a complex composed of meanings, but a possibility, which has meanings, i.e. simple objects, as constituents. So it is a function of those meanings. And, Wittgenstein may have implied (TLP 4.026–4.03, quoted above), we understand sentences, including sentences we have never heard before, by ‘calculating’ their sense from (our knowledge of ) the meanings of their constituents and their mode of combination. How pre cisely this unconscious process is carried out would (presumably) be a matter for psychology to investigate (cf. CL 68). 

In The Basic Laws of Arithmetic, where he split judgeable contents into sense and meaning (Bedeutung), Frege held that the senses of sub-sentential constituents consisted in their contribution to the determination of the sense of the sen tence, i.e. to the thought expressed by the sentence. ‘If a name is part of the name of a truth-value, then the sense of the former name is part of the thought expressed by the latter name’ (BLA i §32). Towards the end of his life, Frege went considerably further in the direction of such a compositional conception of thoughts (or propositions). For he now claimed not only that a thought is composed of the senses of sentential constituents, but that the senses of senten tial constituents are ‘thought-building-blocks’ (Gedankenbausteine (PW 225, cf. 243 (NS 243, cf. 262))). It is noteworthy that there is a grave tension between the decompositional conception that is involved in the priority of judgement over concepts and the synthetic conception of thoughts as composed of thought building-blocks. As noted, Frege then invoked the thought-building-block conception to explain the possibility of our understanding sentences we have never heard before. For, he now suggested, we construct the sense of the novel sentence out of parts that correspond to the words (PMC 79, 12th letter to Jourdain).