What then is the structure of language? Wittgenstein divided all sentences into the complex and the atomic, and asserted that the former were built up from the latter by rules of formation which could be fully interpreted in terms of Russell’s logic (as this had been expounded in Russell and Whitehead’s Principia Mathematica (1910-1913)). Atomic sentences are those which employ the primitives of the language: the elementary names and predicates which, being themselves indefinable serve to pick out (or ‘picture’) what Wittgenstein called atomic facts. Only a completed proposition can be true or false, and so only a completed proposition can tell us anything about the world. Hence there can be no more basic constituent of the world than that which corresponds to the atomic sentence. This basic constituent is the atomic fact, and the world is therefore the totality of such facts.
Corresponding to complex propositions are complex facts, and to understand these complex facts we must understand the complexity of the language used to express them. This complexity is entirely given by the Fregean and Russellian logic. Thus ‘the King of France is bald’ is (although it seems not to be) a complex sentence, since its true structure (that is, its structure as represented by the new logic) shows it to consist of three incomplete sentences, combined and completed by quantification and the connective ‘and’. Many sentences are like that. They seem to be basic, but are in fact complex. In general many of the things we refer to are logical constructions (or fictions). Sentences which describe them are shorthand for more complex sentences referring to the constituents of quite different, but more basic, facts, in which these ‘logical constructions’ do not occur. A sentence like ‘the average man has 2.6 children’ is really shorthand for a complex mathematical sentence relating the numbers of children of men to the numbers of men. ‘The average man’ features in no atomic sentence, which is to say that ‘the average man’ names no constituent of reality. The same is true of the English nation, and of many ‘metaphysical’ entities that have seemed to pose philosophical problems. Wittgenstein was less specific than Russell, and certainly less specific than the logical positivists, for whom nevertheless the Tractatus provided the complete apparatus of philosophical argument, as to which facts are atomic and which are not. He wished to give the clear, statement of the logical structure of the world: its actual contents did not concern him.
The all-important feature of complex sentences is that the connectives which are used to build them must be ‘truth-functional’. That is to say, they must be such that the truth-value of the complex sentence is entirely determined by the truth-values of its parts. This is the ‘principle of extensionality’ that we have already encountered in discussing Frege, and which, according to Wittgenstein, is a precondition of logical thought and analysis. Logic is concerned purely with the systematic transformation of truth-values, and hence a logical language must be transparent to truth-values. It must be possible to see every operation in terms of the transformation of truth and falsehood. (The word ‘not’ has the sense that it turns truth to falsehood and falsehood to truth; ‘if’ that it makes a complex sentence that is false if the antecedent is true and the consequent false, otherwise true; and so on.)
The notion of a truth-functional language gives exactness and cogency to Wittgenstein’s claim that there is a real distinction between atomic and non-atomic sentences. He is able to say not only what the distinction is, but more importantly, how we are able to understand it. There is no difficulty, with a truth-functional language, in explaining how the understanding of atomic sentences leads to an understanding of all the infinite complexes that can be built from them. (This is another application of a principle of Frege’s, discussed here on pp. 245-6.) The conditions for the truth of a complex sentence formed truth-functionally can be derived immediately from the truth-conditions of its parts. And hence if we understand the truth-conditions of the parts, we understand the whole.
Moreover, Wittgenstein is able to provide a novel and seemingly utterly clear distinction between the necessary and the contingent, the analytic and the synthetic, the a priori and the a posteriori. These distinctions become one distinction, that between logical truth and contingency. A sentence is a logical truth if it is made true by every substitution of terms for the ‘primitive’ parts which it contains. (A primitive part being one which admits of no further definition.) The paradigm example of the logical truth is the truth-functional ‘tautology’. Consider the sentence ‘p or q’. The definition of ‘or’ reads thus: p or q is false if both p and q are false, otherwise true. The definition of ‘not’ is: not-p is true if p is false, false if p is true. From which it follows that the sentence ‘p or not-p’ is always true, whatever the truth-value of ‘p’. So, no matter what we substitute for the primitive term ‘p’, the resulting sentence will always be true. Sentences of this form are therefore necessarily true, and can be seen to be true a priori by anyone who understands the logical operations of the language.
This theory of necessary truth has the consequence, Wittgenstein thought, that necessary truths are empty: they say nothing because they exclude nothing. They are compatible with every state of affairs. The world is described by the totality of true atomic propositions: these are true, but, being atomic, might have been false, since there is nothing in their structure to determine their truth-value. Another way of putting this is that facts exist in ‘logical space’. This logical space defines the possibilities; the true atomic sentences describe what is actual, while tautologies reflect properties of logical space itself.
There are deep metaphysical problems raised by this account of language. First there is the problem of the relation between atomic sentences and atomic facts. Wittgenstein calls this relation one of ‘picturing’, and this metaphor has misled many of his commentators. He also says that the relation cannot be described, but only shown: indeed it was his view that what is most basic must be shown; otherwise description could never begin. Precisely what is meant by ‘showing’ is not clear. Perhaps the best way to understand this theory—sometimes called the ‘picture theory of meaning’—is as a denial, to use a later phrase of Wittgenstein’s, that we can use language ‘to get between language and the world’. We cannot give an account in words of the relation between an atomic fact and an atomic proposition except by using the proposition whose truth we are trying to explain. We cannot ‘think’ the atomic fact without thinking the sentence which ‘pictures’ it. The limits of thought are the limits of language. Wittgenstein concludes his book with the laconic statement: ‘that whereof we cannot speak we must consign to silence.’
One of the problems for the philosophy of the Tractatus is indicated in that very utterance. Only atomic sentences, truth-functional complexes, and tautologies are meaningful. But what of the theory which says so? It is not an atomic sentence, nor any complex of such: it purports to say, not how things are but how they must be. But it is not a tautology. Is it then meaningless? Wittgenstein actually says ‘yes’, and with that bold gesture moves on to the conclusion of his philosophy, adding that his propositions must serve as a ladder to be thrown away by those who have managed to ascend it.
Wittgenstein and linguistic analysis
There is about the Tractatus something of the fascination of Kant’s first Critique: the fascination of a doctrine that struggles as hard as possible to describe the limits of the intelligible only to be compelled, in the course of doing so, to transcend them. Wittgenstein nowhere acknowledges the likeness of his thought to Kant’s, or indeed to anyone’s except Russell’s, but the parallel between the two philosophers becomes more and more striking, so striking, indeed, that some have seen the argument of the posthumous Philosophical Investigations as completing at last the work of Kant’s Transcendental Deduction.
Wittgenstein’s later philosophy evolved out of a reaction to the earlier, or rather to a certain extremely influential interpretation of it. In the Tractatus the metaphysics of logical atomism is presented with almost no reference to any specific the
ory of knowledge. Russell’s own version of the theory was decidedly empiricist, identifying the ‘atomic facts’ as facts about the immediate contents of experience (or ‘sense-data’ as Russell called them). Using the apparatus of Wittgenstein’s theory, Russell was then able to restate a version of empiricism in the sceptical spirit of Hume, proposing to construe every entity in the world other than sense-data as a ‘logical construction’. Whether or not we do mean, when referring to tables, to refer to logical constructions out of sense-data, it is, Russell thought, all that we ought to mean. As he put it, ‘wherever possible, logical constructions are to be substituted for inferred entities’. Philosophy thus took a step in the direction of logical positivism, according to which all metaphysical, ethical and theological doctrines are meaningless, not because of any defect of logical thought, but because they are unverifiable. The slogan of positivism—that the meaning of a sentence is its method of verification—is taken from the Tractatus, as was much of the apparatus whereby it sought to rid the world of metaphysical entities. But its spirit was that of Hume, and its principal theories were restatements of Hume’s ideas concerning causality, the physical world and morality, in terms of an ‘analytic’ rather than a ‘genetic’ theory of meaning. By the time this programme was under way, in the work of Rudolf Carnap (1891-1970) and others of the so-called ‘Vienna Circle’ (see especially Carnap’s Logical Structure of the World, 1928), Wittgenstein had renounced all allegiance to atomism and its progeny, had ceased publication and begun a hermetic, and often nomadic, existence which ensured that, until his death, what influence he had was confined to those privileged to know him personally, or to catch sight of the manuscripts which he occasionally allowed to pass from his hands. Among these manuscripts the most famous—The Blue and Brown Books—reached Oxford in the 1940s, and there precipitated the school of ‘linguistic analysis’ for which J.L.Austin (19111960) and Gilbert Ryle (1900-1977) were already preparing the way. But that school, consisting as it does of figures too many and too minor to warrant our attention, and being characterised less by any theory than by the refusal to subscribe to one, is not one that I shall discuss. Nor shall I consider the later development of logical positivism in America, where it entered into a fruitful marriage—through Carnap’s pupils Nelson Goodman and Willard van Orman Quine—with the local ‘pragmatism’ of C.S.Peirce, (1839-1914), William James (1842-1910) and C.I.Lewis (1883-1964). Instead I shall conclude this work with an outline of certain arguments expressed in the Philosophical Investigations (1953), The Remarks on the Foundations of Mathematics (1956) and elsewhere. Because they relate directly to the history of the subject as I have so far described it, these arguments will give some indication, however slight, of the extent to which Wittgenstein’s later philosophy has transformed and even brought to an end the tradition of intellectual enquiry which began with Descartes.
The later Wittgenstein
The emphasis of Wittgenstein’s later philosophy is decidedly anthropocentric. While still interested in questions concerning meaning and the limits of significant utterance, the starting-point has become, not the immutable abstractions of an ideal logic, but the fallible efforts of human communication. At the same time, the human element has not entered through the usual channel of epistemology, but in a wholly surprising way. Wittgenstein introduces it through a priori reflections on the nature of the human mind, and on the social behaviour which endows that mind with its characteristic structure. What is ‘given’ is not the ‘sense-data’ of the positivists, but the ‘forms of life’ of Kantian philosophical anthropology. To put it in another way: the subject of any theory of meaning and understanding is the public practice of utterance, and all that makes this practice possible. Thus Wittgenstein begins his later investigations into the nature of language at the point where Frege broke off. He develops the thesis of the ‘publicity’ of sense, which had already led Frege to reject traditional empiricist theories of meaning. The result is not only a new account of the nature of language, but also a revolutionary philosophy of mind. The metaphysical problems that had occupied Kant, Hegel and Schopenhauer are rephrased as difficulties in the interpretation of consciousness. Construed thus they suddenly seem capable of resolution.
The social perspective caused Wittgenstein to move away from Frege’s emphasis on the concept of truth, or rather, to see this emphasis as reflecting a more fundamental demand that human utterance be answerable to a standard of correctness. This standard is not God-given, nor does it lie dormant in the order of nature. It is a human artifact, as much the product as the producer of the linguistic practices which it governs. This does not mean that an individual can decide for himself what is right and wrong in the art of communication. On the contrary, the constraint of publicity binds each and all of us; moreover that constraint is intimately bound up with our conception of ourselves as beings who observe and act upon an independent world. Nevertheless, it is true that there is no constraint involved in common usage other than usage itself. If we come up against truths which seem to us to be necessary, this can only be because we have created the rules that make them so, and what we create we can also forgo. The compulsion that we experience in logical inference, for example, is no compulsion, independently of our disposition so to experience it.
This kind of reflection led Wittgenstein towards a highly sophisticated form of nominalism: a denial that we can look outside linguistic practice for the thing which governs it. The ultimate facts are language, and the forms of life which grow from language and make language possible. Nominalism is not new, nor has it lacked exponents in our day. Nelson Goodman (b. 1906), for example, has advocated, using arguments that often resemble Wittgenstein’s, a kind of nominalism that incorporates a whole philosophy of science together with a theory of knowledge. What is peculiar to Wittgenstein is the transition that he makes at this juncture from the philosophy of language to the philosophy of mind. During the course of this transition, he attempts to overthrow the major premise of almost all Western philosophy since Descartes—the premise of the ‘priority of the first-person case’.
Wittgenstein uses a variety of arguments, designed to show what this premise really means, and in the course of doing so to demonstrate its untenability. Together these arguments provide what can best be described as a ‘picture’ of human consciousness. This picture has many aspects, some metaphysical, some epistemological: it involves the rejection of the Cartesian quest for certainty, the demolition of the view that mental events are private episodes observable to one person alone, the rejection of all attempts to understand the human mind in isolation from the social practices through which it finds expression. It is impossible here to give all the considerations whereby Wittgenstein upholds ‘the priority of the third-person case’. I shall therefore mention one or two central strands of argument and draw some conclusions as to the historical and philosophical significance of the thesis.
The private language argument
The most famous argument advanced for the Wittgensteinian position is that which has come to be known as ‘the private language argument’. This occurs in many versions in the Philosophical Investigations and has been the subject of much commentary. In outline, it seems to me the argument is as follows: there is a peculiar ‘privilege’ or ‘immediacy’ involved in the knowledge of our own present experiences. In some sense it is nonsense to suggest that I have to find out about them, or that
I could, in the normal run of things, be mistaken. (This is the thought which also underlies Kant’s thesis of the ‘Transcendental Unity of Apperception’, see pp. 137-8.) As a result there has arisen what we might call the ‘first-person illusion’. I can be more certain about my mental states than about yours. This can only be because I observe my mental states directly, yours indirectly. When I see you in pain, I see physical behaviour, its causes, a certain complex state of an organism. But this is not the pain that you have, only some contingent accompaniment of it. The pain itself lies hidden behind its expres
sion, directly observable to its sufferer alone.
That is, in brief, the Cartesian theory of mind, presented as an explanation of the first-person case. Both the theory, Wittgenstein argues, and the thing that it is put forward to explain, are illusions. Suppose the theory were true. Then, Wittgenstein argues, we could not refer to our sensations by means of words intelligible in a public language. For words in a public language get their sense publicly, by being attached to publicly accessible conditions that warrant their application. These conditions will determine not only their sense, but also their reference. The assumption that this reference is private (in the sense of being observable, in principle, to one person alone) is, Wittgenstein argues, incompatible with the hypothesis that the sense is public. Hence, if mental events are as the Cartesian describes them to be, no word in our public language could actually refer to them.
In effect, however, Cartesians and their empiricist progeny have always, wittingly or unwittingly, accepted that conclusion, and written as though we each describe our sensations and other present mental episodes in a language which, because its field of reference is inaccessible in principle to others, is intelligible to the speaker alone. Wittgenstein argues against the possibility of such a private language. He attempts to prove that there can be no difference made, by the speaker of that language, between how things seem to him and how things are. He would lose the distinction between being and seeming. But this means losing the idea of objective reference. The language is not aimed at reality at all; it becomes instead an arbitrary game. What seems right is what is right; hence one can no longer speak of right.
The conclusion is this: we cannot refer to Cartesian mental events (private objects) in a public language; nor can we refer to them in a private language. Hence we cannot refer to them. But, someone might say, they may nevertheless exist! To which Wittgenstein replies, in a manner reminiscent of Kant’s attack on the noumenon, that a nothing will do as well as a something about which nothing can be said. Moreover, we can refer to sensations; so whatever they are, sensations are not Cartesian mental events.
A Short History of Modern Philosophy: From Descartes to Wittgenstein, Second Edition Page 33