A Short History of Modern Philosophy: From Descartes to Wittgenstein, Second Edition (42 page)

The first such theory was logical atomism, adumbrated by Russell, and more or less completely expressed in Wittgenstein’s
Tractatus Logico-Philosophicus
(1921). This work, more succinct even than Leibniz’s
Monadology,
claimed to give the final answers to the questions of philosophy. It was inspired in part by Russell’s famous theory of descriptions, published in 1905, in an article that F.P.Ramsey (19031930) described as ‘a paradigm of philosophy’. This theory will therefore serve as a fitting introduction to Wittgenstein’s work.

The theory of descriptions

It is strange, but nevertheless true, that one of the most important publications in modern philosophy should have had, as its ostensible purpose, the explanation of the meaning of the word ‘the’. What is the difference, Russell asks, between the sentence ‘a golden mountain exists’ and the sentence ‘the golden mountain exists’? The first expression is explained by the new logic as follows: the predicate ‘golden mountain’ is instantiated, or, more formally, there exists an
x
such that
x
is a golden mountain. This proposition is clearly false. But what about the second proposition? Here the word ‘the’ seems to change the predicate ‘golden mountain’ into what Russell would call a denoting phrase (and what Frege had called a name). This is a strange effect of grammar. It has a yet stranger logical consequence, namely, that the sentence seems to refer to something—the golden mountain. But how is that possible, if no golden mountain exists? Here, Russell argued, we have a paradigm case of a grammatical form which conceals the logical form of a sentence. Taking his cue from his own and Frege’s implicit definition of number, he offers an implicit definition of the word ‘the’. We cannot say explicitly what the term ‘the’ denotes, but we can show how to eliminate it from all the sentences in which it occurs.

Consider the sentence, ‘the King of France is bald’. For this to be true, there must be a king of France, and he must be bald. Moreover, to capture the distinctive sense of the word ‘the’ we have to add that there is only
one
king of France. The conditions which make the sentence true give us its meaning; hence we can say that ‘the King of France is bald’ is equivalent to the conjunction of three propositions: ‘there exists a king of France; everything which is a king of France is bald; and there is only one king of France.’ (More formally—there exists an
x
such that: x is a king of France and x is bald, and, for all
y,
if
y
is a king of France,
y
is identical to
x.)
It follows from this analysis that, if there is no king of France, then the original sentence is false. The phrase ‘the King of France’, which seemed to be a denoting phrase or name, is in fact no such thing, but rather a predicate attached to a concealed existential claim. The King of France is, as Russell put it, a logical fiction. (There is a historical antecedent for this kind of philosophical theory in Bentham’s theory of fictions.)

Philosophically, Russell directed his arguments against certain phenomenologists (notably Alexius Meinong (1853-1920)) who had wanted to conclude that, if we can think of something, such as the golden mountain, then that thing must, in some sense, exist. (If you don’t like the word ‘exist’, then another—‘subsist’—is offered to allay your logical susceptibilities.) Russell did not fully grasp that Meinong and his associates were not so much engaged in exploring the logic of denotation, as in examining the ‘intentional object’ of thought. Be that as it may, however, Russell’s argument lent itself to instant generalisation, and in this generalised form provided a basis for the philosophy of the
Tractatus.

Logical atomism and the
Tractatus

According to the
Tractatus,
everything that can be thought can also be said. The limits of language are, therefore, the limits of thought, so that a complete philosophy of the ‘sayable’ will be a complete theory of what Kant had called ‘the understanding’. All metaphysical problems arise because of the attempt to say what cannot be said. A proper analysis of the structure of the terms used in that attempt will show this to be so, and thus either solve or dissolve the problems.

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 theory 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.