Wittgenstein, Ludwig Josef Johann (1889–1951)

3. The picture theory of meaning

The Tractatus consists of nearly eighty printed pages of numbered remarks. The numbers do not run consecutively but are designed to indicate the relative importance and role of the remarks. There are seven major sentences and each of them (except 7) has subordinate and clarificatory remarks following it, labelled ‘2.2’, ‘5.4’ and so on, down as far as such numbers as ‘4.0312’.

The topics that preoccupied Wittgenstein when he arrived in Cambridge included the nature of logical truth and Russell’s Theory of Types. On both of these matters Russellheld that we need an account of very general features of the world and of the kinds of things in it. But Wittgenstein soon came to think that the route to insight was through the contemplation of the nature and presuppositions of individual meaningful sentences such as ‘Socrates is wise’ and that this contemplation showed Russell’s approach to be misguided.

The central fact about such individual sentences is that each says one thing – that Socrates is wise, for example – but is essentially such that it may be either true or false. A false sentence is both out of touch with the world, inasmuch as it is false, but also in touch with the world, inasmuch as it succeeds in specifying a way that things might be. Wittgenstein holds that all this is possible only because the sentence is complex and has components which represent elements of reality, which exist whether the sentence is true or false and are (potentially) constituents of states of affairs. So, in rough illustration, ‘Socrates’ represents Socrates and ‘is wise’ represents wisdom. The truth or falsity of the sentence then depends on whether these elements are or are not assembled into a fact.

Not all sequences of sentence components are acceptable. A mere list of names (for example, ‘Socrates Plato’) does not hang together as a sentence. And although it looks as if we may apply a predicate to itself (as in ‘‘‘is in English’’ is in English’ or ‘‘‘is wise’’ is wise’) it seems important to disallow such sequences as truth-evaluable sentences, on pain of falling into Russell’s paradox. Russell’s account of these matters is that elements of reality come divided into different types – individuals, properties and so on – and that a sentence is to be allowed as meaningful, and so truth-evaluable, only if the elements picked out by the components are of suitably related types.

Wittgenstein maintains, against this, that we do not need rules to bar sentences which would lead to paradox, because when we properly understand the nature of our language we see that we cannot formulate the supposed sentences in the first place. We think we can only because we have misidentified that component in ‘Socrates is wise’ whose presence in the sentence attributes wisdom to Socrates. This component is not the phrase ‘is wise’ but the property which the word ‘Socrates’ has when the words ‘is wise’ are written to the right of it. To see why this is plausible, consider the fact that there could be a language in which properties are attributed to people by writing their names in different colours. If, for example, we could claim that Socrates is wise only by writing ‘Socrates’ in red letters then we could never formulate any analogue to ‘‘‘is wise’’ is wise’ because we could not take the redness of ‘Socrates’ and make it red. And although we have given a linguistic role to ‘Plato’ (as representing Plato) we have not given any role to the property of a name which it acquires when we write ‘Plato’ to the right of it. That is why a mere list of names does not hang together to make a statement.

Wittgenstein generalizes this idea to claim that the formal properties of any element of the world, that is, the properties which fix its potential for combining into facts with other elements, must be mirrored in the formal properties of the linguistic component which represents it. So the kind of item we call a sentence, and which we often wrongly think to be a complex object, is really a fact. In a sentence certain linguistic components are put together experimentally in a structure which mirrors the formal structure of some possible state of affairs (see Theory of types §1).