Wittgenstein, Ludwig Josef Johann (1889–1951)

5. Simples

The ideas outlined in the last two sections are already present in the sets of notes which Wittgenstein wrote in late-1913 and 1914. But the Tractatus in its complete form incorporated several further important ideas. One of these, perhaps adopted from Frege, is the view that sense must be determinate, that is, that every meaningful sentence must be either true or false in every possible state of affairs. But Wittgenstein differs from Frege in thinking that ordinary language, although misleading in surface form, is in order, and so already fulfils this condition of determinacy.

Determinacy entails that there must be ‘objects’, that is, utterly simple, eternal and unalterable elements, out of which all facts are composed. Moreover the links between our language system and reality must be set in place at this basic level. Suppose that language–world links were set up so as to connect a basic linguistic component with some element of reality which was not basic. The existence of this element would be contingent and would depend upon some simpler elements being suitably combined in a fact. A sentence containing this imagined basic component is clearly not true in a world where the simpler elements are not suitably combined. But it is equally unhappy to say that it is false, because the component itself does not specify what the simpler elements are or that they must be combined, and so it is no part of its meaning that their failure to be combined is relevant to its falsehood. To insist on the undefinability of this imagined basic element of language is to insist that it has meaning only through its connection with the item it represents. So in a world lacking that item it has no meaning, and sentences containing it are neither true nor false. But this, given the assumption of determinacy of sense, is a reductio ad absurdum of the idea that meaning can be conferred in this imagined way.

We may have an apparently basic sentence component which is linked to a contingently existing item (for example ‘Socrates’ as a name of Socrates). But this is only possible because a definition of that component can be given in our language system. The link between Socrates and his name is thus not a basic point of attachment between language and the world (contrary to the impression given in our earlier rough and ready example). It is a consequence of these ideas that there must be a complete analysis of every sentence of our language into a truth-functional combination of elementary propositions, the components of which are simple signs representing objects.

But what are these simple objects? Wittgenstein, like Russell but unlike Frege, does not allow for any contrast between sense and reference within the meaning possessed by names of simples. This puts one demand on simples: they cannot be items with distinguishable aspects, that is, items which can be conceived of in several logically distinct ways. If they were, then there would also be the possibility of one name for a simple as conceived one way and another non-synonymous name for it as conceived another way – contrary to the denial of the sense–reference distinction. So a simple is the kind of thing which, if apprehended in such a way that it can be named, is apprehended exactly as it is in its entirety.

In so far as Wittgenstein drops any hints, it is that simples are phenomenally presented items, such as points in the sensory field and the properties they have, for example, shades of experienced colour. But he cannot give this answer officially because to do so would clash with another of the themes brought to prominence in the later development of the Tractatus. This is the claim that all necessity is logical necessity, and hence would be revealed as tautological in a complete analysis (see §7 below). A corollary of this is that all atomic facts are independent of each other and no elementary sentence can entail or be the contrary of any other. Such things as colours cannot then be ‘objects’ because attribution of different colours to one thing, as in ‘a is red’ and ‘a is green’, produces sentences which are contraries.

The topics so far discussed are treated primarily in the remarks following the main sentences numbered 2, 3 and 4. The remarks following 5 and 6 deal mainly with implications of this atomist conception for certain issues in logic (generality and identity for example) and for the nature of science, mathematics and statements of probability. On the last mentioned subject, Wittgenstein’s brief remarks are one important source for the approach later developed by Rudolf Carnap (see Carnap, R. §5; Logical atomism §1).