THE GENERAL THEORY OF REPRESENTATION

The grand metaphysical theory with which the Tractatus begins is nothing but what is required, on Wittgenstein’s view, by the very possibility of language. But what, exactly, does that require? In the light of the work of Frege and Russell, Wittgenstein will have found himself with two fundamental assumptions and a pair of problems. The two fundamental assumptions are the correlation assumption and the objectivity assumption which were identified in the previous chapter:

(Corr), or something very close to it, seems just obvious:1 it is what underlies the claim, which has been accepted almost without question at least since Aristotle, that languages are systems of signs. And (Obj) seems forced on us once we accept the general orientation towards the world which comes with Frege’s rejection of psychologism: it is correlations with items in the world which make languages meaningful, not associations with things in speakers’ minds. And the two problems which Wittgenstein faced are these:

These problems need a little explanation. In the case of (P1), an issue arises for each of the three basic kinds of expression in a Fregean grammar: singular terms, predicates, and sentences. Singular terms are naturally just defined to be terms whose meaningfulness depends on their being correlated with particular, individual objects. The question then is which, if any, expressions of ordinary language (and other symbol systems) should be counted as singular terms. Frege had been generous in his inclusion of ordinary expressions: in particular, he counted ordinary proper names and definite descriptions as singular terms. The problem, then, was to understand how an expression of this kind could have meaning, if there was no real object with which it was correlated. Frege’s use of his technical notion of ‘sense’ provided a solution to the problem whose merits were, at best, unclear. With his theory of descriptions, Russell found a way to be more sparing in what he counted as a singular term. In fact, neither definite descriptions nor ordinary proper names were included. The category of singular terms — what Russell himself would call ‘logically proper names’ — was restricted to those terms which are correlated with items with which we are acquainted. These will be items about whose existence we cannot be mistaken, so an expression will only be counted as a singular term when we

can be sure that there really is an object with which it is correlated. The problem with the case of predicates is clear from

Frege’s difficulty with the concept horse, together with the difficulties which seem to face Russell’s alternative approach. Predicates are naturally understood to be in some sense incomplete, to contain in them a gap where a singular term may be placed. This thought reflects the fact that the predicate in Frege’s grammar contains the copula, or the verb, which has traditionally been seen to be what is responsible for the binding together of the parts of a sentence to form a single unity. The difficulty can be seen if we consider whether, if predicates are meaningful in virtue of being correlated with some entity in the world, the entity in question itself incorporates some counterpart to the sentence-unifying grammar which predicates are traditionally understood to have. If it does — if the worldly counterpart to a predicate is itself an incomplete entity — we have Frege’s problem with the concept horse: it will, at best, be impossible to say what the predicate refers to, by actually using the concept of reference, since every attempt to do that will inevitably treat the worldly counterpart to the predicate as a complete entity.2 If, on the other hand, we adopt Russell’s solution, and treat the worldly counterparts of predicates as being no different at the level of the most fundamental logical category from the worldly counterparts of singular terms — they will all just be objects (Russell’s ‘terms’) — then we seem unable to make sense of the grammar of predicates: how do these linguistic items have the sentence-unifying grammar which they seem to have? It looks, on the face of it, as if any way of correlating predicates with items in the world will lead to serious problems, so long as we continue to think that predicates are the agents of the unification of sentences. As for sentences themselves, the differing views of Frege

and Russell again serve as a warning. Frege and Russell both at some point took the meaningfulness of sentences to require correlations with entities in the world.3 In Frege’s

case, the entities were odd in themselves — the True and the False — and provided no distinction in meaning among all the true sentences, on the one hand, or all the false sentences, on the other. In his early theory, Russell took sentences to be correlated with ‘propositions’ — sentence-like worldly counterparts of sentences. But this faced the difficulty that it was hard to make sense of there really being such sentence-like counterparts of false sentences.4 In response to this, Russell moved to his ‘multiple-relation’ theory of judgement, thereby abandoning the thought that sentences need to be correlated with entities in the world — and he then faced difficulties making sense of the unity of sentences. In addition to the versions of problem (P1) which arise in

the case of singular terms, predicates, and sentences, there is another class of expressions which is crucial to Frege’s system, but about which neither Frege nor Russell had anything very significant to say. What are we to make of the logical constants — the formal counterparts of such expressions as ‘if’, ‘not’, ‘and’, and ‘or’ — or the quantifiers (which correspond to ‘all’ and ‘some’)? In the Theory of Knowledge manuscript, Russell at least acknowledged that some explanation needed to be given of the meaning of these expressions, and quickly (if rather vaguely) assumed that there must be ‘logical objects’ with which they are correlated. But this is problematic, for reasons which will be considered in some detail in Chapter 5. So much for the various forms of problem (P1). Problem

(P2) — over the explanation of the unity of the sentence — is not wholly unconnected with them. If languages are meaningful in virtue of a correlation between linguistic items and something extra-linguistic, it is natural to think that the distinctive unity and completeness of sentences must mirror some extra-linguistic unity (even if the extralinguistic unity is itself no more than a projection of a linguistic unity).5 But where is that extra-linguistic unity to be found? It seems that it cannot be something created by an act of judgement — as Locke, and the Russell of the

‘multiple-relation’ theory held — since that looks incompatible with the generally world-directed conception of language enshrined in (Obj). And it is not immediately obvious how it can be anything in the world, since it is hard to see how there could be any appropriate extra-linguistic unities in the case of false sentences. In fact, it seems that this problem lies behind the form of problem (P1) which arises in the case of predicates. Finding a counterpart in the world to the sentenceunifying grammar which is traditionally assigned to predicates belongs with the early Russell’s solution to the problem of explaining the unity of the sentence — and therefore seems to require the postulation of objective sentential counterparts even to false sentences. On the other hand, supposing that the worldly correlates of predicates have nothing in them which corresponds to the distinctive grammar of predicates seems — on the face of it, at least — to force us to adopt the Lockean, act-of-judgement account of the unity of sentences. We can take it that Wittgenstein adopted (Corr) and (Obj)

as the only thing to think about language, and that, as a result, he faced problems (P1) and (P2) in these uncomfortable forms. The theory of language of the Tractatus can then be seen as his solution to them. That theory is the application to language of a general theory of representation. The rest of this chapter will be concerned with the general theory; we will deal with the application of the general theory to the case of language in the next chapter.