SENTENCES AS MODELS

The Tractatus’s theory of language is at base the application to language of the general theory of representation which was examined in Chapter 3 — the theory that representations represent in the same way as the Paris courtroom model. Accordingly, the basic claim of the theory of language of the Tractatus is what is stated at 4.01:

But ‘propositions’ are first mentioned at 3.1: what has been going on in the sections from 3.1 to 4.0031? Very roughly, these intervening sections do two things: they justify the very idea that propositions might be models of reality; and they develop that idea in such a way as to justify the metaphysics of the 1s and early 2s (the metaphysics which was outlined in Chapter 1). The sections which follow 4.03 elaborate some of the consequences for philosophy of the claim

that propositions are models, and introduce the theory of logic. (I will be considering the theory of logic in Chapter 5, and the account of philosophy in Chapter 7.) Language is introduced with this remark:

The point is a little clearer in the Pears and McGuinness version:

This remark raises two questions immediately. First, what is a ‘proposition’? The word is a translation of the German ‘Satz’. It is not entirely clear how we should understand it, however. It is most naturally understood as being used to refer to a sentence — or, rather, a particular kind of sentence: a declarative sentence, one which is grammatically suited to say something true or false. But even to say that a Satz is a declarative sentence does not settle matters finally: after all, what is a sentence? Wittgenstein seems mostly to use the word ‘Satz’ to refer to a sentence with a meaning (as in 3.12), but there are places where he cannot mean that (6.54, for example). This is a point which I will return to (in section 4C below): for the moment, it is enough just to be aware of the issue. The other question raised immediately by 3.1 is exactly

what claim Wittgenstein means to be making here. He might be taken to be making either or both of the following claims:

I suggest that Wittgenstein is actually concerned to assert both (i) and (ii). It is (ii) which is crucial to the sequence of thought of the following remarks:

It is only if 3.1 includes the assertion of (ii) that we have any reason to think that every thought can be expressed in a notation which reveals its true form (which is what 3.2 claims). On the other hand, it is only if 3.1 includes the assertion of (i), that the Tractatus’s general theory of representation can be applied to language in general, and hence, in particular, to attempts to say something philosophical (whose significance will be clear in Chapter 7 below). To begin with, I will present just an outline ofWittgenstein’s

application to sentences of his general theory of representation. But there is one thing to be clear about from the start: the application is meant to be completely literal. Wittgenstein is not claiming that sentences are somehow like pictures or models; nor is his claim that sentences are pictures metaphorical. His claim is that the analysis of models which he provides in the 2.1s and 2.2s applies completely straightforwardly and literally to sentences — or, at least, to certain basic sentences. Sentences just are models, strictly and literally. Recall the core commitments of the general theory of

representation:

If sentences are to be pictures or models, it follows from (M1) and (M2) that they must have elements; accordingly, Wittgenstein says:

And, given this, (M3) requires this:1

After all, different numbers of components cannot have precisely the same possibilities of combination. But a sentence is not just a mixture of the words which are

its pictorial elements. In a formulation which echoes 2.14, Wittgenstein says:

That is, just as pictures or models in general are facts (2.141), so are sentences:

As Wittgenstein recognizes, we do not readily think of sentences as facts: instead, we are inclined to think of them as complex objects. I take it that this is one of the key ‘misunderstanding[s] of the logic of our language’ which lie at the heart of the problems of philosophy, according to the Preface (TLP, p. 27).3 But Wittgenstein thinks that the true

nature of sentences becomes clearer if we imagine them having something other than a written form:

Here we see a sentence taking on the explicit appearance of a model, like the Paris courtroom model. And later on he uses exactly the language he used when he first (in NB 7) referred to the courtroom model:

Of course, if we insist that sentences are facts, and not complex objects, that makes a difference to how we can talk about them. That is part of the point of the following remark:

(Though this remark is important in other ways, to which I will return in section 4F.)

In fact, if sentences are facts, and not complex objects, there will be some difficulty in talking about them at all:

This last point is of crucial importance in the general motivation for the theory that sentences are pictures or models. Wittgenstein here makes a radical distinction between the

relation which holds between a name and the object for which it stands, on the one hand, and the relation between a sentence and the fact which obtains if the sentence is true, on the other. A sentence is not any kind of name: to suppose that it is would be to treat sentences — which, like all pictures or models, are facts — as complex objects. That difference is reflected in many ways in language, but among the most important is this. It is a fundamental fact about language that every language contains an indefinite number of sentences which any competent speaker of that language can understand without having previously encountered them. Wittgenstein seems to have taken this fundamental fact to prove that sentences are pictures or models:

Wittgenstein certainly has a case here, though I think he is overstating it. What is correct is that the theory that sentences are pictures or models can explain how it is possible for someone to understand a sentence which she has not previously encountered, without having had it explained to her. The reason is this. As we saw in the last chapter, a model’s being the model it is cannot, according toWittgenstein, depend on its being correct. If sentences are pictures or models in the same way, then the meaningfulness of a sentence — or, at least, of a sentence which is a representation — must be independent of whether it is true. Wittgenstein holds the following view of what it is to understand a sentence:

And he concludes, correctly:

We can have this understanding because the following is true:

This falls directly out of the claim that sentences are pictures or models, on the general conception of representation which we considered in the previous chapter. For on that conception, sentences are not meaningful because of any correlation between the sentences themselves and any facts in the world: if we are not to follow the early Russell down the path to objective falsehoods (false facts), that would make the meaningfulness of a sentence — its being the representation it is — depend on its being true (see Chapter 2, section 2D). Instead, sentences, like all pictures or models, are meaningful in virtue of their elements being correlated with items in the world. Consequently, all one needs in order to understand the meaningfulness of a sentence is to know which items in reality its elements are correlated with. The way in which I think Wittgenstein overstates his case

in 4.02 amounts to this. What he offers is a plausible — one might think compelling — case for thinking that the view that sentences are pictures or models provides a good (perhaps even the best) explanation of the fact that we can understand sentences we have not encountered. But even that falls short of proving that sentences are models, given just the fact that we can understand sentences we have not come across before, which is what 4.02 seems to claim. In general, inferences to the best explanation make it rational to believe something: they do not prove that thing to be true. The important final point of the application to sentences of

the general account of pictures or models is this. Sentences, like pictures or models generally, have the following limitation: whatever else they may represent or depict, they cannot represent or depict their own form. In the general account of representation, Wittgenstein explains this point in terms of the impossibility of a picture standing ‘outside’

(‘ausserhalb’) its own form — outside the possibility of its components being arranged in the way they are (2.173, 2.174). That spatial metaphor is re-used in the theory of sentences in connection with the mathematical multiplicity which model and reality must share:

And it returns in 4.12, in a clear echo of 2.172-2.174:

We saw earlier that a certain notion of ‘showing forth’ or ‘displaying’ is used in connection with form in the general case of representations:

A similar notion is now used in connection with the sense of a sentence:

And it is used quite explicitly in remarks about form which are precisely parallel to those made in the general theory of representation:

An even more dramatic conclusion, however, is drawn here than was drawn explicitly for the general case of representations:

This is more dramatic, because of the implicit claim it makes about the form of each sentence. What the general theory of representation tells us is that no representation can represent its own form; but that seems to leave it open for the form of one representation to be represented by another representation. Accordingly, we might think that, although no sentence could represent its own form — state its own sense — it might be possible for the form of one sentence to be represented by another. But this possibility is what is explicitly ruled out by 4.1212: no sentence can state the form of any sentence. This claim is only legitimate if every sentence has the same form. We will consider what that means in a little more depth in section 4E below, and again when we consider the theory of logic in Chapter 5. We therefore see here the general theory of representation

applied explicitly, literally, and in careful detail to the case of sentences. Sentences, like pictures or models generally, represent in virtue of having elements which can be correlated with items in reality, and in virtue of those elements having the same ranges of possible combination as the corresponding elements of reality — that is to say, the same form as reality. But this brings with it a necessary limitation, with sentences as with pictures or models in general: no sentence can represent or depict its own form. So much for the outline of Wittgenstein’s account of sentences as models of reality. Now we need to look at it in a bit more detail, in order to understand how it answers the problems about language which Wittgenstein inherited from Frege and Russell, and how it generates the metaphysics of the 1s and 2.1s.