ABSTRACT
David Hume’s first Enquiry ends with this famous paragraph:
In the second paragraph of a paper which was strongly influenced by Wittgenstein’s Tractatus, Rudolf Carnap writes:
And lest anyone should be in any doubt, Carnap insists:
The ‘principles’ which lead to Hume’s result underlie Carnap’s conclusion too. Hume insists that all knowledge either falls within the province of ‘demonstration’ or is concerned with ‘matter of fact’: this is the principle known as Hume’s Fork. Carnap holds that all statements are either (i) ‘true solely by virtue of their form’, (ii) negations of these (which are therefore contradictory), or (iii) empirical statements (true or false) (Carnap 1956: 76). Since the first two of Carnap’s categories of statement fall within what Hume counts as the province of ‘demonstration’, it is clear enough that Carnap is committed to something very like Hume’s Fork. It is because statements of metaphysics fall into none of the relevant classes of possible statements that Hume and Carnap dismiss them as ‘sophistry and illusion’, or simply meaningless. What Hume and Carnap are here ruling out is the possi-
bility of the class of statements which Kant called synthetic a priori, which he took to be central to philosophy, as well as to mathematics. Hume’s province of ‘demonstration’ broadly coincides with the class of truths which Kant counted ‘analytic’ (together with the negations of analytic truths) — that is, the non-synthetic; and he insists that truths concerning ‘matter of fact and existence’ can only be known by experience — that is, a posteriori. We have already seen that Wittgenstein also rejected the possibility of synthetic a priori truths. It should therefore come as no surprise to find him rejecting metaphysics. Nor should it surprise us that this rejection is broadened (like Carnap’s) to include ethics (Hume simply regarded morality as not being a proper object of reason at all). But the character of Wittgenstein’s rejection of metaphysics seems quite different from Carnap’s or Hume’s: where they seem keen to push past metaphysics
and get on with science, Wittgenstein’s attitude seems more poetic and contemplative. Part of the difference of approach here is a difference in
these philosophers’ attitude to their own work. If we reject metaphysics on the ground that all truths are either analytic or a posteriori, we seem bound to be in some difficulty over that rejection itself. Suppose we ‘take in our hand’ Hume’s first Enquiry, and ask whether it contains any ‘abstract reasoning concerning quantity or number’, or any ‘experimental reasoning concerning matter of fact and existence’. We seem bound to answer No, in which case, according to Hume’s own principles, his work ‘can contain nothing but sophistry and illusion’. Similarly, it is hard to see how we can claim that Carnap’s statement that all statements are either (i) analytic, (ii) negations of analytic truths, or (iii) empirical, is itself either analytic, a negation of an analytic truth, or empirical. So it seems that Carnap’s own statement must be counted as meaningless, in the strictest sense of the word, by its own lights. The rejection of metaphysics on any such grounds as these seems bound to be paradoxical. Neither Hume nor Carnap seems to be aware of any dif-
ficulty here: they seem concerned simply to dismiss certain types of work from which they think they can clearly distinguish their own. Wittgenstein, however, seems to see the problem quite clearly:
The task of this chapter is to explain Wittgenstein’s reasoning in more detail, and to try to make sense of his response to the paradox which seems to be involved in rejecting metaphysics. I will approach these two aspects of the task in that order, though it should be made clear that this already involves taking a stand on the interpretation of Wittgenstein’s approach to the paradox. There are some interpreters of the
Tractatus who endorse what Wittgenstein says in 6.54, and conclude that (at least the bulk of) the sentences of the Tractatus are indeed nonsense. These interpreters must have some difficulty in making sense of the reasoning which leads to the conclusion that any attempt to say something metaphysical will end in nonsense, and therefore end up supposing that the conclusion is reached in some other way. This interpretation strikes me as clearly wrong — though I will postpone the argument for that claim until we address the paradox explicitly. I think the Tractatus contains arguments for the conclusion that any attempt to say something metaphysical must result in nonsense. Our first task is to try to understand them.
