Friday, November 16, 2007

6 The general form of truth-functions is: .

This is the general form of propositions.

I had had “of the truth-function” and “of the proposition,” but Wittgenstein (Letters to Ogden p. 34) says the “the” should be left out, and the words made plural if necessary to accommodate this (I think it is necessary to do so).

McManus (p. 140) renders the idea here as that “Every proposition is an elementary proposition or a (possibly very complex) complex proposition.” He sees it as problematic because no argument is really given in its favor and because it seems to bring metaphysical commitments with it. If there is a general form of propositions then there is, he suggests on p. 141, a general form of the world (see 2.04). Wittgenstein’s claim is in effect that “all logical incompatibility is a matter of contradiction,” (p. 153) but this is only a possibility, not something that Wittgenstein had proved must be the case. For instance, if a spot is red it cannot also be blue. But is “This spot is red” a contradiction of “This spot is blue”? Or could it be a kind of empirical knowledge that a spot cannot be both red and blue? Wittgenstein assumes that the meanings of the logical constants that connect elementary propositions into complex propositions are topic-neutral, the same in all contexts. He later abandoned this assumption. (See, e.g., PG 269 and RPP I 38.) At the time it probably seemed bland and inoffensive. He later saw that it brought unwanted problems and commitments.

White (p. 35) refers to 6 as “the central claim to which the book builds up.” Yet Wittgenstein has made a mistake, according to White. In note 43 (p. 152) he says that Russell silently corrects the text of 6 on p. 14 of his introduction to the Tractatus, giving “a satisfactory informal exposition of what Wittgenstein should have said.” As written “the formula at proposition 6 is radically incoherent.” (p. 103) Wittgenstein’s notation gives us a rule for moving from a propositional variable to a proposition, but what it is supposed to do is give us a rule for moving from one proposition to the next proposition in the series. 6.001 fixes the problem, or as good as does so (see pp. 103-4), according to White.

No comments: