Kalhat's insightful paper (2008) is devoted to accounts of logical necessity proffered by Wittgenstein and defended by Baker and Hacker (1985), Schwyzer (2001) and Glock (1996c; 2003c). It challenges these accounts on two grounds. First, the attempt to explain logical necessity by appeal to linguistic rules or conventions fails; second, even if some such explanation were adequate, it would fail to be genuinely reductive of logical necessity, since normative notions presuppose modal notions.

I shall not take issue with Kalhat's interpretation of Wittgenstein, which I regard as by and large correct. I also concede that he has pointed out serious lacunae and difficulties in the Wittgensteinian position. Nevertheless, I shall argue, he has not succeeded in demonstrating that linguistic or conventionalist accounts are hopeless. Furthermore, if a viable linguistic account of logical necessity can be provided, modal notions may not have been reduced to normative ones, but they will have been explained in terms that render them less mysterious. That is to say, the explanation will not rely on unexplained metaphysical necessities.

The Wittgensteinian Position

Our topic is propositions which are logically rather than physically necessary. For Wittgenstein, these include the propositions of logic (e.g., those of the form ‘∼(p & ∼p)’) and mathematics (e.g., ‘7 + 5 = 12’), as well as analytic propositions, broadly conceived. The latter include definitional truths like

(1) All bachelors are unmarried.

Kalhat succinctly summarises Wittgenstein's position. Like the logical positivists, Wittgenstein seeks to preserve a connection between (1) and the meaning of the word ‘bachelor’. Verifying (1) requires attendance not to the marital status of men, but to the meaning of ‘bachelor’ and ‘unmarried’. By the same token, rejection of (1) betokens linguistic misunderstanding rather than factual ignorance. Unlike the logical positivists, Wittgenstein does not maintain that (1) follows from the meaning of its constituents; instead he maintains that (1) is partly constitutive of that meaning. According to Wittgenstein, (1) is a ‘grammatical proposition’. That is to say, it standardly expresses a rule for the correct use of at least one of those constituents and thereby determines their meaning instead of following from it.