John F. Post

Shades of possibility

Martin is right: the crucial question is whether the RA’s of predicates vary with worlds. 1 Still, we cannot answer the question until we know what kinds of possible worlds there are. The RA’s might be invariant in one class of worlds but not in another. In my view, that is exactly what happens: the RA’s are invariant in sortally possible worlds, but not in all logically possible worlds. This distinction between shades of possibility will be clarmed below. It stands in the way of a category solution to the Liar’s Revenge. Martin is therefore compelled to deny the distinction. What he says is that the category solution requires the abandonment of the technical notion of a logically possible world. This conclusion reflects curious priorities, and I would reverse it. What is required is the abandonment of the category solution, at least for paradoxes like the Liar’s Revenge. That solution was already in trouble on other grounds: the exclusion of exclusion negation, for one; and what Martin himself calls “grave shortcomings” both in the claim “that ‘true’ and ‘false’ apply truly and falsely only to semantically correct sentences,” and in the “arranged marriage to the supervaluation treatment of truthvalue gaps.” By contrast, the intended notion of logical possibility is in good shape, as is the correlative distinction between those worlds which are logically possible and those which are possible in some further sense as well. Indeed, we shall see that in certain contexts this distinction follows from a still more fundamental one, between logical and non-logical truths, and beyond that, between logical and non-logical words. Thus if we are forced by the Liar’s Revenge, or by anything else, to choose between the category solution and such distinctions, surely the distinctions take priority. What kinds of possible worlds are there? Rather, what kinds of worlds W are alternatives to the actual world G? That W is an alternative to G implies, among other things, that certain truths in G remain true in W, while others do not (unless W=G’). Which truths must remain true for W to be an alternative to G?