The Logic of What Might Have Been 论文

摘要

In earlier work I argued (following Hugh Chandler) that the conventionally accepted system S5 of (first-order) modal propositional logic, and even the weaker system S4, embody an invalid pattern of modal reasoning; they are fallacious systems for reasoning about what might have been.1 I argued, in fact, that the characteristic S4 axiom schema, IkDEIILI-or equivalently, the principle that for any necessarily true proposition p, the proposition that p is necessarily true is itself necessarily true-is not only not logically true, some instances are in fact untrue. I argued, that is, that for some necessary truths p-for example, that a certain table does not originate from a certain hunk of wood-the fact that p is necessary cannot itself be correctly deemed necessary. Instead, although any such proposition p is necessary, the claim that p is necessarily necessary is untrue, and indeed some claim of the form DLI. . ..lp is altogether false. While some of my audience have found these arguments against S4 modal logic persuasive, many have found them unconvincing. I have repeatedly encountered two particular objections, which are probably best regarded as two parts of a single objection. This objection, however, betrays a serious misunderstanding of my position, or a failure to appreciate the full force of my (Chandleresque) arguments, or both, and is based on a confusion among concepts central to the foundations of contemporary semantics for