Modal Logic and Contingentism: A Comment on Timothy Williamson’sModal Logic as Metaphysics

Abstract

Logic, as standardly conceived, is the science of consequence: a logic tells us which claims follow from which. Quantified modal logic (QML) is supposed to tell us which claims follow from which in a language which provides the means to express both metaphysical modality and quantification. One might think on this basis that we can determine which is the correct QML independently of substantive questions of science and metaphysics: modal logic, on this view, cannot tell us whether it is possible that there be no numbers; nor can it tell us whether, necessarily, everything is at bottom physical. At most, it might be held, logic can tell us what follows from these claims. We might dub this view neutralism about QML, since it holds that the correct QML must be neutral on substantive disputes in modal metaphysics. It is difficult to find an extended, full-throated defense of neutralism in the literature. But Timothy Williamson’s Modal Logic as Metaphysics provides an extended, full-throated criticism. Williamson aims to show how, in particular, the model theory of QML bears on a substantive, if highly abstract, dispute in modal metaphysics. Consider one of the most obvious things about the Sun: it is such that there is something identical to it. More briefly, it is something. Being something, of course, does not make it unique. It shares this feature with everything. Is 1Of course, there are applications of the study of the formally specified languages of QML in which ‘ ’ is interpreted as something other than metaphysical modality. Those applications of the formalism are irrelevant to our discussion. 2Perhaps [Kaplan, 1989, pp. 42-43] offers a defense.