Abstract

According to dispositionalism about modality, a proposition <p> is possible just in case something has, or some things have, a power or disposition for its truth; and <p> is necessary just in case nothing has a power for its falsity. But are there enough powers to go around? In Yates (2015) I argued that in the case of mathematical truths such as <2+2=4>, nothing has the power to bring about their falsity or their truth, which means they come out both necessary and not possible. Combining this with axiom (T), it is easy to derive a contradiction. I suggested that dispositionalists ought to retreat a little and say that <p> is possible just in case either p, or there is a power to bring it about that p, grounding the possibility of mathematical propositions in their truth rather than in powers. Vetter’s (2015) has the resources to provide a response to my argument, and in her (2018) she explicitly addresses it by arguing for a plenitude of powers, based on the idea that dispositions come in degrees, with necessary properties a limiting case of dispositionality. On this view there is a power for <2+2=4>, without there being a power to bring about its truth. In this paper I argue that Vetter’s case for plenitude does not work. However, I suggest, if we are prepared to accept metaphysical causation, a case can be made that there is indeed a power for <2+2=4>.