Counting Possibilia

Timothy Williamson supports the thesis that every possible entity necessarily exists and so he needs to explain how a possible son of Wittgenstein’s, for example, exists in our world: he exists as a merely possible object (MPO), a pure locus of potential. Williamson presents a short argument for the existence of MPOs: how many knives can be made by fitting together two blades and two handles? Four: two, at the most, are concrete objects, the others being merely possible knives and merely possible objects. This paper defends the idea that one can avoid reference and ontological commitment to MPOs. My proposal is that MPOs can be dispensed with by using the notion of ‘rule of an art’. I first present a solution according to which we count instructions describing physical combinations between components. This account, however, is not completely satisfactory and I claim that one can find a better one: in answering Williamson’s question, we count classes of possible worlds in which the same instance of a general rule is applied.