THE NATURAL NUMBERS

Mathematical truths, such as the proposition that 7 + 5 = 12, involve nothing but mathematical entities. These entities, however, are also to be found, as some sort of constituent, in contingent and empirical truths. Thus, it may be observably true that there are just seven black swans on the lake. Let us begin by considering what would be the truthmaker for a truth such as this one.

Given a Factualist metaphysics as starting point, we will be looking for a state of affairs to be the truthmaker. It is clear that it will be, in part at least, a molecular state of affairs. This molecular state of affairs will be a conjunction of seven states of affairs, each involving a particular, where the particulars are wholly distinct from each other (Siamese swans we will bar) and each particular has properties sufficient to make it a swan. The blackswan-making properties, of course, may differ from particular to particular. Presumably there is no universal of black-swanhood. To get the force of ‘just’ we shall need in addition the higher-order state of affairs that this is the totality of black-swan-presently-on-this-lake states of affairs. Here we shall not concern ourselves further with this totality-fact.

Each of the seven states of affairs is truthmaker for the truth that there is at least one black swan on the lake.