 (3) follows from (1) and (2), with the conclusion (5) deducible from (1), (2) and (4). Moreover, both (2) and (4) are, if not analytically true, simple mathematical truths. (1), on the other hand, is an empirical fact, van Inwagen notes. The argument is clearly valid and the three premises that support the conclusion are all highly plausible. Should we not just accept that numbers exist? Many philosophers think so but some philosophers demur. Amongst the latter are those who think that the meaning of ‘there exists’ varies from context to context [Hilary Putnam and Eli Hirsch are two prominent advocates whose ideas we review]. There are others who think that the existential quantifier carries no ontological import [Azzouni, J. 1997]. If one accepts Quine’s two assumptions about the existential quantifier, however, and regards the argument as sound, hasn’t one thereby accepted realism about numbers? 