I’d expect the ontological status of numbers to be non-contingent — after all, what in the world could they be contingent on? Abstract objects seem to be the kind of things that exist necessarily, if they exist at all.
I guess I was being dense that month 🙂 because I didn’t see what the objection was supposed to be. But now I do. If numbers are the kinds of things that are not necessary then they must depend on something to exist. But what could numbers depend on? Since there is no plausable candidate we should conclude that if numbers exist they would do so necessarily. Here is what I should have said.
Whether a given possible world has non-physical elements is surely a contingent fact about that possible world. The worlds which do have non-physical elements will most likely have numbers and those that don’t won’t. If this were the case then the existence of numbers is contingent on which possible world best describes the actual world (or if one doesn’t like this way of characterizing the actual world as a possible world we can say it depends on what is actually the case). In some worlds, the existence of numbers may be contingent on whether they were created by some non-physical being. In short there are a couple of different ways in which the existence of numbers could turn out to be contingent.