>The mathematician hunkered in a foxhole, earning his pay, finds it difficult to set aside the prejudice that he is grappling with something real—to keep up morale, if nothing else.<p>This is true of myself as much as I think Platonism leads to strange ideas about things in other regards. There is also an idea known as logicism that I think might explain a bit better what universal mathematical objects are.<p>I am not a mathematical philosopher myself, maybe some day, but when Franklin says numbers can be relations to things, I think that the fact that there are uncountable sets which means there is not a way to map the natural numbers in any "relation" to that set seems like it undermines the Aristotelian idea of linking mathematical objects with physical things.