I don't know to which of several questions "about the natural numbers and odds and evens" you refer. My guess is that it's this: "Can you give ONE real life example where it physically matters in the slightest whether some people think that the set {0,1,2,3,4,5,6,7,8,...} is twice as large as either the set {0,2,4,6,8,...} or the set {0,1,3,5,7,...} as opposed to the accepted er... wisdom that all three sets are equal in size?"
But I shouldn't have to guess what you're referring to. (This has happened before. Please try to help an old man with failing memory (and failing psychic powers).
The full (if not Erpeline-satisfactory) answer will, I hope, be in the treatise on mathematical entities. But I did give you a tangential sort of answer to the above question in my anecdote about two people curious about different aspects of reality. The physicist's answers are murky and uncertain at best; the mathematician's answers are crystal clear and decisive. But that's all predicated on human beings' being curious animals, who want to know the truth. Surely the mathematician can be satisfied on this count in a sense in which the physicist can't.
By the bye, mathematical truths are not truths about mere words, based on arbitrary definitions, but truths about the observable world. But I'll have to spell that out in THE ESSAY.