I recently started with Mathematical Form & Function by Saunders Mac Lane. I came across following passage:
Finitists hold that infinite sets (and geometrical infinities) are just convenient fictions, while only the finite is “real”. This we must later consider. For that matter, is a finite set real? On the fourth day of Christmas did my true love send me four Colley birds or a set of four Colley birds? Where is the set?
I can't understand what author seems to prove with this example. Is he implying that Set is an imaginary concept which we developed but doesn't actually exist in physically. But then it would apply to number itself (four) as the only real things here are the birds. Or is there something else I am missing.
There is nothing "real" about mathematics, period.
We only define mathematical objects, and we associate some fractions of the reality and certain mathematical constructions, thus, creating models so that they fit the said fractions of reality pretty well. There are no "true" mathematical objects which come uniquely from "reality".