> but I have no idea what existence refers to. A lot of brilliant famous mathematicians in history have been befuddled on that point as well. I think it's a l

> but I have no idea what existence refers to. A lot of brilliant famous mathematicians in history have been befuddled on that point as well. I think it's a linguistic issue, which perhaps you are hinting at. If I say "that rock exists", in the real world, that meaning of "exists" is parallel to, yet different than if I say "prime numbers exist". It's hardly the first time that one word meant more than one thing. The linguistic "exists" is a "deictic" -- I can point to the thing. The mathematical "exists" means "come, let us reason together, and I can demonstrate to you abstractly that this one thing is inescapably implied by this starting point". (Phrasing borrowed from Leibniz's commentary on Calculus Ratiocinator) They both have a similar final state, I suppose: that we are convinced of the "existence" of a thing, but nonetheless the existence in each case is in a separate realm.