>Aatu Koskensilta wrote: >> herbzet writes: >> > Bill Taylor wrote: >> > >> >> Or whether the number 6 really exists. Does it? >> > >> > It *could* exist -- therefore, mathematically, it *does* exist. >> >> This is a traditional and appealing idea. But just what is meant by >> "could" here? What sort of possibility is involved? > >For rhetorical punch, I purposely left out the modifier, which is "logical". > >What logically could exist -- that is, what is not inherently self- >contradictory -- has mathematical existence.
The problem with this is that there could be two different mathematical objects, A and B, such that neither is inherently self-contradictory, but the existence of A contradicts the existence of B. They can't, therefore, both exist.