Daryl McCullough wrote: > herbzet says... > >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.
Hard to answer in the absence of a concrete example.
Are you saying, perhaps, that Riemannian geometry precludes Euclidean geometry?