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.
(This may be a traditional idea, but I arrived at it during an exchange of posts with MoeBlee.)
In particular, there appears to be nothing self-contradictory in the notion of infinite sets -- they could exist, therefore, mathematically, they do.