
Re: Mathematics as a language
Posted:
Nov 4, 2010 7:11 AM


herbzet says... > > > >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 >> selfcontradictory, 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.
Well, the existence of a set that cannot be wellordered contradicts the existence of a wellordering of the universe of sets. Both are consistent, but they can't both exist.
 Daryl McCullough Ithaca, NY

