herb z
Posts:
1,187
Registered:
8/26/06


Re: Mathematics as a language
Posted:
Nov 5, 2010 1:33 AM


Daryl McCullough wrote: > 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.
You mean if the universe of sets is wellordered, then every set is wellordered?
What does "a well ordering of the universe of sets" mean, anyway?
 hz

