On 11/3/2010 6:52 AM, herbzet wrote: > > > 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.
Corollary: CH is false. Proof: Since Cohen 1963 we know that it is logically consistent to assume that there exists S, subset of P(N), equipollent neither to N nor to P(N). By your principle above, S mathematically exists. Therefore CH is false.