On Nov 3, 3:23 am, Herman Jurjus <hjm...@hetnet.nl> wrote: > 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).