
Re: Mathematics as a language
Posted:
Nov 3, 2010 8:58 AM


On 11/3/2010 1:19 PM, Marshall wrote: > 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). > > Consistent with what? In what theory?
Coconsistent with ordinary mathematics, of course. (I.e. with ZFC, and then also with any weaker theory.)
 Cheers, Herman Jurjus

