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


Re: Mathematics as a language
Posted:
Nov 4, 2010 2:38 AM


Marshall wrote: > Transfer Principle wrote: > > Herman Jurjus wrote: > > > herbzet wrote:
> > > > 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. > > > > Corollary: CH is true. > > > Proof: Since Goedel 1940 we know that it is logically consistent to > > assume that there exists f, a bijection between the set of countable > > ordinals (i.e., aleph_1) and P(N). > > > > By the principle above, f mathematically exists. Therefore CH is true. > > QED > > > > (Note: The above "corollary" stems from an earlier sci.math discussion > > regarding the relationship between CH and Pen Maddy's "MAXIMIZE".) > > We have concluded that a consequence of herbzet's idea is > that there are
there exist
> systems in which CH is true and systems in which CH is false. > > So, we're all good ... right?
Pretty much.
 hz

