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
Mom: Dont enter politics, my son. If you tell the truth men will hate you, and if you tell lies the gods will hate you. Since you must either tell the truth or tell lies, you must be hated either by men or by the gods.
Son: I shall do it, mother. For if I tell lies, men will love me for it; and if I tell truth the gods will love me. Since I must tell truth or lies, I shall be beloved of men or gods.