Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/3/84; site talcott.UUCP Path: utzoo!linus!philabs!cmcl2!seismo!harvard!talcott!gjk From: gjk@talcott.UUCP (Greg Kuperberg) Newsgroups: net.math Subject: Re: Re: Nova's Mathematical Mystery Tour Message-ID: <350@talcott.UUCP> Date: Sun, 10-Mar-85 22:18:53 EST Article-I.D.: talcott.350 Posted: Sun Mar 10 22:18:53 1985 Date-Received: Tue, 12-Mar-85 09:03:20 EST References: <143@ihlpa.UUCP> <460@petsd.UUCP> <6353@boring.UUCP> Organization: Harvard Lines: 24 > The same must apply to classical mathematicians. Even though CH is in- > dependent of the axioms of ZF Set Theory, it is conceivable (although high- > ly implausible) that someone will some day come up with new methods of > mathematical reasoning that are *obviously* valid, using which CH can be > decided. The situation is different from the one concerning Euclid's Fifth > Postulate. None of Euclid's axioms is `true', obvious or not. There are > `geometries' in which there can be several lines through two given points > (e.g., great circles on a sphere). However, a `mathematics' in which both > a proposition and its negation can be true is unacceptable to classicists, > intuitionists and constructivists alike. ... > Lambert Meertens Really? I had always thought that there were two "classes" of sets: in one class, the CH is true, and in the other it is false. That is, just like there are other geometries in which Euclid's fifth is false, there are "universes" in which CH is true and other "universes" in which it is false. If this duality is valid, how can one possibly come up with new methods by which CH can be decided? Or is this duality valid in the first place? --- Greg Kuperberg harvard!talcott!gjk "2*x^5-10*x+5=0 is not solvable by radicals." -Evariste Galois.