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Most mathematicians don't care at all about CH and among those who do not all believe that ZFC+CH is more intuitive than ZFC+not CH (really it makes no sense to
by ginnungagap 8y ago
Most mathematicians don't care at all about CH and among those who do not all believe that ZFC+CH is more intuitive than ZFC+not CH (really it makes no sense to believe whether it is true or not unless you believe in some platonic universe of sets, but I do maths, not philosophy), for example Gödel himself thought that the continuum could be aleph_2, Woodin's Omega logic argued the same (but this is somewhat controversial) and the proper forcing axiom also implies that the continuum is aleph_2
- bnjmn 8y agoPlease see my reply to @baddox. You say you do math and not philosophy, but the whole CH independence proof kinda moves this discussion out of the realm of (ZFC-based) math, doesn't it? If you don't want to consider philosophy here, there's not much more to say.
- ginnungagap 8y agoPlenty of math is done outside of ZFC, a lot of modern set theory for example, but that doesn't make it philosophy. Even Grothendieck's EGA has a couple of arguments that cannot be carried out in ZFC in the generality he presents them in, but I wouldn't call EGA a philosophy treatise nor an algebraic geometer a philosopher