[FOM] "Mathematician in the street"
joeshipman at aol.com
Mon Aug 10 18:25:48 EDT 2009
Charles, surely you can't be saying that an MIS who has an opinion on
AC and CH typically thinks it makes no difference that one is an
"axiom" and the other is a "hypothesis"?
I have found that physicists and pop-math writers routinely regard both
CH and AC as "assumable", but that every actual mathematician I know
who is capable of stating AC and CH is aware that they have different
"statuses" in terms of acceptability of proofs using them.
From: Charles Silver <silver_1 at mindspring.com>
So, in general, I think an MIS will believe in the truth of AC
CH if he/she has knowingly used that one in a proof or would gladly
use it if the occasion came up.
For those who have only *heard* about AC and CH (even though they
may have unknowingly used one or the other in a proof--harder to
believe CH is used without knowing it, though), my notion is that they
believe them to be true even more strongly than those who know what
they mean. I'll emphasize this: the MIS who's only *heard* of AC and/
or CH, believes in it (them) even more strongly than those who know
what they mean--my opinion, anyway.
More information about the FOM