[FOM] Three quick comments.
W.Taylor at math.canterbury.ac.nz
Tue Oct 23 19:05:31 EDT 2007
Alex Blum <blumal at mail.biu.ac.il> responds:
-> Given your logo, how does focusing on truth differ from focusing on
-> clarity in mathematics?
There is indeed a large overlap between these two concerns!
But perhaps they are not identical.
There can be truth without clarity, (one might suggest 4CT & FLT);
and there may be clarity without truth-falsity, (AC & parallel axiom).
-> How would you apply your priorities to whether CH is true or not.
My personal feeling is that once this is known to be independent,
it is neither true nor false in any absolute sense; which amounts
to saying there is no obvious standard model. OC the cumulative
hierarchy might be claimed as standard, but it is still undetermined
in that it is still undetermined what nature of sets are gathered
at every level.
My personal feeling is that in fact AC is false (in sets of reals),
and that because of this CH is either true or false, depending on
how it is worded. As I noted here before, it is possible to give
two versions of CH which are equivalent in ZFC, but not so in ZF,
and that one could be said to be "clearly true" and one "clearly false".
"Clearly", in this context, depends on one's interpretation of
the existential quantifier (for sets).
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