[FOM] extramathematical notions and the CH
tom.dunion at gmail.com
Sun Jan 27 12:46:10 EST 2013
In the "Con(ZFC) is trivial" thread (Jan. 22, 2013) Harvey Friedman said
>> As Goedel pointed out, it [Con (ZFC)] cannot be proved in ZFC, but
>>might be proved using extramathematical notions.
Sure, why not? Perhaps the CH itself might eventually be
generally accepted as true (or false) for like reasons.
As Rudy Rucker, for one, has remarked, "...it could be that one of the
reasons set theory is stalemated by the continuum
hypothesis is that we have not yet made enough attempts to identify
the problem with some problems outside of pure mathematics." (see his
1982 book Infinity and the Mind, p. 253)
In particular, physics has issues that may encroach on f.o.m.
topics.Though a FOM-like forum, the "theoretical physics stack
exchange" did not prove viable, there are yet some who seek a "realistic"
underpinning for quantum mechanics (some even to the point of
considering a logically possible "local hidden variables" theory) who look
to issues such as a non-standard theory of probability.
And in the case of the late Prof. Itamar Pitowsky (note here:
acknowledged explicitly his need of at least a consequence of Martin's
Axiom, if not the full strength of the CH. Perhaps some such thinkers
might be enticed to engage these types of issues at FOM.
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