[FOM] extramathematical notions and the CH
sasander at cage.ugent.be
Wed Jan 30 04:48:01 EST 2013
> Physics may have much to teach us about math, but in my opinion it will have nothing to say about non-absolute math like CH. I would be very interested in criticisms of this opinion.
I agree with Joe Shipman. For instance, given that we can only measure up to finite precision, how would we even measure
if a given object is computable or non-computable?
Even if there were to be non-computable objects "out there", we would run into problems of the following nature:
Harrington's theorem (WKL_0 is \Pi_1^1-conservative over RCA_0) implies that there is both a recursive and non-recursive model for \Pi_1^1-statements provable in WKL_0. One can then argue that physics does not really involve even \Pi_2^1-statements, as "there exists a function" is actually "there exists a function up to finite precision", and the latter is an arithmetical quantifier.
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