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Topic: ZFC really really really sucks -- really!
Replies: 20   Last Post: Jan 20, 2013 6:30 AM

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Posts: 838
From: nyc
Registered: 6/6/10
Re: ZFC really really really sucks -- really!
Posted: Jan 7, 2013 4:12 PM
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> An article by Nic Weaver is worth a read:
> df
> Here's a quote:
> "An essential incorporation of impredicative
> mathematics in basic physics would involve a
> revolutionary shift in our understanding of physical
> reality of a magnitude which would dwarf the passage
> from classical to quantum mechanics [...} the
> likelihood of ZFC turning out to be inconsistent [is]
> much higher than the likelihood of it turning out to
> be essential to basic physics. The assumption that
> set-theoretically substantial mathematics is of any
> use in
> current science is simply false"
> By "impredicative mathematics", he means mathematics
> with the powerset axiom.
> I actually think Weaver misses the essential point,
> which is this:
> The notion of falsifiability, which is the
> cornerstone of science, can be formalized in such a
> way that it can be made the cornerstone of
> mathematics, and it is eminently reasonable to do so;
> if we don't accept falsifiability as part of the
> e underlying logic of our mathematics, then our
> mathematics is deficient as a language for science.
> Impredicative mathematics is not compatible with
> falsifiability.

What is your notion of falsifiability other than that of counterexamples which falsify a theory?

> The conclusion is that the claim that it is even
> remotely possible that impredicative mathematics
> (e.g. ZFC) has an essential role to play in science
> is a truly extraordinary claim that requires truly
> extraordinary evidence, and such evidence is woefully
> lacking.
> ZFC is crackpot mathematics.

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