FOM: Comment on Riis

[Moshe' Machover]

Riis says:

>If it (against expectations) should turn out that Wiles proof contain
>an argument which cannot be formalised in ZFC, Wiles proof would be in
>serious trouble - not ZFC.

Nothing can be less certain. It is quite possible that the `hidden lemma'
in Wiles' proof (if such will be detected) will be considered true, and
lead to a modification of ZFC. Isn't this how the postulates of ZFC
(notably, AC) were invented?

It is not that the practice of mathematicians is valid because it can be
formalized in ZFC. Rather, mathematicians accept ZFC as foundations because
it justifies what their valid arguments. This was the whole purpose of
Zermelo's 1908 aximatization.


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