FOM: Books, foundations, intuitionism, NF

Vaughan Pratt pratt at cs.Stanford.EDU
Sat Mar 7 14:24:20 EST 1998

From: Harvey Friedman <friedman at>
>This is from Godel, Collected Works,
>ed. Feferman et al, vol. 1, page 247. Godel vehemently rejected this point
>of view in a great many of his writings. He regarded intuitionism as a way
>of "tieing one's hands."

Encouraged by Torkel Franzel, I took a closer look at your quotation
of Goedel (a 1932 review of Heyting's "The intuitionist's way of
founding mathematics", 1931) and now do not see how you infer from
the quotation rejection by Goedel of *any* aspect of intuitionism.
(My previous objection to your attribution to Goedel of such rejection
was the weaker one that Goedel at least did not reject the semantic
content of intuitionism.)

Forty pages later in Collected Works, Goedel extends to arithmetic a
suitable variant of Glivenko's translation of the ordinary propositional
calculus into intuitionistic propositional calculus.  Nowhere in this
famous paper is there the slightest hint of rejection of intuitionism,
to the contrary it is hard to see how to take it as other than strong
technical support for intuitionism.

What are the "great many writings" that you had in mind?

You may be thinking of Hilbert, who took just this position on
intuitionism with words to the above effect.

Vaughan Pratt

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