FOM: Intuitionism, Godel

Vaughan Pratt pratt at cs.Stanford.EDU
Tue Mar 10 12:22:56 EST 1998

From: Pratt 8:06PM 3/7/98:
>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.

From: Harvey Friedman 11:36PM 3/9/98
>I didn't say it was from there. You'll find it in his philosophical papers
>in the Collected Works.

I found it where you said: Collected Works Vol.I p.247.  That page
contains a review, look for yourself.  This is the second of three reviews
by Goedel, of respectively Carnap on logicism, Heyting on intuitionism,
and von Neumann on formalism, texts of invited lectures presented at the
second Conference on Epistemology of the Exact Sciences, Koenigsberg 1930.
As observed on p.196 op.cit, the reviews are entirely reportorial:
Goedel does not pass judgment on any of these three -isms.

>VP>What are the "great many writings" that you had in mind?
HF>His philosophical papers in the Collected Works. My "great many" was of
HF>course silly.

A specific page number of Collected Works where Goedel speaks negatively
of intuitionism would be very welcome.

>There are plenty of better historical experts on Godel than me on the fom,
>and they can set you straight on this.

One of us anyway.

Your extensive remarks on semantics not being algebraic are very useful in
understanding where you're coming from.  It is clear that some logicians
don't find the algebraic viewpoint on semantics helpful, but the extensive
literature on the subject, much but not all originating from the universal
algebra and category theory schools of thought, makes it clear that
many do.  That the do's are not being understood by the don't's is a
most unfortunate breakdown in communications.  It is a nice question
how to apportion the blame between the do's, the don't's, and the subject.

Vaughan Pratt
Interests: Foundations of computation and mathematics

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