FOM: Kreisel's realism

William Tait wwtx at
Tue May 8 18:14:57 EDT 2001


I have not asked Putnam, but his paper was first published in 1975 
and my guess is that he is referring to the remark in the Saaty paper.

Kreisel's remark may not intend to reject the sui generis character 
of mathematical objects, but rather to affirm that their objectivity 
derives from the objectivity of discourse about them. Anyway, that 
would be a sensible thing to say---which is, of course, no guarentee 
that it is what Kreisel meant.


>In his survey lecture on mathematical logic from
>1965 (Saaty, Lectures on Modern Mathematics, Vol. III),
>Kreisel discusses these questions on pp. 98-99.
>In particular, he distinguishes sharply between
>the "requirement of objectivity" (basically the use
>of classical logic), and the assumption of mathematical
>objects external to us.  This survey paper was heavily
>influenced by Goedel, and Kreisel in general gives
>Goedel's assumption of mathematical objects a respectful
>hearing.  Later, he was much more negative on this subject,
>so I think perhaps Putnam had in mind some later remark
>of Kreisel.


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