Path: utzoo!mnetor!uunet!lll-winken!lll-lcc!ames!elroy!cit-vax!ucla-cs!hbe
From: hbe@math.ucla.edu
Newsgroups: sci.philosophy.tech
Subject: Re: Classifying the Axiom of Choice
Message-ID: <9734@shemp.CS.UCLA.EDU>
Date: 24 Feb 88 20:43:01 GMT
References: <7123@agate.BERKELEY.EDU> <8768@sunybcs.UUCP>
Sender: news@CS.UCLA.EDU
Reply-To: hbe@math.ucla.edu (H. Enderton)
Organization: UCLA Mathematics Department
Lines: 13

In article <8768@sunybcs.UUCP> rapaport@gort.UUCP (William J. Rapaport) writes:
>I guess you [weemba@garnet.berkeley.edu} have not read Kant.  All mathematical
>propositions are synthetic apriori for him.  By that, I'd take the Axiom of
>Choice as synthetic apriori, too.

Kant's classification of mathematical truths as synthetic a priori seems
in light of Godel to be more wrong than right.  The a priori statements
form merely a recursively enumerable set, and hence cannot include even
all the true statements of arithmetic.  I think that the analytic
a posteriori is an unjustly neglected category in the philosophy of
mathematics.  I am not sure, however, that I want to put the axiom of
choice into it.

--Herb Enderton, hbe@math.ucla.edu