Path: utzoo!mnetor!uunet!lll-winken!lll-lcc!lll-tis!ames!hao!gatech!udel!princeton!mind!greg
From: greg@mind.UUCP (greg Nowak)
Newsgroups: sci.philosophy.tech
Subject: Re: Classifying the Axiom of Choice
Message-ID: <1927@mind.UUCP>
Date: 23 Feb 88 23:48:23 GMT
References: <1890@mind.UUCP> <25011@linus.UUCP> <7123@agate.BERKELEY.EDU> <8768@sunybcs.UUCP>
Reply-To: greg@mind.UUCP (greg Nowak)
Organization: Cabal of Fools
Lines: 27

In article <8768@sunybcs.UUCP> rapaport@gort.UUCP (William J. Rapaport) writes:
}In article <7123@agate.BERKELEY.EDU> weemba@garnet.berkeley.edu (Obnoxious Math Grad Student) writes:
}>
}>I favor analytic a posteriori, myself.  "analytic", since all mathematical
}>truths are, and "a posteriori", since AC is based on our derived perceptions
}>of sets.
}
}I guess you've not read Kant.  All mathematical propositions are
}synthetic apriori for him.  By that, I'd take the Axiom of Choice as
}synthetic apriori, too.


This is taking the question perhaps too literally. After Kant,
developments in non-Euclidean geometry made it clear that geometry was
not synthetic a priori in the way that Kant thought it was. It's
pretty clear, pace Matthew's support of analytic a posteriori, that
mathematical propositions are either synthetic or analytic a priori.
Now that further research has moved geometry up to the level of
analytic propositions, the search for synthetic a priori propositions
moves on. If anyone is really interested, there's an article by
Michael Friedman in the 1985 volume of Philosophical Review on "Kant
and Geometry" that discusses the synthetic/analytic distinction quite
well.

-- 


                              greg