Path: utzoo!mnetor!uunet!husc6!mit-eddie!uw-beaver!cornell!rochester!udel!princeton!mind!greg
From: greg@mind.UUCP (greg Nowak)
Newsgroups: sci.philosophy.tech
Subject: Re: Classifying the Axiom of Choice
Message-ID: <1919@mind.UUCP>
Date: 23 Feb 88 02:14:45 GMT
References: <1890@mind.UUCP> <25011@linus.UUCP> <7123@agate.BERKELEY.EDU>
Reply-To: greg@mind.UUCP (greg Nowak)
Organization: Cabal of Fools
Lines: 26

In article <7123@agate.BERKELEY.EDU> weemba@garnet.berkeley.edu (Obnoxious Math Grad Student) writes:
}In article <25011@linus.UUCP>, bwk@mitre-bedford (Barry W. Kort) writes:
}>My choice is to classify the Axiom of Choice as synthetic and
}>a posteriori.
}
}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'm about to violate my own proscription against discussing the
Kantian philosophy behind the question. Most people agree that the
"analytic a posteriori" class of propositions is empty. Do you have
grounds independent of your consideration of AC for considering the
class non-empty?

Your argument is nonspecific to AC and can easily be extended to the
rest of mathematics. To the extent that Kant himself considered
geometry to be synthetic a priori, you may be using the terms
differently than Kant did. Are you?



-- 


                              greg