Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.2 9/18/84; site watdaisy.UUCP
Path: utzoo!watmath!watdaisy!gjerawlins
From: gjerawlins@watdaisy.UUCP (Gregory J.E. Rawlins)
Newsgroups: net.math
Subject: Re: Re: Nova's Mathematical Mystery Tour (truth of CH)
Message-ID: <7078@watdaisy.UUCP>
Date: Mon, 18-Mar-85 01:14:49 EST
Article-I.D.: watdaisy.7078
Posted: Mon Mar 18 01:14:49 1985
Date-Received: Mon, 18-Mar-85 07:43:13 EST
References: <143@ihlpa.UUCP> <460@petsd.UUCP> <6353@boring.UUCP> <350@talcott.UUCP> <529@mcvax.UUCP> <6355@boring.UUCP>
Reply-To: gjerawlins@watdaisy.UUCP (Gregory J.E. Rawlins)
Organization: U of Waterloo, Ontario
Lines: 43

In article <6355@boring.UUCP> lambert@boring.UUCP (Lambert Meertens) writes:
>	[...much of the article deleted, hopefully I captured the main points..]
>In set theory, zermeloids are studied.  These are supposed to formalize sets.
                                         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>But they cannot form the *foundation* for the use of sets
>in mathematical reasoning, if only since it is impossible to discuss the
>meaning of a theory without using the notion of `set'.  	
>	[.....]
>So I reject an approach in which sets are defined as `whatever objects
>satisfy the axioms of ZF Set Theory' as unsound and viciously circular.
>	[.....]
>(It is a red herring to call these models `universes' as though they all
>have equal status: there is the original system that we tried to formalize
                    ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>and there are bogus, non-standard models that are an artefact
>of the inherent limitations of formalization.)  Similarly, the formal
>undecidability of CH does not imply anything about the status of CH; it
>still might be plain right, or plain wrong.  (In case you are interested in
>my position, I actually think that CH is devoid of meaning.)

	With all due respect, the above argument just tells me that you 
are a Platonist (in the sense that you assume the a priori existence of
objects whose essence we then try to *model* by formal axioms and
inference rules). Some mathematicians are not; they are quite
happy making up (formal) axioms and inference rules and churning
out theorems. Personally I agree with you in that when I do
mathematics *it is as if* the things (numbers, sets, circles,
whatever) exist, but I can see no logical reason why they must
exist. Your argument does not convince because you implicitly assume
that such things as numbers do in fact exist, the fact that I
happen to share that belief (as do many mathematicians) does not
imply that it is a true statement. Logically I see no fallacy in
having undecidable hypotheses, and I don't see that it need
interfer with the process of doing mathematics. So I recommend
that we get back to "discovering" things about the "real world",
since it is impossible to refute an argument whose basis axioms
are not purported to correspond to anything at all.
	Cheers.
-- 
Gregory Rawlins CS Dept.,U.Waterloo,Waterloo,Ont.N2L3G1 (519)884-3852
gjerawlins%watdaisy@waterloo.csnet                              CSNET
gjerawlins%watdaisy%waterloo.csnet@csnet-relay.arpa              ARPA
{allegra|clyde|linus|inhp4|decvax}!watmath!watdaisy!gjerawlins   UUCP