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From: sullivan@harvard.ARPA (John Sullivan)
Newsgroups: net.math
Subject: Re: Re: Nova's Mathematical Mystery Tour (truth of CH)
Message-ID: <488@harvard.ARPA>
Date: Fri, 15-Mar-85 23:15:54 EST
Article-I.D.: harvard.488
Posted: Fri Mar 15 23:15:54 1985
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Organization: Aiken Computation Laboratory, Harvard
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> 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.)
> 
>      Lambert Meertens

CH might be plain right or plain wrong only if you think there are real objects
out there which are uncountably infinite sets.  The undecidability of CH says
there are models for ZF+CH and ZF+~CH.  It may turn out that as we increase
our understanding we can come up with a new set of axioms (more "obvious" than
CH) which will allow us to deduce either CH or ~CH (and, we hope, not both!).
Then it would be plain right or plain wrong.  But I think it is likely that
this will never happen, since we don't get much real-world experience with
infinite sets.

Compare the situation with non-Euclidean geometry.  Is the parallel postulate
plain right or plain wrong?  I don't think so.  Even though we have much
better intuition about geometry than about uncountable sets, I don't think
that helps too much.  Both systems have useful applications to the real world.

	John M. Sullivan
	sullivan@harvad