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From: play@mcvax.UUCP (Andries Brouwer)
Newsgroups: net.math
Subject: Re: Re: Nova's Mathematical Mystery Tour (truth of CH)
Message-ID: <533@mcvax.UUCP>
Date: Thu, 14-Mar-85 11:35:22 EST
Article-I.D.: mcvax.533
Posted: Thu Mar 14 11:35:22 1985
Date-Received: Sun, 17-Mar-85 21:09:57 EST
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Reply-To: play@mcvax.UUCP (Andries Brouwer)
Organization: CWI, Amsterdam
Lines: 15

>I do not see an essential difference between axioms and inference rules; an
>axiom is simply an inference rule with an empty set of antecedents.  I
>think Andries is wrong when he says that adding inference rules to ZFC that
>make CH decidable would lead to a contradiction.  In particular, if adding
>CH itself as an axiom leads to a contradiction, then one can formally infer
>`not CH'.  (In case ZFC+CH is only omega-inconsistent, standard
>metamathematical reasoning would still lead to the conclusion that CH
>is false.)
>
>     Lambert Meertens

But I *do* see a difference between an axiom and a rule of inference.
The former is a requirement on one particular situation; the latter
(in the context of our discussion) formalizes a way of reasoning
that is supposed to be universally valid.