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From: minsky@media.mit.edu (Marvin Minsky)
Subject: Re: Truth and infinity
Message-ID: <1995May11.020302.14756@media.mit.edu>
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References: <3oef70$ov@vixen.cso.uiuc.edu> <mike.800059522@mik.uky.edu> <Pine.SUN.3.91.950510120529.24739A-100000@altair.herts.ac.uk>
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Date: Thu, 11 May 1995 02:03:02 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:27912 sci.philosophy.meta:17987

In article <Pine.SUN.3.91.950510120529.24739A-100000@altair.herts.ac.uk> Stephen Kelly <comrstk@herts.ac.uk> writes:
>
>A number of fallacies about logical truth and mathematical infinity 
>have come up over the last few days.

[snip]

>Now, interestingly enough, the power set of a countably infinte set is 
>itself countably infinite. We can see this by taking it in stages
>1. the power set of a countably infinite set contains a countably 
>infinite set of sets of cardinality 1
>2. the power set of a countably infinite set contains a countably 
>infinite set of sets of cardinality 2
>......
>etc.
>
>The power set of a countably infinite set is made up of all of these 
>sets - so it is a countably infinite set of countably infinite sets. 
>Thus, it is countably infinite.

Oops. You ought to read Cantor's thesis.  You missed almost all the
members of that power set--namely all the infinite subsets.
f'rinstance, the set of even integers.  I fear you've contributed
another fallacy.


