Newsgroups: sci.logic,comp.ai.philosophy
From: rbj@campion.demon.co.uk (Roger Bishop Jones)
Path: cantaloupe.srv.cs.cmu.edu!das-news2.harvard.edu!news2.near.net!news.mathworks.com!news.duke.edu!news-feed-1.peachnet.edu!gatech!howland.reston.ans.net!news.sprintlink.net!demon!campion.demon.co.uk!rbj
Subject: Re: Expressibility (was "Penrose's new book)
References: <1994Oct26.172830.3987@oracorp.com> <1994Oct27.020638.28742@news.media.mit.edu>
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Date: Sat, 29 Oct 1994 06:27:16 +0000
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In article <1994Oct27.020638.28742@news.media.mit.edu>
           minsky@media.mit.edu "Marvin Minsky" writes:

> In article <1994Oct26.172830.3987@oracorp.com> daryl@oracorp.com (Daryl
>  McCullough) writes:
> 
...
> >So, you can get around the incompleteness theorem by giving up
> >expressibility.
> 
> Yes, and so far as I can see, all this adds up to: 
> 
>         You can gain consistency only by giving up expressibilty. 

This should be:

	You can gain *completeness* only by giving up expressibility.

However *expressive* a logical language is, you can make the logic
consistent by weakening the proof rules.  (assuming that expressiveness
is understood to be about what you can *say*, i.e. semantics, rather than
what you can *prove*, and that consistency is strictly about what you
can prove) 

> 
> (See also Daryl's next message.)  In particular, when you try to
> express commonsense ideas that happen to be self-referent you expose
> yourself to diagnalization.  If it were more often understood how
> pervasive this is, then computer science students would be more
> suspicious of first order logic.  When do you need self-reference?
> Certainly when you make up things like

Why should computer science students be suspicious of first order logic?

-- 
Roger Jones
rbj@campion.demon.co.uk
