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Article 7691 of comp.ai.philosophy:
Xref: newshub.ccs.yorku.ca comp.ai.philosophy:7691 sci.logic:2375
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>From: vidalnaq@alcatel-alsthom.fr (G. Vidal-Naquet)
Newsgroups: comp.ai.philosophy,sci.logic
Subject: Re: Self-Reference and Paradox (was Re: Human intelligence...)
Message-ID: <1992Nov19.093736.28605@aar.alcatel-alsthom.fr>
Date: 19 Nov 92 09:37:36 GMT
References: <1992Nov14.151559.13227@oracorp.com>
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In article <1992Nov14.151559.13227@oracorp.com>, daryl@oracorp.com (Daryl McCullough) writes:
> 
> In comp.ai.philosophy, we were discussing the meaningfulness of
> self-referential sentences, and I noticed that many people seem to
> think that such sentences are inherently invalid, or meaningless, or
> paradoxical. The paradigm example, of course, is the liar paradox
> 
>      This sentence is false.
> 
> Another paradoxical phrase is (I think it's called Richard's paradox):
> 
>      The smallest number that cannot be defined in fewer than twenty
>      words.
> 
> (It seems to define a number, and only takes twelve words to do it,
> contradicting the definition of the number.)
> 
> In my opinion, the problem with such sentences are not with their
> self-referential character, but with their use of an unrestricted
> notion of truth (or falsity).
> 
...
> Daryl McCullough
> ORA Corp.
> Ithaca, NY
In my opinion the problem with this type of ssentences is the level  they
 deal.  In my course on logic, I learned that formula expresses a property
 of a given structure, or of a class of structures, and that the truth value
of a formula can be determined from the structure.  Now the important point
is that there is a distinction betweeen the formula and the structures that
they reference. Such paradox as the liar come from mixing the structure
obtained by formulas and the truth values, with the semantic function that
 gives the value of a given formaulas with respect to a structure. That is 
essentially mixing a set with functions.


