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>From: petry@pythagoras.math.washington.edu (David Petry)
Subject: Re: Self-Reference and Paradox (was Re: Human intelligence...)
Message-ID: <1992Nov19.000227.9652@u.washington.edu>
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Organization: University of Washington, Mathematics, Seattle
References: <BxtBwx.LvH@unx.sas.com> <1992Nov18.051456.24550@u.washington.edu> <BxwzLy.H3E@unx.sas.com>
Date: Thu, 19 Nov 1992 00:02:27 GMT
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In article <BxwzLy.H3E@unx.sas.com> sasghm@theseus.unx.sas.com (Gary Merrill) writes:
>
>In article <1992Nov18.051456.24550@u.washington.edu>, petry@corona.math.washington.edu (David Petry) writes:
>|> In article <BxtBwx.LvH@unx.sas.com> sasghm@theseus.unx.sas.com (Gary Merrill) writes:
>|> >
>|> >In article <1992Nov14.151559.13227@oracorp.com>, daryl@oracorp.com (Daryl McCullough) writes:
>|> >
>|> >|> 
>|> >|>     This sentence is false.
>|> >|> 
>|> >|> refers to an unrestricted notion of falsity, and is therefore
>|> >|> meaningless. We can replace "false" by a restricted notion of falsity
>|> >
>|> >This sort of thing has been tried before. One problem is that the displayed
>|> >sentence is *not* meaningless in any normal sense of this term.  We
>|> >know perfectly well what it means -- and that's the problem.
>|> 
>|> Well, we think we know perfectly well what it (the paradoxical sentence)
>|> means, but we humans use non-monotonic logic.  That is, we are willing to 
>|> reject our previous conclusions in light of new knowledge.
>|> 
>|> For example,  if you found out that I had just written down the sentence
>|> "2+2 = 5" and was pointing to it while I exclaimed "This sentence is false",
>|> you would quickly change your belief about the meaning of that exclamation.
>|> 
>|> I've always felt that that observation is crucial to the understanding of
>|> the so-called paradoxes.
>
>Really?  How?  What you point to is that the meaning of a sentence is
>dependent upon context.  My claim remains that given the original
>context of the example (in which the subject of the sentence refers
>to the sentence itself), we know what the sentence means.  The fact
>that the sentence *could* mean something else in *another* context
>hardly allows us to escape the paradox.


The question is, how do you know that in the original context the subject
refers to the sentence itself?  The answer is that you have been taught
to "see" paradox.  Many, perhaps most, people that have not been taught
to see the paradox will ask the question "What sentence is being referred
to?" when they see the sentence "This sentence is false."

Anyways, I find that most people who defend the paradoxes have at their
command laws of logic which I never even imagined could exist.  I will
probably drop out of this discussion.


David Petry



