Newsgroups: sci.logic
From: leemike@eecg.toronto.edu (Michael Lee)
Subject: Re: Self-Reference and Paradox (was Re: Human intelligence...)
Organization: CSRI, University of Toronto
Date: 19 Nov 92 09:01:15 GMT

In article <1992Nov19.000227.9652@u.washington.edu> petry@pythagoras.math.washington.edu (David Petry) writes:
>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? 
>
> `some text deleted'
>
>David Petry
>

You're quite right, it has been one way to work around the paradox
of `this sentence is false', by asking what sentence does the phrase
`this sentence' refer to.  Suppose I was to supplant the phrase
`this sentence' with `this sentence is false', forming the following:
     `This sentence is false' is false.
Hence the above imposes falsity no longer onto itself but something
other than itself clearing the paradox.  However, consider the following
sentence:
     `Yields a falsehood when appended to its own quotation' yields
      a falsehood when appended to its own quotation.
Is it an antinomy regarding any contextual situation you may perceive?
Another antinomy which comes to mind is Russell's paradox of self
membership of classes which can be framed in the following query:
      What of classes of classes that are not members of themselves?
You can find a complete and thorough analysis of this paradox in
any introductory book on set theory.  With regards to set theory, it
is quite an important one.

I think the appearance of antinomies creates the need that some tacit
and established form of reasoning must be made explicit and reworked 
in order to avoid these antinomies.

regards,
  michael lee