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From: dave@cogsci.indiana.edu (David Chalmers)
Newsgroups: comp.ai,talk.philosophy.misc
Subject: Re: Fun with the semantics of paradox
Message-ID: <17158@iuvax.cs.indiana.edu>
Date: 2 Feb 89 18:54:51 GMT
References: <583@soleil.UUCP> <1361@ncar.ucar.edu>
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Reply-To: dave@cogsci.indiana.edu (David Chalmers)
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In article <1361@ncar.ucar.edu> gary@cgdra.ucar.edu (Gary Strand) writes:
>  What I think is happening is that people are assuming that a given English
>sentence must have some kind of logical truth/falsehood to it, merely because
>we can state it as a sentence. 
>
>  I can think of literally thousands of perfectly good sentences that are in 
>fact total nonsense, to wit:
>
>  "Bananas are elephants."
>  "All good men are Buicks."
>  "Truth is defined to be that which is sugar."
>  "For something to be false means that it is wavy like a reed in a gale."
>
>  All these sentences are perfectly good from a purely syntactical viewpoint,
>ie they are gramatically correct, but that says nothing about whether or not
>they actually MEAN anything.

Sure these sentences mean something.  They're quite coherent to me.  The only
trouble with them is that they're FALSE.  This is a far cry from being
meaningless.

>  I think this also applies to such things as:
>
>  "This sentence is paradox."
>
>  "The following sentence is false."
>  "The previous sentence is true." (or whatever the doublet is)

Now these sentences (at least the last pair, anyway) are different.  The last
pair cannot be assigned truth-values (not even false ones), which means that 
something different is going on.  This leads a lot of people to the conclusion
that they're meaningless.

For a lot of people, the reason they draw this conclusion is that (for them)
meaning is DEFINED in terms of truth-value.  Personally, I think this is
putting the cart before the horse.  Truth-value or no truth-value, these
sentences are meaningless because they are CONTENT-FREE.  They say nothing
about the world; they say nothing interesting at all about anything but their
own truth-value.  And as truth-values have to be ultimately grounded in
reality, this is equivalent to saying nothing at all.

Someone might say to me: 'in Godel's theorem, doesn't he construct some silly
sentence equivalent to "This statement is false", and use it to draw powerful
conclusions about mathematics?  So how can you say that this sentence is 
meaningless?'.  But the beauty of Godel's construction is that at the SAME
TIME as the sentence is talking about itself, it is also talking about a
complex mathematical proposition (because the statement can be interpreted on
two levels).  So this seemingly "meaningless" sentence is in fact grounded in
hard reality.

So that's the lesson: meaning comes first, and truth-value second.

And I should set one thing straight.  There is absolutely no paradox about
the statement "This sentence is paradox."  The statement is simply false.

    Dave Chalmers      (dave@cogsci.indiana.edu)
    Center for Research on Concepts and Cognition
    Indiana University