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From: aam9n@uvaee.ee.virginia.EDU (Ali Minai)
Newsgroups: comp.ai
Subject: Re: Fun with the semantics of paradox
Keywords: Undecidable, Ambiguous
Message-ID: <418@uvaee.ee.virginia.EDU>
Date: 20 Jan 89 15:01:03 GMT
References: <1883@buengc.BU.EDU> <2996@uhccux.uhcc.hawaii.edu> <7282@venera.isi.edu>
Organization: EE Dept, U of Virginia, Charlottesville
Lines: 60

In article <7282@venera.isi.edu>, smoliar@vaxa.isi.edu (Stephen Smoliar) writes:
> In article <905@ubu.warwick.UUCP> mirk@uk.ac.warwick.cs (Mike Taylor) writes:
> > ........What, then is a meaningless sentence?  Surely
> >either an ambiguous sentence or an inconsistent one is meaningless?
> >Or do people simply mean not well-formed?
> >
> This has been giving me trouble, too.  Another possible interpretation is that
> "meaningless" refers to sentences that are not well-formed;  but then, of
> course, they are not really sentences, in which case it does not make sense
> to talk of their having truth values.

At the risk of being called naive, let me suggest that meaningless sentences
are those that obey all rules of syntax, but do not make sense in the
context of mundane experience. "Mundane experience", of course, must be defined
in subjective terms. For example, the sentence:

     The colour of her fear was a brilliant orange.

would be considered meaningless by the vast majority of people in most
contexts, though it is certainly well-formed (compare, "The colour of her
skirt was a brilliant orange"). However, in a poem, or indeed, in any
piece of literary writing, this sentence *could* make a great deal of
sense. That this definition of meaninglessness requires a context should
not put us off. After all, ambiguous and undecidable sentences too
are so only in the context of the logic defined by us. One could
convert an undecidable sentence into a decidable one by changing the nature
of the logical substrate which provides the context, e.g. by allowing
contradiction. That we do not is again because of mundane experience.
Thus, logic is merely a subset (in a loose sense) of this experience.
Sentences which are inconsistent within this logic are ambiguous or
undecidable (since logic forces us to think in combinations of 'true'
and 'false'). Sentences which are outside the domain of logic, and
contradict perceptual/linguistic convention, can be considered meaningless.
Meaninglessness cannot be defined in terms of "truth" and "falsehood",
hence the problem. 

The statement (above) that "... either an ambiguous or an inconsistent
sentence is meaningless", is, in my opinion, based on a very narrow
and rigid notion of "meaning". As someone pointed out, some paradoxes
can be seen as having two co-existent meanings, only one of which can be
valid at any specific time---rather like a bistable system.

Another issue here is that most paradox arises aout of a confusion between
the language of an assertion and the meta-language by which we judge it.
For example, the paradox in, "This sentence is false" goes away as soon
as we distinguish between the two *levels* of meaning that---together---
generate it.

I hope this makes sense. But then, what does!

Ciao,
     Ali


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The opposite of one great truth is another great truth.
                                                        Niels Bohr.

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