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From: bph@buengc.BU.EDU (Blair P. Houghton)
Newsgroups: comp.ai,talk.philosophy.misc
Subject: Re: Fun with the semantics of paradox
Message-ID: <1883@buengc.BU.EDU>
Date: 12 Jan 89 18:13:15 GMT
References: <551@soleil.UUCP> <1975@cadre.dsl.PITTSBURGH.EDU> <43519@linus.UUCP>
Reply-To: bph@buengc.bu.edu (Blair P. Houghton)
Followup-To: comp.ai
Organization: Boston Univ. Col. of Eng.
Lines: 49

In article <43519@linus.UUCP> bwk@mbunix (Barry Kort) writes:
>In article <1975@cadre.dsl.PITTSBURGH.EDU> geb@cadre.dsl.pittsburgh.edu
>(Gordon E. Banks) enters the fray on Dave's paradoxical sentence:
>
>>In article <551@soleil.UUCP> peru@soleil.UUCP (Dave Peru) writes:
>
>>>When you view the meaning of a paradox, your brain is on a razor's edge.
>>>Depending on what side you fall, the paradox is decidedly true or false.
>>>Example:  This statement is false.
>
>>On the contrary, when presented with a paradox, one's mind tends to first
>>call it true, then false, then true, then false as one considers it
>>over and over.  It is not resolvable.
>
>I disagree.  I suggest that we consider the law of logic that trips
>us up here:  Aristotle's Law of the Excluded Middle.  This law says
>that a sentence must be either True or False.  There are no other
>possibilities.  We now know better.  A sentence may be formally
>undecidable.  A sentence may be ambiguous, admitting multiple meanings.
>A sentence may be a meaningless sequence of words, admitting no meaning
>whatsoever.

Hurm.  Astirottle rears his ponderous head.  He'd never read Rudy Carnap's
eminently unreadable "The Logical Syntax of Language."  All sentences
(ansatzen) can be reduced logically to their syntax; semantics are irrelevant
to logic.

Paradox is no different.  "I am not me" and "this ansatz is untrue"
both reduce to 
     _
S => S

or, actually
      _
S <=> S

Such things are essential in developing the contextual meaning of words.
I.e., while syntax (logic) is not dependent on semantics, semantics is
dependent on syntax.  In other (invisible) words:

Sy => Se

Hand me a paradox of any sort, give me twelve years to finish Carnap's
book, and I shall decompose your paradox into it's syntactic contradictions.
It will have no semantic ones.

				--Blair __
				  "2B + 2B,
				   es ist die frage."