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Article 2359 of comp.ai.philosophy:
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>From: bill@NSMA.AriZonA.EdU (Bill Skaggs)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech
Subject: Re: Machine Translation (was re: Searle's respons
Message-ID: <1991Dec21.184951.2303@arizona.edu>
Date: 22 Dec 91 01:49:49 GMT
Article-I.D.: arizona.1991Dec21.184951.2303
References: <45303@mimsy.umd.edu> <1991Dec21.000014.6836@husc3.harvard.edu> 
 <1991Dec21.111459.2302@arizona.edu> <1991Dec21.164621.6848@husc3.harvard.edu>
Reply-To: bill@NSMA.AriZonA.EdU (Bill Skaggs)
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>Mikhail Zeleny:
>>Simple.  Correct translation is a matter of finding an approximate synonym;
>>synonymy is a semantic relation; if machines can't compute semantic
>>relations, they can't translate anything.

Bill Skaggs:
>Synonymy is a semantic relation, but it may correspond (by "coincidence")
>to a syntactic relation, for example when translating from English
>to Pig Latin.  So the conclusion does not follow.

MZ:
>There are two issues here.  One is formal: for first-order languages,
>semantic relations can't be determined by syntax pace L\"owenheim-Skolem.
>On the other hand, the structure of natural languages is not likely to be
>first-order.  In this case, simpler considerations like that of Putnam's
>permutation trick, come to bear on the issue; refer to a parallel thread.

I agree; that's why I used the word "coincidence".  I am quite happy
to accept that syntax does not determine semantics; I merely deny that
this poses a difficulty for AI.  All it shows is that the relationship
between syntax and semantics is something like a "synthetic *a priori*".

MZ:
>On the other hand, you might wish to maintain that the semantic properties
>of two natural languages may be isomorphic, inducing a syntactical
>isomorphism; or perhaps that in the absense of such isomorphism, the
>synonymy transformation might be coextensive with some syntactical
>manipulation.  The fallaciousness of this claim can be seen even in cases
>of closely related languages like English and French, by considering, e.g.
>the French word `conscience', ambiguously translatable as `conscience' or
>`consciousness'.  Furthermore, the question of figurative meaning transfer
>(e.g. as evidenced in the use of metaphor, irony, etc.)  is rightly
>considered to be intractable not only by purely syntactic, but even by
>semantic means.

I think you are right, but a number of clever philosophers (e.g. Jerry
Fodor) would disagree.  Fodor believes that there is a "language of
thought" common to all human beings, into which all utterances are
more or less mechanically translated.  This translation process would
induce an isomorphism between different languages.

MZ:
>>The fact that semantic relations are non-recursive is a direct consequence
>>of G\"odel's Second Incompleteness theorem.  In any language containing
>>elementary arithmetic, as well as a recursive semantic relation "...
>>expresses ...", we may apply the arithmetization trick to the said relation
>>with predictable results.

BS:
>This argument has been conclusively refuted many times.  I don't
>feel like writing it out all over again.  

MZ:
>Not only is this spectacularly arrogant claim made in error; it is also
>remarkably hypocritical, given the vehement demands for self-contained
>elementary explanations you made at the time of our initial exchange
>several weeks ago. 

Sorry, I just couldn't resist the urge to copy your own style of
argument for once; it's so much easier.

MZ:
>Incidentally, if you really believe yourself to be
>capable of refuting this argument, I urge you to publish: Thomason and
>Putnam, the authors of different versions thereof would be happy to
>consider your rebuttal of their views.  This is a genuine conundrum, so to
>arrropriate the words of John McCarthy, if you can solve it, you'll become
>well known for more than invective.

Well, I'll sketch the refutation, but you won't like it.  The essential
claim is that human minds are effectively no more powerful than finite
state automata.  Therefore semantics, in the strong sense in which
you use the word (and the sense it must have for the theorem to apply),
is something humans are not capable of possessing.  Therefore human
language cannot have semantics in this sense; therefore G\"odel's
result need not apply to human language.

(To anticipate at least one objection:  All of the empirical evidence
for human's "referring" to things can potentially by duplicated by
finite state automata, so empirical data cannot possibly prove the
existence of reference (in the strong sense).)

	-- Bill

I will be away for the next week, so I will not be able to follow
up on responses.  Merry Christmas.


