From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.ecf!news-server.csri.toronto.edu!rpi!think.com!snorkelwacker.mit.edu!hsdndev!husc-news.harvard.edu!zariski!zeleny Mon Dec  9 10:48:59 EST 1991
Article 1959 of comp.ai.philosophy:
Xref: newshub.ccs.yorku.ca rec.arts.books:11319 sci.philosophy.tech:1344 comp.ai.philosophy:1959
Path: newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.ecf!news-server.csri.toronto.edu!rpi!think.com!snorkelwacker.mit.edu!hsdndev!husc-news.harvard.edu!zariski!zeleny
>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: rec.arts.books,sci.philosophy.tech,comp.ai.philosophy
Subject: Re: Existence
Message-ID: <1991Dec8.160548.6317@husc3.harvard.edu>
Date: 8 Dec 91 21:05:46 GMT
References: <1991Dec6.165648.6234@husc3.harvard.edu> <1991Dec6.204854.2218@arizona.edu> <JMC.91Dec7230031@SAIL.Stanford.EDU>
Organization: Dept. of Math, Harvard Univ.
Lines: 112
Nntp-Posting-Host: zariski.harvard.edu

In article <JMC.91Dec7230031@SAIL.Stanford.EDU> 
jmc@SAIL.Stanford.EDU (John McCarthy) writes:

JMC:
>Unaccustomed as I am to agreeing with Mikhail Zeleny, I even agree
>with his use of the word "presumptuous" applied to Bill Skaggs's
>posting.  Namely, Skaggs has taken as obvious a position on an
>issue which is still highly controversial among mathematicians
>and philosophers - the reality of certain mathematical objects,
>real numbers, sets, etc.

I am honored, Professor, and would only add that if you take the trouble of
considering the fundamentat points made in my AI arguments, you would find
yourself in agreement with them, at least if you still appreciate the
issues raised in your 1969 "Machine Intelligence" article.

JMC:
>I think most mathematicians are anti-Platonist when they come
>to philosophy, although they are often effectively Platonist
>in their work.  However, Goedel was explicitly Platonist,
>carefully distinguishing what was true from what might be
>proved and even from what might be known in any sense.
>
>Not only did Goedel hold this view, which was rather unpopular
>throughout his life, but this view motivated his three greatest
>pieces of work, his completeness theorem for first order logic,
>his even more famous incompleteness theorem and his work on
>the continuum hypothesis.
>
>To oversimplify only slightly, the first two pieces of work
>related truth and provability.  In one case he showed they
>agreed and in the second case he showed they were different.
>When he showed the consistency of the continuum hypothesis,
>he distinguished between the real numbers, which are not
>denumerable and certain models of the axioms of the real
>numbers in set theory, which could be denumerable because
>of the inability of the axioms of set theory to cover all
>the facts about sets.  Cohen's proof of the independence
>of the continuum hypothesis used the same basic idea -
>only the technical details were different.

Indeed this is so, and I would merely add that G\"odel's discussion of his
means of proof in the Introduction to his 1929 completeness paper is most
germane to our subject.  On the other hand, I would direct your attention
to the shortcomings of your own approach that arise in the light of the
above.  First of all, applying circumscription to the first-order axioms of
the ZFC would result in selecting Cohen's generic model, rather than the
standard one, i.e. your automatic reasoner would automatically dismiss the
intended interpretation of the set-theoretic universe in favor of the
non-standard one.  Secondly, your purely syntactical understanding of
reflexion principles in your review of Penrose (I have the copy you sent
me, but would appreciate a full reference) seems in direct contradiction
with the G\"odelian realism you advocate above, insofar as the latter
explicitly subordinates our confidence in proof-theoretic matters to
considerations of intrinsic meaning of mathematical theories.  Should you
wish to be consistent, you would have to conclude that an agent operating
solely with a given set of axioms and rules of derivation would never be
capable to exhaust all mathematical reasoning.  In other words, reflexion
is a result of semantic deliberation, not a mere \omega-closure.

JMC:
>Of course, many people, perhaps most mathematical philosophers, still
>disagree with Goedel's Platonism, but they don't dismiss it so
>cavalierly as Bill Skaggs does.  I happen to agree with Goedel for
>reasons of artificial intelligence.  Concisely, put I think success in
>AI theory will require a theory of how a mind embedded in a world can
>find out about the world.  Such a theory has got to assume the world
>exists and there are facts about it that the mind may or may not
>discover.  Even if the facts are conjectured, the mind may never be
>completely sure of them.  It is presumptuous and narcissistic to
>declare a question meaningless just because you have no way of
>answering it conclusively.  This holds true both for questions
>about the material world and for purely mathematical questions.

In fact, those are the views advocated in your 1977 IJCAI address, and I am
pleased to see that you are not afflicted with the weathercock mentality of
certain analytic philosophers.  If only you were to add consistency to your
philosophical virtues, the world would be a much better place.

JMC:
>The need for such a theory should put AI on the side of Platonism
>rather than on the side of positivism.  Of course, there are
>positions not well classified along this spectrum.

A final observation: in calling your discipline `Artificial Intelligence',
you implicitly align yourself with proponents of Christianity, Marxism,
and other redemptive religions, and distance yourself from the rest of
scientific discourse favoring epistemology over eschatology.  Artificial
intelligence may or may not be possible, and in the final analysis the
question of its possibility will only be answered through scientific
inquiry; however, if there is a final purpose to any science, the task of
the scientist is to discover, rather than stipulate it.  Anyone who favors
the latter is better off starting a religious movement, if only for tax
purposes.

>--
>John McCarthy, Computer Science Department, Stanford, CA 94305
>*
>He who refuses to do arithmetic is doomed to talk nonsense.


`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'
: Qu'est-ce qui est bien?  Qu'est-ce qui est laid?         Harvard   :
: Qu'est-ce qui est grand, fort, faible...                 doesn't   :
: Connais pas! Connais pas!                                 think    :
:                                                             so     :
: Mikhail Zeleny                                                     :
: 872 Massachusetts Ave., Apt. 707                                   :
: Cambridge, Massachusetts 02139           (617) 661-8151            :
: email zeleny@zariski.harvard.edu or zeleny@HUMA1.BITNET            :
:                                                                    :
'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`


