From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!bonnie.concordia.ca!thunder.mcrcim.mcgill.edu!snorkelwacker.mit.edu!hsdndev!husc-news.harvard.edu!zariski!zeleny Tue Feb 11 15:26:04 EST 1992
Article 3616 of comp.ai.philosophy:
Xref: newshub.ccs.yorku.ca comp.ai.philosophy:3616 sci.philosophy.tech:2107
Path: newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!bonnie.concordia.ca!thunder.mcrcim.mcgill.edu!snorkelwacker.mit.edu!hsdndev!husc-news.harvard.edu!zariski!zeleny
>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech
Subject: Re: Robotic Follies
Summary: logic of belief and minsky's fragmented mind
Message-ID: <1992Feb10.123736.8691@husc3.harvard.edu>
Date: 10 Feb 92 17:37:31 GMT
References: <1992Feb5.021730.29817@nuscc.nus.sg> <1992Feb5.090941.8498@husc3.harvard.edu> <1992Feb6.221125.26525@nuscc.nus.sg>
Organization: Dept. of Math, Harvard Univ.
Lines: 209
Nntp-Posting-Host: zariski.harvard.edu

In article <1992Feb6.221125.26525@nuscc.nus.sg> 
smoliar@iss.nus.sg (stephen smoliar) writes:

>In article <1992Feb5.090941.8498@husc3.harvard.edu> 
>zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:

MZ:
>>  Like
>>I said elsewhere, my exposition of Churchian semantics (an example of a
>>formal belief theory, the very possibility of which has been denounced by
>>Minsky on a priori grounds) can be found in the following articles:
>>
>>	<1991Nov10.004631.5292@husc3.harvard.edu>  
>>	<1991Nov22.154821.5774@husc3.harvard.edu>  
>>	<1991Nov27.115032.5957@husc3.harvard.edu>
>>	<1991Dec20.134023.6825@husc3.harvard.edu>
>>	<1991Dec21.015234.6837@husc3.harvard.edu>    
>>
>>Again, a summary will be posted on request.

SS:
>I accept your invitation;  but, just to make sure we agree upon the ground
>rules (assuming you are willing to do so), let me lay out the basis for the
>current argument.  Specifically, we are disputing the following words posted
>by Minsky in article <21879@life.ai.mit.edu>:

MM:
>>  What
>>I've said about "belief" in a philosophical context was that the idea
>>that "Jack believes X" is not a reasonable thing to discuss formally.
>>(For example, in the context of "believes" vs. "knows".) Simply
>>because the human mind is not a simple data-base plus processor, or
>>axiom-set plus -rule(s) of inference.  Instead, the situation normally
>>is much more complex, one part of your mind (one ensemble of agencies)
>>maintaining one assumption, justification, protected-goal, etc., while
>>other parts are denying , rejecting, suppressing, opposing, etc.
>>corresponding positions.  Thus you can love/dislike, etc.  There isn't
>>simply a person/homunculus inside your head, but a big
>>self-conflicting organization.

MM:
>I THINK what is really at stake here is Minsky's claim about whether or not the
>mind can be reduced to a data base enhanced with processing (which may be taken
>as logically equivalent to an axiom set enhanced by rules of inference).  Thus,
>the part of your exposition which most interests me concerns whether you are
>refuting this claim or demonstrating that it is irrelevant to whether or not
>be can discuss belief formally.  I have seen several formal systems which
>purport to provide an adequate handle for belief.  (I found Robert Moore's
>thesis, "Reasoning About Knowledge and Action," an excellent introduction
>to the state of this "art.")  What I have NOT seen is a cogent argument which
>demonstrates that such systems are effective in the more complex situations
>which Minsky has outlined above.  I hope you can provide such an argument,
>because I doubt that you can provide one that our usage of the word "belief"
>precludes all those complex situations.

Let's back up a bit.  In article <1992Feb1.183054.8327@husc3.harvard.edu>,
I responded to the above claim by Minsky as follows:

MZ:
>I will pay a bounty of US $100 to anyone who is the first to present me
>with proof that the above straw man view has ever been held by any thinker
>outside of the AI community, in particular by a known philosopher.

As I said to Pontus Gagge, this is not meant to attribute the above view to
the esteemed author of "The Society of Mind" himself; indeed, Minsky seems
to be arguing against his own coreligionists like John McCarthy and Daryl
McCulloch, who make claims to the effect that the human mind may be taken
as functionally equivalent to a formal theory.  You may recall that in my
discussions with Messrs McCarthy and McCulloch I argued that these claims
were unwarranted.  Hence, my position in the Minsky affair is that his
heterodox stance in the AI community is insufficient to make his position
philosophically sound, for the same reason that two wrongs don't make a
right.  By the same token, if you are looking for an adequate formal
treatment of belief, I would recommend the writings of non-partisan
philosophers like Frege and Church, who have the advantage of not being
beholden to the computational mind ideology.

In order to demonstrate that I described the theory in question on prior
occasions, I quote myself from the above referenced article
<1991Nov22.154821.5774@husc3.harvard.edu>:

MZ:
>							I conclude
>that an adequate semantical theory must be both intensional and strongly
>anti-haecceitist, such as Church's Logic of Sense and Denotation,
>characterized as follows.  Taking an extensional formalized language
>(Church uses his version of simple type theory, but other choices can
>surely be made), we define a transfinite hierarchy of successive levels of
>such languages, successively connected by concept relations of appropriate
>types and levels.  For a given language, the terms of the first ascendant
>language are interpreted as denoting the concepts of the objects denoted by
>the terms of the original.  Algebraically speaking, the concept relation is
>defined as a partial morphism with respect to the fundamental relations or
>operations of the language, in this case the application of a function to
>its argument (Church uses the Sch\"onfinkel rediction of $n$-ary functions
>to singulary functions on $(n-1)$-ary functions, and so on); in other
>words, any concept of a function is a function on concepts of the argument.
>Moreover, it turns out that the morphism also respects all derived
>relations, such as the ones occurring in the boolean lattice induced by the
>naturally defined logical consequence relation (of containment) within eash
>propositional type.  The net result is that each intensional type may
>contain a number of concepts, related by the concept relation to a single
>extension; while each of the languages in question obeys the axioms of
>extensionality, this device allows to sneak intensionality back in,
>represented as a possibility of estabilishing stronger identity conditions
>on each ascendant level.  In fact, Church is fond of saying that he views
>intensionality as a relative phenomenon conditioned by stronger identity
>criteria: propositions vs.  truth-values, individual concepts vs.
>individuals, and so on.

This concludes the basic picture of what Charles Parsons calls "intensional
logic in extensional languages".  The fundamental feature of Logic of Sense
and Denotation consists in its containing a name for the sense of every
expression in its language.  By selecting appropriately strong
sense-identity criteria, we may arrive at a logic of belief.  In
particular, Church's Alternative (2), which stipulates that two expressions
are to be taken as synonymous iff they differ at the most in alphabetic
variance of bound variables and replacement of constants by synonymous
expressions (w.r.t. some list of synonyms) is clearly sufficient for any
sort of objective doxastic discourse.

A caveat is in order: note that, since we have to commit ourselves to the
objectivity of belief attribution, we can't identify beliefs with
psychological states of the believer, but must treat them as his
propositional attitudes.  On the other hand, any analysis of belief must
give an account of Aristotle's observation of its logical opacity, i.e. the
fact that the set of a person's beliefs is not closed under the relation of
logical consequence, whence Church's restriction of synonymy relation from,
e.g. a criterion of logical equivalence that would be suitable for alethic
modality.  Furthermore, we must account for denotational opacity of belief,
i.e. the fact that the set of a person's belief is apparently not closed
under substitution of extensional identicals.  Church's system succeeds in
doing that by adopting Frege's principle that terms in belief contexts
denote the entities that would be their senses in ordinary contexts.
Hence, if the terms `the Morning Star' and `the Evening Star' are taken as
coinciding in extension, both of them denoting the planet Venus, their
non-synonymy prevents us from substituting one for the other in a plausible
statement of belief ascription `Solon believed that the Evening Star is the
first star to appear in the evening sky.'  Additionally, extending the
language by postulating multiple senses can give an account of polysemous
cases. 

Note that all laws of extensional logic are taken to hold at each
intensional level; thus we can reason about concepts it the usual way.

Church's most recent theory is that of proposition and concept surrogates;
part of it is published in the collection "Themes From Kaplan", Almog et
al., ed.  It is a treatment of semantics that is purely denotative for
primitive constants of all types, but connotative for syntactically complex
expressions; the basic idea is to represent $n-$ary functions as ordered
$(n+1)$tuples of functions and their arguments; likewise for descriptive
terms and description operators.  Belief is then construed as a relation of
a subject to such ordered structure.  Some computer science work has been
done with this theory of proposition and concept surrogates; you might want
to look at the UCLA dissertation of Bijan Arbab.

SS:
>>>  Your own rhetoric, on the other hand,
>>>is no longer refreshing but has become tedious, "pare un libro
>>>stampato"--just
>>>like the raging of that poor nun seduced and abandoned by Don Giovanni.

MZ:
>>Poor nun indeed... it's nice to know that your taste for dissonance in
>>music has permitted you to appreciate Mozart and da Ponte -- about as much
>>as you appreciate Kant and company.

SS:
>I confess that I have to struggle with my Kant a bit more than with my Mozart,
>but I certainly regard both of them as worth the effort.

If you want to appreciate great art, you must be prepared to struggle with
it just as much as you would with the hardest science.  The claims of
recorded music peddlers notwithstanding, Mozart is not suitable for easy
listening any more than "Principia Mathematica" is suited for light reading.

Incidentally, I heard Minsky's talk at Harvard last Thursday.  He sounded
rather amusing, even if his repetition of the same pithy tales I've heard
him tell to an MIT AI lab audience over six years ago gave lie to his own
claim of cognitive irrelevance of long-term memories.  Moreover, the
evening was long on personal pap, but sadly short of substance; given
Marvin's fondness for Freud, I might have characterized it as his descent
into anecdotage.  Indeed, with his constant references to his unruly
daughters, Minsky reminded me of King Lear, rashly dividing the domain of
his intellect and boldly bestowing it on his ungrateful AI offspring.

Prithee, nuncle, tell me whether a madman be a gentleman or a yeoman...  To
unleash a notorious Quaylism: "How sad it is to have lost one's mind... or
not to have a mind at all".
                                                   

>-- 
>Stephen W. Smoliar; Institute of Systems Science
>National University of Singapore; Heng Mui Keng Terrace
>Kent Ridge, SINGAPORE 0511
>Internet:  smoliar@iss.nus.sg


`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'
: 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            :
:                                                                    :
'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`


