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ProfessorMargaret Boden↓University of Sussex↓School of Social Sciences
↓Arts Building↓Falmer↓Brighton BN1 9QN↓UNITED KINGDOM∞
.<<0273 606755>>
                                            
Dear Maggie:

	Many thanks for your note and for %2Jean Piaget%1 which I
read with interest.  It suggested some ideas which I hope I
will have time to explore.

   	1. The experiment in which children confuse bigness with
length and fatness is a kind of non-monotonic reasoning
which may differ from those studied by Reiter, McDermott,
Doyle and me.  I can formalize it using my %2circumspection%1, but I'm
not happy with it, so I'll look for something more.    

	Like almost everyone else, I can think of other
interpretations of Piaget's results and variant experiments to
test them.  However, one general phenomenon which explain
the counterintuitive failures of some of his subjects may be
compartmentalization of abilities.  Suppose we offer a child
some candy with a  clay-like texture and ask if it's enough and
the child says it wants more and we stretch the piece to make
it longer and ask if it's enough.  My guess is that a child
who has no sense of conservation, according to Piaget's experiment,
will not believe it is being offered more candy than before.
It will be especially inclined to balk if the offer is made
by another child.

	However, I am suggesting that the child's concept
of conservation is compartmentalized to evaluating amounts of food or
something else which it is being offered.

	I guessed something analogous to the sleeping cows variant
of tee comparison experiment.  Also it seems to me that a child
who cannot answer that her sister has a sister may well answer
that cousin Billy has a sister.  It isn't inability to see
another's point of view but rather inability to substitute oneself
into certain contexts.

	2. I regard words like "dialectical" with great suspicion,
but now that I am looking for applications of non-monotonic reasoning,
I thought I found an "entry".  When one assumes a sentence and
eventually gets the opposite by some reasoning, one way out of the
contradiction is to split a concept that occurs in the reasoning.
That is, we say that certain occurrences of some symbol
are to be replaced by occurrences of two different symbols.
This has a certain thesis-antithesis-synthesis quality.
It may be analogous to doubling a gene and modifying one
of the copies.  It is not analogous, however, to considering
dialectics as being causal interaction more complex than a
simple chain.

	After I have remarked on these  suggestive ideas, my
disputatious nature won't let me leave well enough alone.

	1. On p. 47 you criticize teaching a too young child
bits of arithmetic without the concept of set and setting
it to memorize the kings of England.  I tried teaching my
daughter Susie arithmetic with sets after having successfully
taught her to read with totally poor results.  I think
the trouble was that new math set theory is totally
pedantic and dull.  What represented a new way of looking
at mathematics for Frege and Russell is not acceptable
for children because it offers no scope for the imagination.
Somehow small children like to count, and it gives them
the notion of an infinite set, and they play with it.  The
kings of England may also provide hooks on which other facts
can be hung.  I am not sure that not knowing that George VI
came after George III constitutes a refutation.

	2. While I feel some sympathy with Piagetian educational
ideas,, it makes me nervous that you don't ask whether it too
may just amount to speeding up by a few months processes that
will occur anyway.  A skeptic may well doubt the utility of
almost all early education given that children who have been
out of school catch up so quickly.

	3. I don't think that studying dynamic mental processes
can replace studying the epistemology of common sense in children.
The latter will be required for a good understanding of the
former.

	The fact that AI never flew the flag of cybernetics
was a conscious decision on my part that Minsky and I
would be better off at M.I.T. using a term that would
not suggest to anyone that they ask Wiener to comment
on what we wanted to do and make suggestions.  We also
wanted to avoid the whole control theory crowd who
were inclined to take nothing seriously that didn't have
differential equations or Fourier transforms.

	I expect to pursue a number of the references in the book.

	Anyway you have readers.

.reg