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Re: [ontolog-forum] Axiomatic ontology

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sat, 27 Sep 2008 16:16:36 -0400
Message-id: <48DE94A4.3010102@xxxxxxxxxxx>
Rob and Rick,    (01)

Joseph Goguen had made important contributions to category theory,
logic, and related topics.  But he also had a broad view of many
issues in cognitive science, and he collaborated with people who
had strong positive *and* negative views about logic.  Among
other things, he was the editor in chief of the _Journal for
Consciousness Studies_, and he was on the advisory board of the
UCSD Center for Computing and the Arts.    (02)

Arun Majumdar and I had begun some collaborations with Goguen
in 2006, but he died of cancer in 2007 before we were able to
complete the work.  But his life's work was guided by the view
that statements about logic at either extreme are wrong.  His
homepage at UCSD is still available, and I suggest that anyone
who is interested should download papers while it is there:    (03)

    http://www.cs.ucsd.edu/~goguen/    (04)

RF> The work of Schmidhuber and Hutter avoid these "pitfalls"
 > [of logic] by ignoring formal logic and seeking a basis for
 > meaning in prediction/probability.    (05)

That's like a carpenter who struck his thumb with a hammer and
later avoids the pitfalls of hammers by using nothing but saws.
Goguen (like many others, including me) firmly believed in the
value of logic, but he was aware that a complete bag of tools
for processing language would require many more options.    (06)

RF> Frankly I disagree with the one Soames addresses.  I don't
 > think the answer lies in "truth".  My understanding is that
 > there are big problems with determining the "truth" of many
 > statements.    (07)

I would qualify the first two statements, but I agree with
the third.  I agree with Soames and many others that truth
is an important aspect of meaning, and an adequate theory of
semantics should be able determine truth for the kinds of
questions that people routinely answer yes or no.  But I
also agree that there are "big problems" that require more
than just a model theory along the lines of Tarski or Kripke.    (08)

RF>> You haven't seen anything relating Category Theory
 >> with geometric theories in physics have you?    (09)

RM> Actually, I think I have seen that and I think you can
 > find an active dialog on those things here ...
 > http://golem.ph.utexas.edu/category/    (010)

That site has pointers to many good resources.  Among them
is a hundred-page tutorial that emphasizes geometries:    (011)

    Categories for the practising physicist    (012)

The first four pages of that tutorial start with an example
that applies the ideas of category theory to the problems of
cooking potatoes and carrots.  On page 14, it addresses the
question of why tigers have stripes and lions don't.  The
formalism gets much denser in later sections, but the authors
continue to address geometrical issues.    (013)

Another tutorial that relates categories and logic is    (014)

    Introduction to Categories and Categorical Logic    (015)

A good strategy would be to read the first dozen pages of both
of these tutorials before going into more detail in either one.    (016)

Another paper on Coecke's web site shows how category theory
can be used to relate classical physics to quantum mechanics:    (017)

    Classical and quantum structures    (018)

John    (019)

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