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[ontolog-forum] Addendum

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 30 Nov 2010 22:41:04 -0500
Message-id: <4CF5C3D0.7080108@xxxxxxxxxxx>
Ed,    (01)

I forgot to answer the following question:    (02)

> Does John really believe that "all we like sheep" have followed
> Quine uncritically?    (03)

My obvious answer is "No, of course not."    (04)

But my second answer is that we had very little choice.  We were
exposed to a limited number of alternatives about the nature
of logic and its role in language.  The main options were    (05)

  1. Most logicians and AI researchers:  Logic (i.e., predicate
     calculus) is fundamental to all semantics and reasoning.    (06)

  2. Many psychologists, linguists, and some AI researchers:
     Logic is irrelevant to language and human ways of reasoning.    (07)

  3. Some linguists and psychologists:  There is a "natural logic"
     that underlies language, and finding that logic is an important
     goal of linguistic research.    (08)

Groups #1 and #2 had a very narrow view of logic that was based
on a family of logics that all used predicate calculus notation
and some variation of a Tarski-style semantics.  Group #3 hoped
to find something different, but they weren't sure what.    (09)

I was a graduate student in Applied Mathematics at Harvard in the
late 1960s, but I also took a course in logic in the philosophy dept.
And I cross-registered for Marvin Minsky's course in AI at MIT.    (010)

For Minsky's course, I wrote a term paper, in which I presented my
first version of conceptual graphs.  My goal was to reconcile #1,
#2, and #3.  I talked to both professors and other grad students,
but nobody mentioned (or knew) that in the Harvard library, there
was a huge stack of papers about the alternative I was looking for:
Peirce's manuscripts.    (011)

I didn't discover Peirce's existential graphs until 1978 -- when
I read about them in Martin Gardner's Mathematical Games section in
the _Scientific American_.  A lot of other people were developing
versions of semantic networks that used logic, but they never saw
Peirce's EGs until I showed them.    (012)

One of the logicians I spoke to at Harvard was Hilary Putnam.  He
didn't mention Peirce, but he later wrote an article about the history
of logic in which he admitted that he had no idea how much of logic
had been invented by Peirce.  In the following article, written in
1982, he said "In fact — and this may be surprising to others as
it was to me — the term 'first-order logic' is due to Peirce!":    (013)

    http://www.jfsowa.com/peirce/putnam.htm    (014)

Putnam also said "Frege's notation (like one of Peirce's schemes, the 
system of existential graphs) repelled everyone..."    (015)

The only thing that is repellent about existential graphs is their
unfamiliarity to mathematicians who are used to algebra.  In the
following article, written in 2002, the psychologist Johnson-Laird
suggested that Peirce's graphs may be a good candidate for that
Holy Grail of group #3 -- natural logic:    (016)

    http://mentalmodels.princeton.edu/papers/2002peirce.pdf    (017)

P J-L:
> Peirce’s existential graphs are remarkable. They establish the feasibility
> of a diagrammatic system of reasoning equivalent to the first-order predicate
> calculus. They are therefore a precursor to recent systems of diagrammatic
> reasoning (see, e.g., Barwise & Etchemendy, 1992). Peirce, however, took pride
> not in the pedagogical applications of the graphs but in the way they 
> the mental processes of reasoning. They anticipate the theory of mental models
> in many respects, including their iconic and symbolic components, their
> eschewal of variables, and their fundamental operations of insertion and
> deletion. Much is known about the psychology of reasoning (see, e.g., Evans,
> Newstead, & Byrne, 1993). But we still lack a comprehensive account of how
> individuals represent multiply-quantified assertions, and so the graphs may
> provide a guide to the future development of psychological theory.    (018)

In fact, Peirce's own claim was that the rules of inference for EGs
provide "a moving picture of the mind in thought."    (019)

What makes me angry is that Quine was sitting on those manuscripts for
over half a century.  During that time, he was preaching the gospel of
Frege and never suggested that any of his students do a comparative
study of Peirce and Frege.  I was at Harvard, but I had to read about
those manuscripts as a "mathematical game" from Martin Gardner.    (020)

John    (021)

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