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Re: [ontolog-forum] What is logic?

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Fri, 09 Mar 2007 12:35:54 -0500
Message-id: <45F19AFA.9070109@xxxxxxxxxxx>
Till, Jeffrey, and Patrick,    (01)

Re Till's paper on institution theory:  I agree that definition
is almost as broad as mine, and I also agree that institution
theory is well worth considering as an important generalization.    (02)

TM> May I point to a recent paper with title "What is a logic?",
 > that also has a rather broad (but formal!) view on the notion
 > of logic.    (03)

However, institution theory is just one of many formalisms that
can be used, and all of them fall under the general definition
of logic by C. S. Peirce:    (04)

     "the formal science of the conditions of the truth of
     representations" (CP 2.229)    (05)

This definition, although it does not use any formal notation,
is sufficiently general to cover all of them.  It includes any
version of logic that uses any notation, including diagrams
and stylized or controlled versions of natural languages.    (06)

Re John the Evangelist:  I quoted that line partly tongue in
cheek and partly in all seriousness.    (07)

Jeffrey S> If you wish to be precise about defining logic,
 > quoting St. John is not the way to proceed.  That is not
 > what he was talking about at all.    (08)

He was putting his version of the gospel into the framework of
Greek philosophy from Heraclitus (circa 500 BC) to the first
century AD.  He was influenced by the Jewish philosopher,
Philo of Alexandria, who had written extensively on harmonizing
the Jewish Bible with Greek philosophy.  And the words he
used were largely the same as those used by Heraclitus, who
had a very strong influence on Aristotle's teacher, Plato.    (09)

Both Plato and Aristotle used the word "logos" in a way that
was consistent with Heraclitus.  Aristotle explicitly called
speech "external logos" as opposed to internal experiences
(pathemata), which he called "logos in the psyche".  He invented
syllogism as a method for analyzing logos, external or internal.    (010)

PD> ... in the Septuagint (translation of the Hebrew Bible
 > into Greek), which dates to fairly close to that time
 > period, logos was used to translate dabar, or 'word' as it
 > is loosely translated into English. Logos has a fairly wide
 > range of meanings depending upon the writer, time period, etc.    (011)

Unlike the other gospels, which were originally written in Aramaic,
John wrote directly in Greek, and he used the same words -- logos,
panta, and gignomai -- as in fragment #1 by Heraclitus:    (012)

    "all things (panta) come into being (gignomai) according
    to this logos"    (013)

The big distinction that Heraclitus made was between the ever
changing "physis" (nature) and the eternal "logos".  This
distinction was critical for both Plato and Aristotle, even
though there were many differences in detail.    (014)

But the critical point for Heraclitus and Plato is that the
logos consists of the eternal forms as opposed to the ever
changing physis.  Aristotle acknowledged the distinction,
but he treated the logos as descriptive, rather than creative.
That is close to the modern notion, and I don't want to get
into debates about whether Heraclitus, Plato, or John had
different points of view on that question.    (015)

PD> ... if we define logic as broadly as John suggests, then it
 > becomes as vacuous as "Semantic" is in current usage.    (016)

Absolutely not.  Notice the critical terms "precise" and "truth".
Notations that are not precise or capable of being made precise
are not a version of logic.  And representations that do not
or cannot make any assertions about the truth or falsity of what
they represent are not logic.    (017)

As an example, Peirce made the point that a portrait is not
an assertion.  But the combination of the portrait together
with a label that identifies the person portrayed would be
an assertion that could be judged true or false.  Therefore,
that combination would qualify as a notation for logic.    (018)

John Sowa (not the Evangelist)    (019)

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