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Re: [ontolog-forum] What is logic?

To: patrick@xxxxxxxxxxx, "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Fri, 09 Mar 2007 10:16:03 -0500
Message-id: <45F17A33.3090506@xxxxxxxxxxx>
Patrick,    (01)

I changed the subject line of this thread.    (02)

JFS>> Ontology and logic are different subjects.  But I
 >> would add that *every* precise declarative notation that is
 >> capable of making statements that are judged true or false
 >> *is* a version of logic.
 >> UML diagrams, for example, are a version of logic.  The
 >> declarative subset of natural languages forms a version of
 >> logic -- and in fact, NL (actually Greek) was Aristotle's
 >> inspiration for the first formal logic.  And *every*
 >> statement in *every* version of logic that anyone has
 >> ever invented can be translated into natural language.
 >> So anyone who is doing any work on ontology is stating
 >> their results in some version of logic (but possibly in
 >> a rather imprecise and insufficiently understood version).    (03)

PD> My, what a large definition of logic you have.    (04)

That's the traditional definition, which goes back to Aristotle.
Historically, logic evolved from language.  Its name comes from
the Greek logos, which means word or reason and includes any
language or method of reasoning used in any of the -ology fields
of science and engineering.  Aristotle developed formal logic as
a systematized method for reasoning about the meanings expressed
in ordinary language.    (05)

In modern terms, a logic may be defined as any precise notation
for expressing statements that can be judged true or false.  To
clarify the notion of "judging," Tarski defined a model as a set
of entities and a set of relationships among those entities.
Model theory is a systematic method for evaluating the truth
of a statement in terms of a model.    (06)

But Tarski quoted Aristotle as a basis for his approach, and
he claimed that he was formalizing the informal methods.    (07)

John the Evangelist had an even larger definition:    (08)

    "In the beginning was the logos, and the logos was with God,
    and God was the logos.  It was in the beginning with God.
    All things (panta) came into being through it, and without it
    nothing that has come to be came into being."    (09)

In short, being (to on) depends on the logos.  Therefore, the
study of being (ontology) must depend on logic (the study
of the logos).    (010)

John    (011)

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