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Re: [ontolog-forum] axiom

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Tue, 22 Apr 2014 23:31:09 -0400
Message-id: <535733FD.1000908@xxxxxxxxxxx>
Bruce, Ed B, Leo, Ed L,    (01)

> maybe this concept of “axiom” needs a hard-edged definition in
> this “ontolog” context.    (02)

No.  That wouldn't help.  Debates about how to define the word 'axiom'
are as pointless as trying to define the word 'primitive'.  That's a
related question that raises its ugly head from time to time.    (03)

Ed B
> It is worthy of note that 99% of all ontologies, information models
> and UML models consist of nothing but terms and axioms.  Everything
> captured in the model is offered without any evidence for its validity.    (04)

This point is significant.  A very precise formal statement is necessary
for detailed reasoning (or for designing a database or program).  But if
that statement comes out of thin air, its precision does not mean that
it's an accurate reflection of anything in the subject matter.    (05)

> Quine’s notions on ontological commitment (e.g., his slogan, "To be is
> to be the value of a variable"), which is still an often discussed topic,
> especially in metaphysics/ontology.    (06)

That's an example of a criterion that can be used to check what the
terms in an ontology refer to.  Whenever you have a variable x in an
ontology, you can ask the question:  "What does x refer to?"    (07)

If you can't give a clear answer to that question, there is a serious
problem with the ontology.  One of the best features of the methodology
established by Aristotle and his followers was to associate a question
with each category of the ontology.  For example, see slides 5, 6, 7 of
http://www.jfsowa.com/talks/aristo.pdf    (08)

I believe that developing a methodology with a question tied to each
category would be more useful than debating the meaning of 'axiom'.    (09)

Ed L
> the structures you arrive at may look like these...    (010)

I like the idea of using graphic conventions for illustrating the
underlying structures of an ontology.  The tree diagrams we use
in ontology today were invented by Porphyry (or more likely by
somebody even earlier) in the 3rd c. AD.    (011)

See slide 3 and 4 of aristo.pdf for the "pincushion diagrams" that
Paul Slade used to illustrate the difference between Plato and
Aristotle.  Slide 9 for the tree of Porphyry.  Slide 27 shows the
rotating circles by Raymond Lull.  Slides 31 to 32 for Venn diagrams.    (012)

I believe that a good methodology based on criteria such as Quine's
and questions such as Aristotle's supplemented with diagrams of various
kinds -- pincushions, trees, rotating circles, Ed L's examples, etc.
-- can be very helpful.    (013)

I like the multiple kinds of UML diagrams, and my only complaint would
be that the number of different kinds of diagrams should be open ended.    (014)

Note the diagrams in organic chemistry, Feynman diagrams in nuclear
physics, circuit diagrams in EE, etc.  Every subject can benefit from
diagrams that are well matched to the structures it studies.    (015)

John    (016)

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