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Re: [ontolog-forum] Foundation ontology, CYC, and Mapping

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Wed, 03 Feb 2010 22:47:36 -0500
Message-id: <4B6A4358.90108@xxxxxxxxxxx>
Pat and Chris M,    (01)

PC> Thanks, that is getting closer to specifics, but I am still unclear
 > exactly where the logical inconsistencies lie.    (02)

The inconsistencies lie in the choice of axioms.  All versions of set
theory are based on two dyadic relations:  subsetOf and elementOf.
The differences lie in the axioms that are asserted in each theory.    (03)

You could call subsetOf and elementOf primitives, but they don't
behave the way that you have been claiming for the kinds of
primitives you want.  In particular, their "meaning" is determined
by the axioms and each version of set theory has a different set
of axioms.    (04)

That is one of the main reasons why I keep saying that this search
for primitives is misguided.  It's totally irrelevant what set of
words (or predicates or relations or types or concepts or whatever)
you start with -- because all the serious work is done by the axioms.    (05)

As soon as you add more axioms to a theory, the "meaning" of the
so-called "primitives" changes.    (06)

John    (07)

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