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Re: [ontolog-forum] Search engine for the ontology

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Chris Menzel <cmenzel@xxxxxxxx>
Date: Mon, 3 Mar 2008 08:45:17 -0600 (CST)
Message-id: <alpine.DEB.1.00.0803030835460.31873@xxxxxxxxxxxxxxxxx>
On Mon, 3 Mar 2008, Barker, Sean (UK) wrote:
> The objection to ontologism from the mathematical point of view is
> that alternative choices of axioms give alternative mathematical
> systems. The non-Euclidean geometries are variations on the fifth
> postulate that all non-parallel lines meet. The way I was taught, say,
> ring theory, was that it was group theory with additional axioms. That
> is, the mathematical system you get is dependent on the axioms you
> use.  Similarly, the logic you get depends on the axioms, such as the
> number of truth values you choose.
> Given that systems can contradict each other if they have different
> axioms, it is difficult to see that a single meta system could derive
> all mathematical principles...    (01)

Worse, even if we ignore this cogent objection, the mathematical goal of
"ontologism" is (provably) impossible to reach.  By Gödel's
incompleteness theorem, we can't even have a complete set of principles
for elementary arithmetic, let alone all of mathematics.    (02)

-chris    (03)

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