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

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Wed, 17 Feb 2010 14:30:02 -0600
Message-id: <1266438602.23598.215.camel@xxxxxxxxxxxxxx>
On Wed, 2010-02-17 at 11:32 +1300, Rob Freeman wrote:
> On Wed, Feb 17, 2010 at 6:50 AM, Christopher Menzel <cmenzel@xxxxxxxx>
> wrote:
> > ...
> > As for charge #3 that you direct at Pat above, Pat has never claimed
> > that a FO would include a complete, consistent, recursive
> > axiomatization of arithmetic.  You should be more careful about
> > lecturing others about what they don't understanding.
> This reduces the debate, once again, to a definition of the words
> "foundation ontology".    (01)

No, it doesn't have a thing to do with that.  The issue has only to do
with (your mischaracterization of) Pat's understanding of a FO.  You
claimed that Pat's project is impossible, which might well be true, but
the *reason* you gave for its impossibility was Goedel's incompleteness
theorem, i.e., the impossibility of a complete, consistent, recursively
axiomatizable theory of arithmetic.  I simply responded that Pat had
never claimed that a FO will include such a theory.  Therefore, it is
illegitimate for you to argue that his project is impossible on those
grounds.  That Goedel's theorem might show that some OTHER notion of a
FO is impossible is entirely irrelevant.    (02)

> Pat's exact words were (Feb. 1):
> "If you doubt that incompatible theories can be described in terms of
> common, more basic elements, try presenting some incompatible theories
> (and show how they are logically incompatible) and I will show how it
> can be done."    (03)

Which implies exactly nothing about whether a FO will include a theory
of arithmetic.    (04)

> I'm happy you agree the axiomatic set theories of mathematics are such
> incompatible theories.    (05)

I agree with no such thing; the claim in question is either trivially
false ("Any two distinct set theories are incompatible) or trivally true
("There are incompatible set theories.")  In point of fact, virtually
all set theories in common use -- ZF-style theories -- share a robust
axiomatic core.  Only a few quirky set theories that are primarily of
theoretical interest -- notably, those like Quine's NF that allow a
universal set -- are incompatible with that core.    (06)

> If Pat will now include the caveat, "not mathematics" (or anything
> based on manipulations of symbols?) I suppose that is progress of a
> sort.    (07)

I can make no sense of this whatever in the context.  (This is not an
request for clarification.)    (08)

> BTW Pat went on to say:
> "... (but if you do that, gird up your loins like a man and be
> prepared to *admit* that the general principle holds, and don't run
> off and bring up some orthogonal objection or keep adding more
> examples ad infinitum - I don't want to waste time for no productive
> purpose)."    (09)

His characterization of your posts about his project seems entirely
correct and his exasperation is understandable.    (010)

> Your other arguments are with the authors of my references. As I
> understand it you dispute the first author's use of the word
> "theories" instead of the word "logics".    (011)

There isn't really anything to dispute, as if there are two sides to the
issue.  "logic" is simply the wrong word.    (012)

> And you dispute second authors their proud claim of precedence for
> Thoralf Skolem.    (013)

They never claimed precedence for anything.  And again there is nothing
to dispute.  The authors simply gave an incorrect informal
characterization of the L-S theorem.    (014)

Chris Menzel    (015)

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