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

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: Rob Freeman <lists@xxxxxxxxxxxxxxxxxxx>
Date: Fri, 5 Feb 2010 16:03:17 +1300
Message-id: <7616afbc1002041903x20d8bf9av4ca396811aa95e0f@xxxxxxxxxxxxxx>
Have been scanning through messages of the last couple of days trying
to get an idea what point the discussion has reached.    (01)

My impression is that in the face of a nice exposition by Chris M, Pat
C conceded it *might* not be possible to describe all of the
incompatible axiomatic set theories of mathematics "in terms of common
more basic elements", but hopes such exceptions will be sufficiently
rare for it not to matter:    (02)

Pat C: "I do not know how to prove that *every* pair of incompatible
theories can be specified by axioms using some common set of agreed
terms.  To make the FO project worth funding, don't think it is
necessary to prove that *mathematically*, but if we can conclude that
exceptions would be rare..."    (03)

It is good we seem to have reached a point where Pat C is not
contesting an objection in principle, but is resting his argument for
a FO on the hope that the objection won't matter.    (04)

Matthew. You seem to be suggesting a theory capable of deriving all
the axiomatic set theories of maths which you call "4D
extensionalism". Am I right that you think it might be possible to
derive all of mathematics using this theory?    (05)

Doug. You made a distinction between what can be DEFINED and what can
be DERIVED and said of the axiomatic set theories of mathematics:    (06)

"Although the theories are not DERIVED from a single theory, they
should be able to be DEFINED using terms less rigorously defined."    (07)

I'm not sure what you mean by "defined". How is what you mean by
"defined" different from what can be achieved using, say, the binary
code which computers already use?    (08)

John. You said of my statement that "I can't imagine how to model an
infinity of theories, let alone move between them, unless it is by
generating them" that we model real and natural numbers 'but we don't
"generate" them unless we need them.' Which I don't think I need to
argue at this point. I would rather emphasize the similarities in our
arguments, viz. no single theory which explains all others.    (09)

If there are any other important comments to me I've missed, could
someone point me to them.    (010)

-Rob    (011)

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