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

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Matthew West" <dr.matthew.west@xxxxxxxxx>
Date: Sun, 7 Feb 2010 08:57:00 -0000
Message-id: <4b6e805e.1818d00a.1220.ffffa8b2@xxxxxxxxxxxxx>
Dear Rob,    (01)

> >> 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?
> >
> > MW: Maths is abstract and has nothing to do with 4D which is about
> > individuals.
> I don't see how this gels with your statement on Feb. 3.
> <<<
> RF> On 1) I agree. I just don't think it is possible to find a theory
> > which will map between all other theories (see my post to Pat C
> asking
> > him to find a FO for mathematics.)
> MW: It is the search for such a theory that has lead me to 4D,
> extensionalism of individuals and classes, and possible worlds, as used
> in
> ISO 15926. I am quite happy to issue the challenge to identify some
> other
> viewpoint that cannot be mapped into or out of it
> <<<
> "Some other viewpoint" seems to me to include all the theories of
> maths.    (02)

MW: However, that was not my intent. What I meant was viewpoint of the
world. Also it is not itself an all encompassing theory, but a framework
within which as much of an all encompassing theory as you wish can be
> If you want to restrict your theory in some way which excludes maths
> that's OK (although the proof for maths addresses all manipulations of
> symbols, so is quite general.) But then it wouldn't address my point
> to Pat C about FO.    (03)

MW: I forget what that was now. Because Maths is abstract you can have
anything you like that is internally consistent within some theory. Some
theories will build on others, some will not. Some will start from
alternative foundations. The approach I take has space for them, but does
not need all of them to describe the world around us.
> Either way, I take it you are not contesting the impossibility of a FO?    (04)

MW: It depends what you think an FO is, which seems to be one of the
questions that need to be settled still. However, I don't think it
reasonable to expect to develop a single ontology that everyone will sign up
to.    (05)

Regards    (06)

Matthew West                            
Information  Junction
Tel: +44 560 302 3685
Mobile: +44 750 3385279
http://www.matthew-west.org.uk/    (07)

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