Dear Chris,
Well I agree that anything defined by axioms is affected when
those axioms change. However, at least some primitives just are –
membership would be one of them. Are you therefore arguing that in using
membership in the axioms that define other things, that that affects the
meaning of membership itself (as an example)?
I can see that there are clearly subsets of membership that are say
set membership and type membership, but I’m not sure that that changes
the meaning of membership.
Regards
Matthew West
Information Junction
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From: Chris Partridge [mailto:partridge.csj@xxxxxxxxxxxxxx]
Sent: 04 February 2010 14:52
To: 'Matthew West'; mail@xxxxxxxxxxxxxxxxxx; '[ontolog-forum] '
Subject: RE: [ontolog-forum] Foundation ontology, CYC, and Mapping
I copy in John’s comment ( he uses ‘elementOf’
where
you use ‘membership’) :
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.
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.
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.
As soon as you add more axioms to a theory, the
"meaning" of the so-called "primitives" changes.
From: Matthew West
[mailto:dr.matthew.west@xxxxxxxxx]
Sent: 04 February 2010 14:10
To: mail@xxxxxxxxxxxxxxxxxx; '[ontolog-forum] '
Subject: RE: [ontolog-forum] Foundation ontology, CYC, and Mapping
Dear Chris,
Could you elaborate please.
Though, as I think John Sowa pointed out in general (apologies
if it was someone else), the ‘root primitive’ membership has
different senses / meanings in the two cases – so it is not exactly the
same.
Regards
Matthew
West
Information Junction
Tel: +44 560 302 3685
Mobile: +44 750 3385279
matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx
http://www.informationjunction.co.uk/
http://www.matthew-west.org.uk/
This email originates from Information Junction Ltd. Registered
in England and Wales No. 6632177.
Registered office: 2 Brookside, Meadow Way, Letchworth Garden
City, Hertfordshire, SG6 3JE.