Assumption: set is a subtype of type, (01)
Hence: every instance of set is an instance of type, (02)
Hence, in particular {the moon, Matthew West, my left big toe} is a type (03)
This is an absurd conclusion. (04)
Hence the assumption is wrong. (05)
Even the set {all hats} is not a type; rather it is the extension of
a type (modulo the question of time, which is tricky, here} (06)
And the set {all hats in Cory's closet} is a subset of the extension of a type.
BS (07)
At 07:16 AM 2/4/2006, you wrote:
>MW,
>In semantic core I actually came to a "provisional" conclusion that set is a
>subtype of type and that the range of set operations was type. I can then
>talk about all the hats in my closet and many of the typical type operations
>are covered by the set operations. I also have an enumerated set whereby
>the membership is asserted. This is one of those conclusions that came based
>on "this is how all the pieces fit" rather than deep theory - and it rather
>surprised me. I will be interested to see how it works out here.
>I have NOT assumed all sets (or types) have static membership as that would
>be an orthogonal restriction in the model I have.
>
>-Cory
> > -----Original Message-----
> > From: ontac-dev-bounces@xxxxxxxxxxxxxx [mailto:ontac-dev-
> > bounces@xxxxxxxxxxxxxx] On Behalf Of West, Matthew R SIPC-DFD/321
> > Sent: Saturday, February 04, 2006 6:07 AM
> > To: ONTAC Taxonomy-Ontology Development Discussion
> > Subject: RE: [ontac-dev] Representation of attributes
> >
> > Dear Chuck,
> >
> > > >
> > > > MW: The key distinction I would tend to make is that a set
> > > > has extensionality as the basis for identity. That is, if two
> > > > sets have the same members, then they are the same set.
> > > >
> > > > MW: Types on the other hand, are not necessarily expected
> > > > to be the same if they have the same members.
> > >
> > > Yes - all good aspects that I intend to borrow for my own evolving
> > > definitions. Thank you.
> > >
> > > I might also interject that what I call Types and what I
> > > call Classes, are
> > > in themselves Sets. Every Type is a Set, yet not every Set
> > > is a Type -
> > > which agrees with what Barry stated about Types being an
> > > Extension of Sets.
> >
> > MW: The problem saying that every type IS a set (Barry actually says
> > every type HAS a set - at a point in time) is that as a type some may
> > have changing membership, yet sets essentially have unchanging membership.
> >
> >
> > Regards
> >
> > Matthew West
> > Reference Data Architecture and Standards Manager
> > Shell International Petroleum Company Limited
> > Shell Centre, London SE1 7NA, United Kingdom
> >
> > Tel: +44 20 7934 4490 Mobile: +44 7796 336538
> > Email: matthew.west@xxxxxxxxx
> > http://www.shell.com
> > http://www.matthew-west.org.uk/
> >
> >
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