Barry,
While I hesitate to disagree with you in this domain, that doesn't seem to
hold up. (01)
You may define a set by rule; the set of all furry animals.
Or, by enumerating membership; {green, blue, rock} (02)
You may define a type by rule; containers of food
Or by enumerating membership DaysOfWeek = {Monday, Tuesday, Wednesday... } (03)
You may perform set operations on the extent of types and may mix sets and
types in the same set operations - and doing so may define a set or a type. (04)
Simply by being a member of a set, instances can now satisfy a new predicate
(memberOf set). Many feel that a type is defined by such predicates. (05)
While I am not suggesting they are the same thing, this would suggest that
the relation between sets and types to their members/extent is the same
relation. I still struggle with the difference, other than type being
intent to define a conceptual grouping rather than an arbitrary grouping. (06)
-Cory (07)
> -----Original Message-----
> From: ontac-dev-bounces@xxxxxxxxxxxxxx [mailto:ontac-dev-
> bounces@xxxxxxxxxxxxxx] On Behalf Of Smith, Barry
> Sent: Monday, February 06, 2006 7:59 PM
> To: ONTAC Taxonomy-Ontology Development Discussion
> Subject: RE: Categorization (was RE: [ontac-dev] Representation of
> attributes)
>
>
> You can include items on a list. Any items you like. The
> set-membership relation is like the relation between an item on a
> list and the list.
>
> To stand in the instance relation to a type, in contrast, you need to
> be of that type and that means that you have to be a certain way: you
> have to have the right sort of DNA, or be created on the basis of the
> right sort of plan using the right sort of machine, and so forth.
>
> BS
>
> At 04:33 AM 2/6/2006, you wrote:
> >Dear Barry,
> >
> >This does not answer my question, which is not about the difference
> >between a set and a type, but between the difference in nature of the
> >membership/instance of relationship.
> >
> >So please what is different in the nature of these relationships (not
> >thing things they bring things into relationship too)?
> >
> >
> >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/
> >
> >
> > > -----Original Message-----
> > > From: ontac-dev-bounces@xxxxxxxxxxxxxx
> > > [mailto:ontac-dev-bounces@xxxxxxxxxxxxxx]On Behalf Of Smith, Barry
> > > Sent: 04 February 2006 13:41
> > > To: ONTAC Taxonomy-Ontology Development Discussion
> > > Subject: RE: Categorization (was RE: [ontac-dev] Representation of
> > > attributes)
> > >
> > >
> > >
> > > >MW: Noone has yet been able to explain the difference (or
> > > even offer an
> > > >explanation) though more than one has asserted a difference.
> > > I am simply
> > > >seeking enlightenment.
> > >
> > > Sets are mathematical objects; the set-membership relation is an
> > > abstract relation, which obtains independently of time and change.
> > > Sets can be defined arbitrarily, as in the {the moon, Matthew West,
> > > redness, 27} case. Sets are subject to arbitrary iterations,
> > > combinations and intersections, ad nauseam, as in the
> > >
> > > {{{{{{{{{{{{{{{{{{{{Matthew West}}}}}}}}}}}}}}}}}}}
> > >
> > > case. Which sets exist is a matter of mathematics and of
> > > arbitrary definition.
> > >
> > > Types are entities (something like invariant patterns, commonalities,
> > > kinds) in reality. Which types exist changes from epoch to epoch
> > > (Darwin tells us) and even from year to year (as new varities of
> > > potato chip are invented). Which types exist is a matter of
> > > observation and scientific exeriment. Types are not subject to
> > > arbitrary iterations, combinations and intersections. There is no
> > > type 'rabbit or steering wheel'.
> > >
> > > BS
> > >
> > >
> > >
> > >
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