SUO: RE: RE: RE: RE: RE: Collections - Aggregation or Set
Dear Chris,
See comments below.
Regards
Matthew
============================================
Matthew West
Operations & Asset Management
Shell Services International
H3229, Shell Centre, London, SE1 7NA, UK.
Tel: +44 207 934 4490 Fax: 7929
Mobile: +44 7796 336538
E-mail: Matthew.R.West@is.shell.com
http://www.shellservices.com/
============================================
> -----Original Message-----
> From: Chris Partridge [mailto:chris_partridge@csi.com]
> Sent: 15 February 2001 12:50
> To: West, Matthew MR SSI-GREA-UK;
> standard-upper-ontology@majordomo.ieee.org
> Subject: SUO: RE: RE: RE: RE: Collections - Aggregation or Set
>
>
>
> Matthew,
>
> 1) Are sets abstract?
>
> I think there is some talking at cross purposes going on here.
MW: It sounds like it.
>
> My original question was what makes something abstract - what
> is the basis
> for the abstract/concrete distinction (as there seem to be a number of
> possibilities). A standard answer (in some communities) with a long
> tradition is that abstract things do not have spatio-temporal
> location - and
> concrete things do. Pat suggested that sets were abstract (a
> position you
> hold - from what you say below). Pat, I seem to recall,
> claimed that sets
> were abstract because they could not have spatio-temporal
> location (sorry if
> I have remembered incorrectly Pat). In other words, his
> 'definition ' of
> abstract was 'having spatio-temporal location'. My point was that some
> people (me and you included) are comfortable with regarding
> some sets as
> having a spatio-temporal location.
MW: I'm not sure its appropriate to count me in. I agree there are
classes that have properties that indicate spatio-temporal location,
but that doesn't mean I think the class has a spatio-temporal location,
it is the members of the class that share a spatio-temporal location
as a common property.
> So for you and I the claims that
> 'abstract means not having spatio-temporal location' and 'sets are
> abstract' - are inconsistent. This is my original point.
>
> As you do not hold to the first claim ('abstract means not having
> spatio-temporal location') you can make the second claim ('sets are
> abstract') without being inconsistent. But this leaves us
> without a notion
> of what your idea of abstract is. Perhaps you can elaborate.
> A common claim
> is that sets are by definition abstract (and sometimes (if one is a
> materialist) that only sets are abstract) - in this case the two terms
> collapse into one another.
MW: Well this would also be true for me. All abstract things are classes.
>
> One place among many to look for a discussion of these
> problems is David
> Lewis's on the Plurality of Worlds - pp. 81-86 Concreteness.
>
> 2) Groups and Collections.
>
> Again I think we are talking at cross purposes.
>
> You say:
> What I think you are doing is asking whether, given the one-to-one
> relationship, is it not possible to merge the two objects?
>
> My point was not that one could merge the notion of set and collection
> (though some mereologists have tried this route).
> My point was rather that one could have a third notion - of a
> group - with
> its own way of working.
MW: What way is there between transitive and intransitive? But I guess you
can define some other behaviour, but I understood the range was relatively
limited.
>
> To return to my question:
> > As you say, in different circumstances one might want to use
> > the set and the
> > fusion approach. However, what happens if you want to use
> > them both in the
> > same situation - or is this just impossible (as you seem to
> > suggest) and if
> > so why?
> And my example:
> > There are examples where we appear to be using both
> > approaches. One of the
> > useful properties of sets (as Frege noticed) was that one can
> > count their
> > members. So if I say 'those two hundred bolts weigh 2 kilo'.
> > Or, that 'there
> > are around 500 nuts in that 10 kilo'. How do we explain this?
> > That we are
> > talking about two closely related things, the fusion and the
> > set? This is
> > possible but requires more work to explain than the surface
> > structure of the
> > phrases suggest.
>
> I presume you would analyse each of these as two statements about two
> different but intimately related things:
> So 'those two hundred bolts weigh 2 kilo' is really saying -
> that class of
> bolts has 200 members and the fusion of the members weighs 2
> kilo. So your
> (our) approach involves some unpacking (revising) of the
> surface structure
> of the sentence. The sentence seems to be talking about one
> thing with two
> properties - but is really talking about two related things
> each with one
> property. And you would say that one of these things is
> abstract, the other
> concrete.
MW: Correct.
>
> Note: this approach suggests that some properties are
> typically (always)
> properties of individual and others of classes - a useful piece of
> knowledge, if true (or if possible to believe consistently).
MW: Yes. Classes seem to me to have very few properties of their own. Count
is one of the few. Perhaps more interesting is the assertion that only sets
can have a count.
>
> As you note:
> >MW: It is impossible because one is transitive and teh other
> transitive. So
> >it is OK to use each for different puposes, but not one for
> both purposes.
>
> It is impossible (or maybe just very difficult) to get an
> interpretation of
> the examples that respects the surface structure using just
> fusion (part)
> and set (member).
>
> But his does not mean it is impossible to come up with some
> interpretation
> that respects the surface structure.
>
> We said:
> > I think it would be difficult to prove option 3 is
> > inconsistent - what is at
> > issue is cost and benefits.
>
> MW: OK, then is Option 3 transitive or intransitive?
>
> CP: Part and group-member are transitive but the combination
> of them (the
> union of their relation classes) part-group-member is not, neither is
> class-member - as explained below.
>
> >
> > In the passage quoted, I mean *some* characteristics of both
> > - a sort of
> > middle way. Maybe it would work something like this. Groups
> > of groups would
> > share members in much the same was as super and sub sets do.
> > The National
> > Gallery Art Collection could be considered as a collection of the
> > collections that have been donated, along with stuff it
> > acquired itself. One
> > of the collections (the Wallace Collection?) would have a
> > painting as a
> > group-member, which would also be a group-member of the
> > overall work of
> > National Gallery Art Collection. So group-member is transitive - but
> > different from part. So a part of a group-member would not be a
> > group-member. We now need to tell a story about whether we
> > can have sets of
> > groups or, indeed, groups of sets.
> >
> > Note: under this scheme we can give an interpretation of the
> > nuts and bolts
> > examples above that respects the surface structure of the phrases.
> >
>
> Under this scheme - the group of 200 bolts (in the example) is a third
> object (existing along with the fusion and the class) which
> behaves like a
> physical object in having a weight (200 kilo) but also like a class in
> having a specific number of members. So we can respect the
> surface structure
> of the sentence - X is the group of 200 bolts, it has the
> property of having
> 200 members and the property of weighing 200 kilo. We are
> trading in ontic
> economy for the ability to be able to respect the surface
> structure of the
> description - and have a thing that can have properties that we have
> previously specified as belonging to disjoint categories.
>
> It seems to me that you are burdening your notion of fusion
> with too much -
MW: I don't follow this conclusion. I am using two very simple
concepts that will be there anyway, rather than creating some
third concept that will be inevitably relatively complex.
> to return to my example:
> > I am a little unhappy with your explanation of fusion.
> > You say:
> > MW: A fusion is some unordered aggregate of members of some
> > "atomic" object
> > type. So for example, a glass of water is a fusion of water
> > molecules. Water
> > molecule is the "atomic" level. What this means is that for
> > any aggregate
> > above the molcular level, the fusion is transitive. When you
> > go below the
> > molecular level, there is a whole part relation, but it is
> > assembly not
> > fusion. The atoms of each water molecule are assembled in
> > some sense into
> > molecules, not roaming around in some soup.
> >
> > This implies that fusions have some notion of the 'atoms'
> > they are composed
> > of build into them. It seems to me that we can regard the
> > 'glass of water'
> > as a fusion of water molecules, a fusion of atoms or a fusion
> > of (what?)
> > superstings. We could also regard it as an extended piece
> of atomless
> > matter. In each case we are talking about the same thing (it
> > seems to me) -
> > but under a different 'mode of determination'.
>
> MW: You are merely indicating different atomic levels that
> you could choose.
> the one chosen is usually indicated by the name of the
> fusion, so "a glass
> of WATER" implies water molecules, "a team of PLAYERS"
> indicates that player
> is the atomic level.
>
> In ordinary language we say 'a glass of water' and we can
> also say for the
> sake of the example 'glass of atoms' - then we seem to have
> three things -
> the fusion (of water molecules of hydrogen and oxygen atoms),
> the set of
> water molecules and the set of oxygen atoms.
>
> So how do we identify the atoms for a fusion? You say 'the one [atomic
> level] chosen is usually indicated by the name of the fusion'
> - but this is
> a statement about the language not what the language is referring to.
>
> It seems to me that the fusion by itself has no natural atomic level -
> whereas the sets do, their members (and the group/collection
> - if we were to
> introduce it, also does). Do you agree?
MW: For me I am quite sure that fusion needs to have one or more atomic
level.
You can choose the level. So when I look at a car park, and can choose if
I am looking at a fusion of cars, or of car parts. (Since the fusion is one
spatio-temporal extent, then we are talking about one object that is both
a fusion of cars, and a fusion of car parts).
MW: Mmmm. I think I may have just shot myself in the foot.
>
> Regards
> Chris