SUO: RE: RE: RE: Collections - Aggregation or Set
Chris,
The points you make are very important for they are the foundation elements
of SUO work. Perhaps we have to agree to the definitions such as
aggregation, set, group, element and etc. The definitions then must be
posted to keep the development, of SUO and related discussions, on the
'straight and narrow'. If we find that we have the need to amend the former
definitions we will do so, but for now let us set a few definitions 'in
stone' as a reference.
Sincerely
Edward
Tel: (732) 427-4122 DSN 987-4122
Fax (732) 427-3440
E-Mail edward.dawidowicz@mail1.monmouth.army.mil
-----Original Message-----
From: Chris Partridge [mailto:chris_partridge@csi.com]
Sent: Wednesday, February 14, 2001 7:04 AM
To: West, Matthew MR SSI-GREA-UK;
standard-upper-ontology@majordomo.ieee.org
Subject: SUO: RE: RE: Collections - Aggregation or Set
Matthew,
I was dealing with two issues in the email. One to do with the abstractness
of sets - the other with how to treat groups.
The football team example was taken from Pat - who said that a football team
could not be a set.
You say:
MW: My view is that Group is a word which is used with different meaning in
different contexts. For this reason I have carefully not used it in the work
that I have done, but when encountered would always start by saying "now
when you say group - do you mean aggregate or set?"
And it seems to me (as you know) that this is probably the most sensible
route - i.e. a combination of options 1 and 2 as required (not just 2) - as
you say below. But it does require some explanation.
It also seems to me that if you have your 'atomic elements' you can
construct either the fusion or the set - the only question is whether it is
useful.
So I would interpret your comment as that you think it is not useful to
treat football teams as a set - but that one could do so. My point about the
abstractness of sets (a pretty standard point) is that if one were to do so
would it have a spatio-temporal location.
You say:
MW: In the sense that the members of the set (in particular the temporal
parts that are members of the set) have a location in common, then this is
fine. But total weight does not work for me. That is transitive.
I think this means that you accept that some finite sets are not abstract.
As to weight, the problem is not that there is no algorithm to calculate
it - rather that it is implausible.
Note: I think the merged ontology suggests they are - am I right Ian? If so,
do we want to change it?
Turning to the group point.
I think one can make a reasonably consistent system using any of the three
(group) options - and probably many more. The issue seems to me more to do
with plausibility, economy (parsimony) and elegance.
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?
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.
You say:
> We
> have the notion of
> a member of a group (collection, or whatever), which has
> characteristics of
> both.
MW: I don't believe you. This would mean it was both intransitive and
transitive. So whilst people may be switching rapidly between the two
concepts, you can't combine them without a problem.
I think it would be difficult to prove option 3 is inconsistent - what is at
issue is cost and benefits.
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.
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'.
This strays into the notion of mass properties.
You say:
MW: Now let us look at a football team. Here the "atomic" level is a player
(much larger than in our water example). I can have some lower and higher
level fusions than the team. A lower level one could be the forwards, the
backs, or the midfield. A higher level one could be the squad, or even the
league players. However, as you rightly say, a players hand is below the
atomic level, and is not a direct member of a fusion, but is necessarily
assembled to someone who is.
In this example, the attractiveness of the set approach is that the level is
built into the object. Similarly with the glass of water - the set of water
molecules is different from the set of atoms.
It seems to me that your notion of fusion here is, in some ways, very close
to the notion of group in option 3. Is a fusion of the lower level fusions a
higher level fusion with the same 'members'? What is the relation between
the team and the league players - part of?
There seems to be another problem - one that, maybe, the military members of
the list can answer. It seems to me that in ordinary usage people are not
always clear about what the atoms of a group are. Take a fleet. We talk
about a fleet (typically of ships). But, it seems to me to be OK to say
that, for example, the 2nd Battalion of Guards are part of the fleet. What
does this mean?
Nevertheless, I agree with you that a combination of options 1 and 2 seems
to make the most sense.
of the a-
-----Original Message-----
From: owner-standard-upper-ontology@ieee.org
[mailto:owner-standard-upper-ontology@ieee.org]On Behalf Of West, Matthew MR
SSI-GREA-UK
Sent: 14 February 2001 11:26
To: standard-upper-ontology@majordomo.ieee.org
Subject: SUO: 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/
============================================
<snip>
> Dear Chris,
>
> > You also wrote:
> > Notice it only arises for entities that are located in space
> > and time: abstract things like sets and numbers are not
> classified in
> > either of these ways. (Note in particular that a set of physical
> > things is not itself physical.)
> >
> > Are you taking physical and abstract as two sides of the same
> > distinction
> > here - or are there more types. It also seems to me that
> the complete
> > banning of spatio-temporal location for sets can be
> > problematic if you want
> > to think of things such as groups (football teams, and so on)
> > as sets. Some
> > people have suggested this - and ordinary language (for what
> > it is worth) at
> > least supports the view that they have a location ("the
> > English football
> > team was in Hungary last week"). So treating sets as abstract
> > seems to me a
> > choice which blocks off the possibility of treating 'physical
> > groups' as
> > sets.
>
> MW: Well I certainly don't see the England Football team as a
> set. I would
> see them as a non contiguous aggregate. So I would have no
> trouble talking
> about the total weight of the team (as I have said elsewhere
> - how much does
> a class weigh?).
> ><snip>
> CP: The issue here is not about how to deal with a particular
> item, but how
> the item influences the overall architecture. We have a
> notion of member (of
> a set), which is not transitive. Where we (well, some people)
> would like to
> somehow say the set of physical things is not itself a
> physical things.
MW: Yes I support this.
> We
> also have a notion of part, which is transitive. Where we
> would like to say
> a whole composed of physical parts is itself physical.
MW: Yes I support this too.
> We
> have the notion of
> a member of a group (collection, or whatever), which has
> characteristics of
> both.
MW: I don't believe you. This would mean it was both intransitive and
transitive. So whilst people may be switching rapidly between the two
concepts, you can't combine them without a problem.
> Note: we use member of and part of for group - and I am
> not sure quite
> where the differences lie (and I would be interested in
> finding out).
MW: My view is that Group is a word which is used with different meaning in
different contexts. For this reason I have carefully not used it in the work
that I have done, but when encountered would always start by saying "now
when you say group - do you mean aggregate or set?"
> It
> seems we now have three options:
> 1. Treat groups as sets. This recognizes that 'member of group' is not
> transitive. But we need to drop the intuition that sets are absolutely
> non-located (a difficult intuition to justify for small
> finite sets). (See
> Max Blacks' "The elusiveness of sets" - The review of
> Metaphysics, 24, pp.
> 614-36, 1971 - for one description of this position.)
> 2. Treat groups as wholes - then we need a version of part of
> that is not
> transitive. I may be part of the football team, but my hand
> certainly is
> not.
> 3. Treat member/part of group as a new kind of relation - and
> groups etc. as
> a new category of things. This is unattractive for reasons of
> ontological
> economy (if you like parsimony).
> Matthew chose option 2.
MW: Lets be clear. I choose 2 for group in this particular context. Give me
another context, I might make a different choice.
> But I am not aware of a sufficiently fine
> distinction here between different kinds of parts. The
> members of a football
> team seem to be privileged parts in a way in which the parts
> of a car are
> not. We tend to think of sets having members with a common
> characteristic,
> this is true of collections. We tend to think of a wholes'
> parts as having
> different characteristics, the car's engine and bodywork are
> different kinds
> of things. More importantly the part relation is transitive,
> but part of
> collection seems not to be. My hand is not a member of the
> football team in
> a way in which I am.
MW: There are some important principles to understand here about fusion. Let
me explain.
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.
MW: Now let us look at a football team. Here the "atomic" level is a player
(much larger than in our water example). I can have some lower and higher
level fusions than the team. Alower level one could be the forwards, teh
backs, or the midfield. A higher level one could be the squad, or even the
league players. However, as you rightly say, a players hand is below the
atomic level, and is not a direct member of a fusion, but is necessarily
assembled to someone who is.
MW: Finally let us look at car parts. Here Chris says that he problem is
that the parts are not all of the same type. This misunderstands the nature
of the atomic class. It is fine that the elements at the lowest level are
"car parts" they do not all have to be engines, or brakes. So understanding
the class of the atomic object correctly is important.
MW: I think this understanding of fusion resolves all the issues you raise.
> For the record, I am attracted to using either 1 or 2 as the situation
> demands it - both seem to me to be useful, and used. 3 seems
> unattractive to
> me because it seems to buy you some local simplicity at the cost a
> significantly increasing global complexity. E.g. are collections of
> collections the same type of thing as collections of physical
> objects - or
> do we have a hierarchy of collections. Is the member of group
> transitive or
> not? (Probably not - but we need to spell this out.)
> It seems to me that spatio-temporal location (or weight) can easily be
> 'defined' for sets, but make more sense for sets that tend to have a
> coherent spatio-temporal location - up to a certain
> granularity (as they are
> disconnected). We can say the football team is in London
> (now) or even in
> this room (now) - depending on how far they are spread out.
MW: In the sense that the members of the set (in particular the temporal
parts that are members of the set) have a location in common, then this is
fine. But total weight does not work for me. That is transitive.
> For sets such as
> the human race, we might say they are on the planet Earth
> now, but this
> seems less satisfactory. We can see a similar issue arising
> for disconnected
> spread out physical objects. If we take masses (as Quine did)
> as the fusion
> (sum) of all the stuff involved - milk as the fusion of all
> the bits of milk
> that there are, have been or will be. Then this is a physical object,
> however it has a uninteresting, useless location and weight
> (particularly if
> we take it as extended over possible worlds). This seems to
> me to show that
> the issue about spatio-temporal location (and weight) is more
> linked to
> usefulness and ease of determination, rather than the nature
> of the things
> itself.
MW: Quite. If you follow the recipe I provide above, you will find that it
works, and you know why you are doing what you are doing.
> Pat Hayes wrote:
> There is a pretty well-investigated subject area of formalisations of
> the notion of 'part', called mereology. It seems clear that the
> set/subset relation and the whole/part relation are intriguingly
> similar in some ways, but also pretty clearly not the same relation,
> no matter what David Lewis thinks. At any rate, one would need to
> make a very strong case to say they were. If you substitute a team
> member, the team has a *different* set of players, yes? If you want
> to say no, then how are you going to talk about what I would call the
> set of players in the team?
> CP: In the case of a configured group, which a football team can be
> interpreted as, we have the positions, which give the team
> its structure.
> Then substituting a team member, is just changing the person
> who plays in a
> position. There is the same set - in the sense of the same
> configutation, it
> is just that one of the positions - a space-time worm - has
> different people
> occupying different stages at different times. So in a perdurantist
> world-view we can explain what you mean by a different set of
> players. The
> situation bets more complex when the team's configuration changes over
> time - e.g. you go from a 3-4-3 structure to a 4-4-2
> structure say (I am not
> a fan of football so these may not be common structures).
MW: The point here is that it is not a matter of choosing BETWEEN a set and
a fusion, the issue is one of using each APPROPRIATELY.
<SNIP>