SUO: RE: RE: RE: Collections - Aggregation or Set
Dear Chris,
I respond in detail to your comments below. However, I will start by making
a statement of what I see as the case in point.
For any class whose members are spatio-temporal extents, there is an object
that is the fusion of those spatio-temporal extents. The class holds the
properties that are true for each member of the set, e.g. the molecular
weight of a water molecule, the fusion holds the bulk properties that are
true of the sum of the members of the set, e.g. the mass of a glass of
water. There is a one-to-one relationship between the set and the fusion.
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 answer is no, because despite the one to one relationship, the nature of
the relationship between the object and its constituents is different in
each case. Let me try to explain with an example.
I have 10 pumps, 6 of them are centrifugal pumps, 4 of them are
reciprocating pumps. I have now introduced some new objects, pump,
centrifugal pump and reciprocating pump. These are classes, and I can have
the class of these, which I will call pump type. Pump is the superclass of
centrifugal pump and reciprocating pump.
Now, for my centrifugal pumps I have a fusion (#1) that is the aggregate of
the centrifugal pumps, and I have a fusion (#2)that is the aggregate of the
reciprocating pumps. I also have the fusion of all my pumps (#3) where #3=#1
+ #2.
Now let us see what happens if we combine the fusion and the set. What I am
saying when I combine these two is that a class can have the bulk properties
of the members of the class as well as the properties that are true for each
member of the class.
Now my centrifugal pumps class has a mass which is the mass of all the
centrifugal pumps, as does the class of reciprocating pumps and the class of
pumps, where mass(#3) = mass(#1) + mass(#2).
So far so good. However, this is not where the story ends. Pump, centrifugal
pump, and reciprocating pump are members of the class pump type. These all
have mass, therefore I can have the fusion of them, So I get that #4 = #1 +
#2 + #3. Well let us assume that we are smart enough to spot that #3 = #1 +
#2, and that with overlapping objects you don't count them twice in either
fusion or class membership, so we end up with #4 = #1 + #2 = #3.
So now I have two classes with the some of the same properties, pump, and
pump type. This is not what you want. The reason that this has happened is
that a non-transitive relation (classification) has had to do dual duty as a
transitive relation aggregation, because the objects constructed from these
different relations were combined.
Am interesting case where simplification looks smart but isn't.
See additional 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: 14 February 2001 12:04
> 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.
>
MW: In my view both are always valid (I can construct both). The key
question is which one do you mean.
> 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.
MW: Not really. The question is in which sense are you refering to them?
>
> 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.
MW: No. the set is still abstract. What is true for all the members, is that
they are at some location (amongst perhaps other things).
> As to weight, the problem is not that there is no algorithm
> to calculate
> it - rather that it is implausible.
MW: as the property of a class - precisely.
>
> 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?
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.
>
> 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.
MW: Again, the key to understanding is that both exist without having to do
anything. the question is which is of interest in which circumstances. The
trick is to use the right one for whatever is at hand, and not to look for a
short cut that can lead to contradictions (like being both transitive and
non-transitive).
>
>
> 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.
MW: OK, then is Option 3 transitive or intransitive?
>
> 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.
>
MW: This sounds a bit like group is equivalent to fusion. Your distinction
between group member and part looks like the difference between assembly and
fusion. This is fine. There is such a difference.
> 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.
>
> 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.
MW: Yes, but if i take parts of the set of water molecules
>
> 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?
MW: Again the issue is one of being clear about what the atomic level is,
not withstanding that it can be what you like.
MW: By the way, with both this military example, and the football one, there
is a good case for arguing that the aggregates are assemblies, not fusions,
in that the parts play a role in the whole, and teh whole is not just the
sum of the parts.
>
> Nevertheless, I agree with you that a combination of options
> 1 and 2 seems
> to make the most sense.
MW: Good
>
>
> 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>
>