Re: SUO: Collections - Aggregation or Set

["Douglas McDavid" <mcdavid@us.ibm.com>]

This thread is one of several where I could make this point, but I like the
example of the team.

It seems to me from an ontological perspective it is very interesting to
talk about the nature of teams, the various kinds of teams that we know of
(professional, university, informal children's teams chosen on a
playground, etc.), how the various kinds of teams differ from one another,
and how they each differ from other forms of human social systems.
Additionally, how human social systems differ from other natural social
systems (ant colonies, schools of fish, cooperating beavers, etc.), and how
living social systems differ and are similar to other living systems, such
as organisms (humans, whales, worms), systemic parts of organisms
(cardiovascular systems, digestive systems etc.), cells, robots, cars,
telecommunication networks, the whirlpool in my bathtub and the Great Red
Spot of Jupiter.  In other words ontological consideration of systems,
whether autopoietic or not, complex and adaptive or not, dissipative
structures or not, legally constituted or not, and any of many interesting
dimensions of this subject.

Is it too soon to start carving up the work of the SUO along these lines?
Or is this ever going to be the focus of this work?  At some level it is
probably important to have exhaustive discussions of how set theory and 4-d
vs. 3-d+time would accommodate meaningful classifications.  It certainly
must be interesting, since we keep gravitating back to these discussions.

I could have easily jumped into the long discussion of relationships vs.
relations.  What I would have said there is that there is that while the
various technical meanings of these terms is interesting, it should be
equally interesting, from an ontological point of view, that there are
large numbers of interesting types of relationships (contractual, proximity
emotional, linguistic, assembly, etc., etc.)  Isn't this what we're about
in this work?  Or is it still just too early to start?


Doug McDavid
Certified Executive Consultant
Business Innovation Services - IBM, US
Member of IBM Academy of Technology
mcdavid@us.ibm.com  --  916-549-4600


Chris Partridge <chris_partridge@csi.com>@ieee.org on 02/12/2001 01:29:55
AM

Please respond to Chris Partridge <chris_partridge@csi.com>

Sent by:  owner-standard-upper-ontology@ieee.org


To:   standard-upper-ontology@majordomo.ieee.org
cc:
Subject:  SUO: Collections - Aggregation or Set




Pat, Matthew, et al,

I am following Pat's suggestion and only replying to the mailing list. (I
am
in two minds about whether I would actually like to be replied to directly
on topics I have contributed to - as sifting through the SUO mailing list
takes time - and I sometimes miss interesting messages - but I also
understand Pat's point of view).

I have merged (or is it aligned) messages from Pat and Matthew on similar
topics.
I've also taken the liberty of changing the title - hopefully making it
more
meaningful.

Chris


-----Original Message-----
From: Matthew.R.West@IS.shell.com [mailto:Matthew.R.West@IS.shell.com]
Sent: 10 February 2001 13:01
To: Chris Partridge; pat hayes; Ian Niles
Cc: standard-upper-ontology@majordomo.ieee.org
Subject: RE: SUO: More Documentation, Please


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. 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. We have the notion
of
a member of a group (collection, or whatever), which has characteristics of
both. 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). 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. 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.
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. 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.
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).

>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.

Yes, and I would indeed block that one, and insist that any axiomatic
ontology make a sharp distinction between a physical group or
collection (such as a team, a shoal or a flock) and a set. If you do
not do this, then for example set-membership will need to have a
temporal parameter. Good luck with adapting ZF (or any other known
set theory) to include temporal reasoning. (And what else is down
that road? Situations? points of view?)
CP: Pat, does this mean you take option 3 above?

Ordinary language is a lousy guide to ontological coherence, as I've
said before. If the idea of 'set' were clear in NL, then people like
Russell and Whitehead would have had a much easier time.

CP: I agree about ordinary language. But I think you are being a bit too
quick about temporalising. The 'problem' that you are referring to is the
standard endurantist problem for 'properties' that change. And you are only
forced to temporalise if you are an endurantist. A perdurantist can use
exactly the same strategy for dealing with the property 'being a member of
group X' as with 'being red'. If one uses temporal stages, then there is no
need for temporalisation. So the issue about temporalising is the old
endurantist-perdurantist choice -  which, as one would guess, raises its
head in the notion of collections.
>In the spirit of starting middle out (with rich middle-level concepts) -
it
>may make sense to defer any decision of abstractness and sets until we
have
>some more material to work on.

Well, if there is one topic in the world that might be said to have
been formalized to death, it is surely set theory. You think the jury
is still out? (And you think we are going to do better than Russell,
Zermelo, Quine, Von Neumann, etc. ?)