RE: SUO: RE: RE: RE: RE: Collections - Aggregation or Set
Pat,
Comments below - marked CP>.
Regards,
Chris
-----Original Message-----
From: owner-standard-upper-ontology@ieee.org
[mailto:owner-standard-upper-ontology@ieee.org]On Behalf Of pat hayes
Sent: 20 February 2001 20:04
To: standard-upper-ontology@ieee.org
Subject: RE: SUO: RE: RE: RE: RE: Collections - Aggregation or Set
Chris, Ive taken the liberty of snipping some of this message to keep
its size in reasonable bounds.
Chris Partridge <chris_partridge@csi.com> wrote:
>*Set*
>
>Maybe we should just agree to differ on set.
>
>I dispute your claim "The very word "set" as used throughout mathematics
and
>logic
>*means* something which is abstract and not spatiotemporally located
>in this sense. This is what "set" means in Tarskian model theory and
>in all the axiomatic set theories."
>
>Max Black's essay (referred to in an earlier email) starts with a quote
from
>a working mathematician's book on set theory - which claims that packs of
>wolves etc. are standard examples of sets. If I had the time, I am sure I
>could come up with other examples. I suspect that most (many?) working
>mathematicians do not bother considering whether sets are 'abstract' or
>spatio-temporally located. They will be happy to (loosely) say packs of
>wolves or other collections can be considered as sets, if they find this
>intuitively useful. Logicians are trained to play a different language
game.
I would agree with Black's mathematical friend that sets may be sets
of physical things. I suspect that the mathematician was either being
'loose' about, or more likely had never considered, the linguistic
implications of claiming that a wolf-pack *was* a set, but certainly
one can allow a collection of physical things to be a set without
thereby saying that the set is spatiotemporally located, which I am
sure is the looseness that most mathematicians (who tend to be
platonist in their working philosophical attitudes) would endorse:
that is, in a debate between a linguist and a mathematician, if the
linguist pointed out that a wolf pack had a spatiotemporal location,
the mathematican would respond that in that case the pack was not
simply a set, rather than that the set of wolves had a spatiotemporal
location. But in any case, one anonymous attribution in one essay by
Max Black isnt a very persuasive body of scholarship. I repeat my
earlier challenge: can you find my any citation of any work by any of
the major writers on set theory - say, Russell, Zermelo, Fraenkel,
Tarski, Quine, von Neumann and toss in any others you feel like -
which suggest that sets are considered to have any qualities other
than purely platonic criteria of membership? More to the point, can
you cite any formalisation of set theory which takes spatiotemporal
location into account?
Let me emphasise some of the problems that would arise if one were to
allow this. Consider a 'physical' set S whose members are
spatiotemporal entities, eg a wolf pack considered as a set. Since
both S and its members have physical properties, what are the
relations between them? Could the members be in one country and the
set in another? (Why not? What axiom of ZF set theory, say, would
prohibit this?) Ask how the relationship between a physical property
applied to the members of S, and the same property applied to S,
changes. The weight of S is the sum of the weights of its members.
The velocity of S is probably something like the average velocity of
the members. The location of S is something like the convex hull of
the locations of the members. The length or height or age of S bear
no discernable relation at all to those of the members of S. In fact
there is no general theory of how the proposed physical properties of
S relate to the similar properties of its members, since the physical
properties of S might depend on anything; they might not even be
determined by the membership of the set (eg consider the age of a
wolf pack or a football team, which may greatly exceed the ages of
any of its members.)
CP>. I like this argument for dividing up what properties can apply to what
types of thing (I think I may have used it in an earlier email).
>*collection*
>
>You suggest talking to Nicola.
>I have done so and he takes a similar position to Matthew (and me).
OK, then I apologise for misunderstanding him (unless his opinions
have changed since the Heidelberg meeting.)
>He only uses fusions/mereo-sums as a basis for his notion of collections -
>and so avoids the problems of having to engineer the relationships between
a
>distinct collection category and the category of sets and fusions. He
places
>the burden of capturing what we mean by collection on the notion of a
>privileged part - and the notion of a whole.
>
>Returning to the art collection example - to illustrate the Guarino/West
>approach. The Wallace collection would be a collection of painting say,
>originally owned by Wallace. So the Wallace collection would be the fusion
>of the paintings, where these paintings had a privileged part relation,
>which would be something like 'part of & part is a painting & painting is
>now part of Wallace collection'. If the Wallace collection was one of, of
>many, in the National Collection, then the National Collection would be
both
>the fusion of the paintings in the collection and the fusion of the
>collections. There would be two sets of privileged parts - one relating the
>National Collection to its constituent collections and another relating it
>to its constituent paintings. Note: though the part of relation is
>transitive, the privileged subsets of the part of are not - transitivity
>being a property of a set of relations.
Ah, I see. So a collection *is* a mereosum, but with a special
'part-of' relation which defines a set of 'privileged parts' , which
are the (necessarily disjoint?) members of the collection. OK, that
works, as long as one bears in mind the implications of the
collection being a mereosum. For example, this means that the Wallace
collection is also a collection of very small pieces of wood, canvas,
dried linseed oil and pigment, though with a slightly different
notion of privileged part; and it is also a collection of largely
organic molecules, with a still different notion, and so on. All of
which does indeed make sense, I agree. Still I can see no real
utility to insisting that the collection *is* the mereosum, and this
identification can be quite misleading. Why not have the collection,
as one thing, and the mereosum of the members of the collection, as
something else?
CP> As I think I have said before. This choice eliminates the need to
(possibly?) have a hierarchy of collections of collections - and a mixed
hierarchy of sets of collections and collections of sets, where these seem
to have no use, at least currently in the ways we are describing the world.
It seems like unnecessary complication - something that surely does not
appeal to an engineer?
>The question of sets (or at least finite sets of physical objects) comes in
>when we want to start distributing the properties among the categories.
>While we are happy letting weight and volume apply to (some) physical
>objects - and not to sets - i.e. restricting it to the category of physical
>objects. It seems less convenient to do let number also apply to this
>category. The problem is (as Frege among others have pointed out) that if
we
>let number apply to physical objects we have to qualify it. In the example
>above, the National Collection will have a number C of collections as its
>art-collection 'members' and a number P of paintings as its paintings
>'members'. It seems easier (from an engineering point of view) to let these
>counting numbers apply to sets - without qualification. (I have discussed
>this point with Nicola, who says he can see the point of it).
I can see the point of it as well, but it seems to me that you are
simply talking about the cardinality of the set of paintings in the
collection. Sure, one can do that without saying that the collection
*is* a set or a mereosum. The cardinality applies to the set, not to
the mereosum; and it is the mereosum, not the set, which has
spatiotemporal properties such as mass and location.
>[NB. Another
>option which would give you unique counting is having a new ontological
>type, collection, which is also concrete.]
Well, I'm quite happy to work within Nicola's framework, though I'd
suggest modifying it just a tad. My earlier emphasis on the need to
consider many different kinds of collection (an emphasis which I
thought I had learned from Nicola :-) can then be seen as referring
to the various notions of 'privileged part' which correspond to
notions like team, flock, pile, etc..
I have one worry with the Guarino/West approach as you characterize it
above.
If a collection is identified with a mereosum (or indeed with a set,
for that matter), then how does one account for the fact that the
membership of a collection may change without altering the identity
of the collection? For example, if a farmer sells some of his sheep,
we say a single flock has become smaller, but both the set of members
and the mereosum are different after the sale than they were before
it. For collections like teams and orchestras and opera companies,
the membership may change entirely without altering the identity of
the collection, in notable contrast to both sets and mereosums.
CP> I have written on this problem in my book (characterizing it as the
'Logical Paradigm'). It is because the view is neither 3d or 4d, perhaps
3.5D. You need to take the full 4-d extension of the flock.
>Other comments below, marked CP>.
>
>Regards,
>Chris
>-----Original Message-----
>From: owner-standard-upper-ontology@ieee.org
>[mailto:owner-standard-upper-ontology@ieee.org]On Behalf Of pat hayes
>Sent: 16 February 2001 20:43
>To: standard-upper-ontology@majordomo.ieee.org
>Subject: RE: SUO: RE: RE: RE: RE: Collections - Aggregation or Set
<big snip>
> >I will take the liberty of calling the two positions - Pat's and
Matthew's
> >(without meaning to commit you to them :)):
> >
> >Pat's Position:
> >Pro - direct explanation of linguistic plural reference.
>
>I wouldnt make this claim, I think you are confused about plural
>reference, and in any case I don't give a damn about explaining
>anything linguistic. We aren't in a linguistic business here.
>
>CP> Maybe a better phrasing would have been - linguistic talk about
>pluralities.
>
> >Con - admits more basic ontological entities - groups etc.
>
>I would list this as a Pro. I think your taste for 'parsimony' is a
>fatal flaw at this stage of the game.
>
> >Con - additional complexity due to accounting for rules for
combinations
>of
> >different types of 'collection' - this is particularly acute if you take
>the
> >spectrum rather than three types route.
>
>This analysis needs to be done somehow, in any scheme. The situation
>just is complex. Some collections relate to the things 'in' them
>differently from others. Either one can set out to list and catalog
>these distinctions, or one can seek to derive them from some
>parimonious, elegant underlying model. A good methodology, I believe,
>is to initially adopt what might be called the botanical stance, ie
>to list and catalog, and then later, when the cataloging is done, to
>try to find some general principles. To succeed at doing the theory
>first one needs to be either extremely lucky or a genius.
>
>CP> I think your first point is not right. It seems to me that if we
>introduce collections as a new kind of object, then we have to explain what
>a set of collections are, what a collection of sets is - if that is
allowed,
>what a collection of collections is - if that is allowed.
Well, what is there to explain? Sets can be sets of anything, so a
set of collections is, well, a set of collections. There might be no
particular utility in such things (actually there is, see below) but
they create no extra explanatory burden. Collections-of are another
matter, I agree: part of the point is that the world 'collection' is
too ambiguous to be ontologically useful, and each separate notion of
'colllection' needs to have its conditions on membership and temporal
identity spelled out in full. This applies to flocks (of sheep),
shoals (of fish) and also to collections-of-collections, if you want
to consider such things. (For example, suppose that the Smithsonian
gives away something from the Wallace collection. Is it then the same
collection of collections?) I concede that I wouldnt have much use
for a collection-of-sets, but unless someone proposes to give
defining conditions for them, I won't let that worry me.
>But it seems to me
>that we are describing a whole structural framework, which we do not need -
>it is unnecessary complexity. What on earth would we want to use the notion
>of a set of some collections for?
Thats easy, since a set of collections is just a property on
collections. Some collections are legally owned by an individual, for
example: that defines a set of collections.
>CP> I agree with reservations, which I think you may also have. One can
just
>describe the surface phenomenon of language (or whatever), but it seems to
>me to be more useful to try and understand the purpose of the distinctions
>one is finding.
I'll agree with that, of course.
> >Matthew's position
> >Pro - ontologically parsimonious
> >Pro - simple, straight-forward rules for combination.
>
>That would be a pro if it were correct. I don't think it is, however.
>CP> Why not? As in the example at the beginning, a collection of
collections
>just involves a fusion. What problems do you see?
See above for one (identity criteria that allow the fusion to change
without changing the identity of the collection.)
> >Con - less direct explanation of linguistic plural reference.
> >
> >It seems to me that we should be trying to identify the different
possible
> >positions and the potential benefits and pitfalls of each (I note in
>passing
> >that this is something in which philosophers can sometimes help - though
of
> >course their scruples may sometimes bear no relation to practical
issues -
> >and so, maybe, can be ignored)
>
>OK. BUt I note that 'pats position' in fact is weaker than 'matthews
>position', since the former says there are many kinds of collection,
>including set and fusion, while the latter says that there are only
>set and fusion and the others can be reduced to these. Maybe the
>second view is correct, but one good way to approach it might be to
>adopt the first view as a weaker working hypothesis, and have someone
>who espouses the second view provide the defining translations in
>terms of set and fusion which would justify the second view. The only
>cost would be a larger working conceptual vocabulary, which people
>are probably going to want in any case, in practice.
>
>CP> As I pointed out above, it seems to me that the 'larger vocabulary'
>would include a range of construction that are never used - and would never
>need to be used. But I would be interested in counter-examples. It seems to
>me that the notion that we are talking about collections as a different
>category of entity is one that the surface of the language seems to give
>credence to. And, like you, I think language can mislead.
>
><snip>
>
> >
> > >
> > >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.
> >
> >The thing that weighs 2 kilo is presumably something that when put
> >onto a scale would register 2 kilo. That would be something like a
> >pile of bolts. A pile is an example of an aggregate which is both a
> >material assembly (in contrast to a set) and has distinguished
> >members - it imposes individuation criteria on its members, so they
> >are countable - in contrast to a mereosum. It is neither a set nor a
> >mereosum. It shares countability with the set of its members, and
> >total mass with the mereosum of its members, but not vice versa.
> >CP: A good description of an aggregate - which is neither a class/set nor
a
> >physical particular. So, I deduce that you have an ontology that includes
> >this.
>
>I dont HAVE such an ontology. I think that any generally useful
>physical ontology will need to include this, and a number of other
>distinct notions of 'collection', in it. I also think that Nicola G's
>overall picture of what is needed to characterise a kind of
>collection is the best Ive seen so far, and suggests a
>general-purpose notion which has set and mereosum as two 'extremes',
>but also includes flocks, piles, shoals and other similar thingies.
>
>CP> See comments on Nicola's approach above. I think your position is
>interesting (academically) and I await Ian Niles' attempt to axiomatise the
>rules for combination - with, hopefully, examples of their uses. However,
my
>experience tells me that, from an engineering point of view, it is
>unnecessarily complex.
Most of the 'combinations' cannot arise: eg you can't have a flock of
sets or a flock of shoals, etc., since flocks must have sheep as
members, by definition. I think this is exactly what Nicola must also
do, ie characterize the notion of 'privileged part' which corresponds
to each kind of collection, and the criteria which determine what
kinds of change can be made to those collections without changing the
identity of the collection as an entity. Given this, one has a
well-defined notion of some kind of collection and a corresponding
notion of member, and then one can talk about the mereosum of the
members, and the set of the members, of the collection (perhaps at a
given time, or of meresums and sets of timeslices through the
members, if one likes that way of talking.) To *identify* the
collection with the mereosum or the set seems to be a further step
which is unnecessary. I know what a flock is, and I know what a
meresum of a set of sheep is, but I'm genuinely unsure whether they
are the same. And moreover I don't really care: I need all three
notions to say what needs to be said about sheep-herding, in any
case. (To identify all three is to guarantee ontological confusion,
and in any case is quite unmotivated.)
Pat
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