RE: SUO: RE: RE: RE: RE: Collections - Aggregation or Set
Pat,
In any normal enterprise there is an attempt (maybe feeble) to follow a
strategy - where the major options are identified (as far a spossible), and
the costs and benefits of them weighed, and a choice made. Once the broad
framework is established the details are worked out. It is unusual for the
strategy to be undertaken with an assumption that there is only one possible
route.
My general point - made a number of times - is that we face a similar
situation with regard to ontologies. There is no one absolute right answer.
That there are a number of strategic options to be made in the ontological
architecture. As in most enterprises these are tangled - a choice of one
option influences the others. A point you, I and others have made a number
of times.
It seems to me that there are two extremes in the positions one can take.
One can say that there is only one right way - mine - and all others are
inconsistent. Or one can say here are the range of options - and the reasons
for picking one or the other. At this stage I think the second position can
be a useful one to take. Even after the event of making the choice, as it
can rationalize why the choice was made. So, my efforts are directed at
trying to make the strategic architectural options clear, so that we are at
least making an informed choice. And, in particular, as we are after a SUO
and not just a SO, to show where a option is attractive locally, it has
implications globally.
In this context, regarding abstractness - my general point is that people
use the notion of abstract in a number of different ways. For it to be
useful as a category in an ontology it needs to be defined reasonably well.
My basic point is that you cannot (maybe should not?) start with the
following:
1. There is an important disjoint distinction between concrete and abstract
objects.
2. Abstract objects are one's with no spatio-temporal location - whereas
concrete one's do.
3. Sets are abstract objects.
4. Sets have a spatio-temporal location.
You quite clearly do not favour 4 - and you also, it seems, recognize an
ontological category of collections (groups, pluralities, or whatever) in
addition to mereosums/fusions and sets. Where these collections are concrete
and so spatio-temporal. It also seems that you seem to favour a spectrum of
types of thing - with sets and fusions as two extremes.
However this is not the only option. Matthew - it seems to me - wants to be
less ontologically promiscuous and only have fusions and sets in his
ontology. However, this position needs to 'explain' seemingly concrete
collections - such as football teams and piles of bolts.
As you do not like Lewis - let me try Simons - Parts - p.145.
"A class of several concrete individuals is itself a concrete particular,
though not a concrete individual. This conception of classes, as 'low-brow'
collections rather than 'high-brow' individuals fits the linguistic
phenomenon of plural reference rather than the requirements of foundations
of mathematics."
Or John Sowa - who quotes Lenat and Guha (Cyc) as saying they "intermix the
usage of collection, set and category".
It seems to me that a key test for distinguishing the two positions and
illustrating the costs and benefits is plural reference (i.e. collections)
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.
Con - admits more basic ontological entities - groups etc.
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.
Matthew's position
Pro - ontologically parsimonious
Pro - simple, straight-forward rules for combination.
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)
It seems to me that trying to make a choice just by picking the view you
like and singing its virtues rather limits the possibilities for rational
analysis. However one benefit may be that it may make for quick decisions.
Of course, it may well be that different applications make different options
attractive. (I suspect that NLP and the Offshore Process Industry have
different needs.) Or that it is just a matter of personal preference, or
belief. In that case, we probably will (and should) end up with a range of
SUO's - as Nicola suggested in his recent email.
My search of Ian Nile's merged ontology gave no results for 'collection' or
'aggregate' - though John mentions 'collection' in Knowledge Representation.
So I presume the approach to this is still open.
Few comments on details below - prefixed by '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: 15 February 2001 20:48
To: standard-upper-ontology@majordomo.ieee.org
Subject: Re: SUO: RE: RE: RE: RE: Collections - Aggregation or Set
Chris Partridge <chris_partridge@csi.com>, replying to Matthew West:
>1) Are sets abstract?
>
>I think there is some talking at cross purposes going on here.
>
>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'.
Yes, that will do. I actually don't like the 'abstract' terminology
since it has all kinds of metaphysical baggage. The key contrast for
me is betwen things in space-time - broadly, 'physical' things - and
things which are not, like sets and numbers.
>My point was that some
>people (me and you included) are comfortable with regarding some sets as
>having a spatio-temporal location.
Well whatever you mean by 'set' isn't what I mean, is all I can say.
>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.
>
>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.
David Lewis holds some very unique views on these issues, it should
be said. He is probably the only philosopher in recent history who
apparently believes that alternative possible worlds are real, for
example. I mention this only to emphasise that reading Lewis and
nothing else is a bit like trying to live on a diet of bran.
CP: But this issue about concreteness is not just a bugbear of Lewis's - see
quote from Simons above. Notwithstanding, I think the passage from Lewis is
useful in clarifying the issue.
>
>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).
Yes, but part-of becomes subset on this route, not set membership.
>My point was rather that one could have a third notion - of a group - with
>its own way of working.
Seems to me that there are many notions of collection, with various
conditions on what can be members and what properties are shared or
held in common. Flocks, piles, shoals, teams, etc., all have their
uses. Sets and mereosums are both extreme cases which involve
removing one or another constraint altogether. For example, sets are
collections which make no stipulations whatever on the nature of
their members other than being clearly individuated from each other
and retaining that individuation when collected; the key properties
of set-membership all follow from that. Mereosums are collections
with the opposite stipulation that there can be no criteria for
individuating one part of the collection from another (strictly,
there can be, but it will be external to the business of making the
collection, ie will depend on some external structure which is
orthogonal to whatever makes those things part of the collection). So
a mereosum has no distinguished parts: it can be taken apart any way
you like and re-merged to get exactly the same sum back again, so
parthood is transitive. Other kinds of collection tend to be
somewhere in between these extremes: part of a sheep isnt part of a
flock, but any subflock of a subflock is a subflock.
>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.
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.
All this seem fairly obvious to me. What is your overall point? At
times you seem to be saying that sets are physical, other times you
seem to be saying the opposite.
CP: As I say above - I think we need to characterize the positions and their
relative costs and benefits before we make an informed choice. My concern
was to make sure that the options were recognises.
CP: My particular point in my correspondence with Matthew was to try to
explain 'Pat's Postion', which is ontologically committed to groups, which
he initially described as impossible.
Pat
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