RE: SUO: RE: RE: RE: RE: Collections - Aggregation or Set
Chris Partridge <chris_partridge@csi.com>:
>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.
I agree about ontologies, but I have been protesting about your use
of technical terminology (particularly "set") in our mutual
metalangauge, not about ontological strategies.
>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
My point is not that I do not favor 4 as what might be called an
ontological option (although indeed I don't), but a rather stronger
point about the language that we are using to conduct this discussion
in. 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. Ordinary-language philosophers
(like Simons, and maybe yourself?) treat such facts with disdain, but
when we are engaged in trying to construct a formal ontology, a
certain basic respect for the mathematical tools we are proposing to
use seems to me to be a prerequisite for making progress. Not to use
the formally defined terminology in our own discussions is rather
like engineers arguing about the real meaning of 'energy'. The fact
the people say they are running out of energy when they get tired
isn't a good argument against the energy conservation law: it is a
good argument, however, for the irrelevance of natural language usage
for engineering. I see our enterprise here as more like engineering
than linguistic analysis.
>- 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.
I agree that is an option. What is not an option, however, is to give
sets a spatiotemporal location. That is simply an error. As nobody
but yourself, as far as I know, has ever on this list even suggested
this as an option, you seem to be producing more heat than light on
this particular point (though not in many other areas, I hasten to
add.)
>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."
Yes, but this quote could be misleading if taken out of context.
Simons, notice, is here referring to plural reference, where one says
something of a 'class' distributively, thereby saying something about
all its members at once and collectively. In this sense of 'class' -
where, as Simons notes, the word is being used not in the
mathematical sense, but 'low-brow' - there is *no* ontological
commitment to the actual existence of the 'class' as an entity: it is
used only as a linguistic device, as a way of referring to its
members. In other words, Simons here is not in fact talking about
classes *at all* in the 'high-brow' sense that we have been
discussing them. (The phenomenon of plural reference is yet one more
reason why one should be extremely careful in drawing any ontological
consequences from linguistic intuitions, by the way.)
>Or John Sowa - who quotes Lenat and Guha (Cyc) as saying they "intermix the
>usage of collection, set and category".
I believe that you will find that whatever they say, that CYC in fact
has a pretty carefully maintained distinction between abstract sets
(it calls them 'collection', but that is just terminology) and
spatiotemporal entities.
>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)
This seems to me to be wholly confused. Plural reference makes no
ontological committment to collections: that is the point of it. If
collections exist as entities, the theoretical concept of 'plural
reference' becomes redundant: it is (ordinary) reference to the
collection.
>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.
>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.
>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.
>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.
<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.
Pat
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