Re: SUO: RE: RE: Collections - Aggregation or Set
Chris Partridge <chris_partridge@csi.com>, replying to Matthew West:
>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.
Let me suggest that this is simply a matter of terminology. What I
mean by 'sets' are definitely, with no room for any further
discussion, abstract entities. To apply any kind of physical
predicate (weight, location, time) to a set is simply a category
error. Now, Chris may wish to define a different notion, and maybe we
will need to come to adopt a more sensitive terminology in order to
communicate adequately, but this would be a debate about terminology,
not about substance.
So, in my sense of 'set', a football team is definitely not a set,
and if one can weigh a flock of sheep then it is not a set either.
This is the sense of 'set' which is axiomatised in virtually all the
known axiomatic set theories and used throughout mathematics for the
last 80-odd years. We will certainly need this notion, whatever we
call it.
>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.
>
>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.
I believe that a better way to characterise Matthew's position would
be that there are two distinct entities: the aggregate and the set.
What one means by the English word "team" may vary with the context,
but it would just be a mistake to identify an aggregate with a set.
>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.
>
>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.
>As to weight, the problem is not that there is no algorithm to calculate
>it - rather that it is implausible.
>
>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.
One cannot coherently manage with only sets or only aggregates: we
need them both. We also almost certainly need mereosums and several
other 'aggregate' notions.
>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?
Of course it is possible to use them both. One can talk about the
mereosum of the members of the set of things in an aggregate, or any
other combination you like.
>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.
As Ive said before, the surface structure of English phrases is not a
useful guide to almost any ontological issues.
Most of this work has already been done. Check out what Nicola
Guarino has written on this topic, and the mereological literature
generally.
Pat Hayes
Pat
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