Re: SUO: RE: RE: RE: Collections - Aggregation or Set
Matthew.R.West@is.shell.com, replying to Chris Partridge:
>I respond in detail to your comments below. However, I will start by making
>a statement of what I see as the case in point.
Several of the following assertions are correct but several of them
are not, with the usual understanding of 'set' and assuming that
'fusion' is an alternative term for a mereological sum. (If it isn't,
I would ask Matthew to tell us what he means by 'fusion'.)
>For any class whose members are spatio-temporal extents, there is an object
>that is the fusion of those spatio-temporal extents.
Yes.
>The class holds the
>properties that are true for each member of the set, e.g. the molecular
>weight of a water molecule,
What does 'holds' mean? One can form a set of anything, even things
that have nothing in common. It would be a mistake to say that a
shared property of all members of a set was a property of the set, or
was (usually) to be identified with the set itself: so what do you
mean here? (And similarly for a fusion 'holding' a property, below.)
> the fusion holds the bulk properties that are
>true of the sum of the members of the set, e.g. the mass of a glass of
>water.
Well, the fusion *is* the sum, so I guess this must be true, but it
is kind of trivial.
>There is a one-to-one relationship between the set and the fusion.
No, several different sets will correspond to the same fusion. For
example, consider a set of people, and the set of all the parts of
those people. The corresponding mereosums are identical. Mereology
divides up the world up more coarsely than sets do.
>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 answer is no, because despite the one to one relationship, the nature of
>the relationship between the object and its constituents is different in
>each case. Let me try to explain with an example.
>
>I have 10 pumps, 6 of them are centrifugal pumps, 4 of them are
>reciprocating pumps. I have now introduced some new objects, pump,
>centrifugal pump and reciprocating pump. These are classes, and I can have
>the class of these, which I will call pump type. Pump is the superclass of
>centrifugal pump and reciprocating pump.
>
>Now, for my centrifugal pumps I have a fusion (#1) that is the aggregate of
>the centrifugal pumps, and I have a fusion (#2)that is the aggregate of the
>reciprocating pumps. I also have the fusion of all my pumps (#3) where #3=#1
>+ #2.
>
>Now let us see what happens if we combine the fusion and the set. What I am
>saying when I combine these two is that a class can have the bulk properties
>of the members of the class as well as the properties that are true for each
>member of the class.
>
>Now my centrifugal pumps class has a mass which is the mass of all the
>centrifugal pumps, as does the class of reciprocating pumps and the class of
>pumps, where mass(#3) = mass(#1) + mass(#2).
>
>So far so good. However, this is not where the story ends. Pump, centrifugal
>pump, and reciprocating pump are members of the class pump type. These all
>have mass, therefore I can have the fusion of them, So I get that #4 = #1 +
>#2 + #3. Well let us assume that we are smart enough to spot that #3 = #1 +
>#2, and that with overlapping objects you don't count them twice in either
>fusion or class membership, so we end up with #4 = #1 + #2 = #3.
>
>So now I have two classes with the some of the same properties, pump, and
>pump type. This is not what you want. The reason that this has happened is
>that a non-transitive relation (classification) has had to do dual duty as a
>transitive relation aggregation, because the objects constructed from these
>different relations were combined.
>
>Am interesting case where simplification looks smart but isn't.
Nice example, and I entirely concur with your overall point.
Pat
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