RE: SUO: RE: RE: RE: Collections - Aggregation or Set
Dear Pat,
See comments below.
>
> Matthew.R.West@is.shell.com, replying to Chris Partridge:
>
<snip>
>
> >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.)
MW: Yes you're right. I was being a bit sloppy and referring to what we
might call classes where the members have something in common. What they
have in common is a "property" of the members of the set/class, and is
usually related to the set/class.
>
> > 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.
MW: I know, but I'm surprised how many times it needs saying.
>
> >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.
MW: You are correct (at least in a 4D world). In a later e-mail I spot my
error. Of course this just makes it more obvious that it is inappropriate to
combine a fusion and a set/class.
>
> >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.
MW: Thanks.
>
> Pat
Regards
Matthew
============================================
Matthew West
Operations & Asset Management
Shell Services International
H3229, Shell Centre, London, SE1 7NA, UK.
Tel: +44 207 934 4490 Fax: 7929
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E-mail: Matthew.R.West@is.shell.com
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