Dear Avril, (01)
> If we consider only sets with rank 1, that is, no inner sets, then
> mereology and set theory become identical. Parts and subsets work
> identically: you can talk about the set {a,b,c} as well as about the
> aggregate abc. (02)
MW: I agree with John and Chris that this is not correct, but let me try to
give a practical reason why, rather than the theoretical reasons they gave. (03)
The real problem is that set theory has the member of relation as well as
the subset (isin) relation. It is the subset relation that works the same
way as part of in mereology (i.e. it is transitive). So if you want to
model, say, my arm as a set then you can use the subset relation to show
that the set my arm is "part of" the set my body. However, I think not many
people would be convinced that my arm is a set. So how about we model my arm
as a particular, and my body as a set, and use the member of relation to say
my arm is a part of (member of) my body (a set). Well I'm still not
convinced my body is a set, but I can have groups of bodies that are
organizations using sets. The problem now comes when I notice that my arm
has parts, and I want to represent my hand as a part of my arm. Well I now
have no way to do it. This time my arm is a particular, and particulars are
not sets, so they do not have subsets and they do not have members, so I
have no way to say that my arm has parts. (04)
The bottom line here is that set theory and mereology are not
interchangeable at any level. There subset of and part of, are analogous,
but that is all. (05)
Regards (06)
Matthew West
Information Junction
Tel: +44 1489 880185
Mobile: +44 750 3385279
Skype: dr.matthew.west
matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx
http://www.informationjunction.co.uk/
http://www.matthew-west.org.uk/ (07)
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