On Thu, Feb 08, 2007 at 01:52:57AM -0500, John Sowa wrote:
> Chris,
>
> I was just trying to express, not very clearly, that there
> is just one mereological totality of Bill + Chuck:
>
> JFS>> In mereology, Bill and Chuck are each parts of the collection
> >> that consists of Bill and Chuck. You can call that pair C, but C
> >> is not a new entity. It is just Bill and Chuck.
>
> CM> John, that is not correct. The mereological sum of Bill
> > and Chuck -- call it Bill+Chuck -- is typically defined in
> > mereology as the smallest thing that has Bill and Chuck as
> > parts. (Equivalently, it is the unique thing X such that
> > anything that overlaps X either overlaps Bill or overlaps
> > Chuck.) It is not "just Bill and Chuck". It is a third
> > thing distinct from the two of them.
>
> The crucial issue is how many potential "entities" exist.
>
> > And in mereology you have Bill, Chuck, and Bill+Chuck.
>
> No. The totality consists of just the sum of Bill & Chuck. (01)
No? John, your own assertion betrays you. "The sum of Bill & Chuck"
(in mereology) refers to something, namely, the sum of Bill & Chuck. It
is neither Bill nor Chuck -- for, unlike Bill and Chuck, it has both
Bill and Chuck as parts. It is a third thing. You are trying to have
your mereological cake and it eat it, too. (02)
> A better example is to consider France, which was subdivided into
> provinces and later subdivided into departments. There is only one
> totality, which is France, and the different ways of subdividing it
> are potential parts. (03)
Right, just as there is the one totality Bill+Chuck and many ways to
divide it into potential parts -- notably, into its Bill part and its
Chuck part, each a totality in its own right. Similarly, you can divide
France by a line running through Paris and Dunkirk into two separate
land masses. So we can distinguish three land masses -- France,
"western" France, and "eastern" France. The analogy is less than
perfect, of course, because Bill and Chuck are autonomous organisms, so
the division of of Bill+Chuck into its Bill and Chuck parts is a more
"natural" one than my division of France. But mereologically the
principle is the same -- non-overlapping entities are distinct from
their sum. (04)
> With mereology, there is no clear answer to how many parts there are
> if you have a continuous area or solid. (05)
Sure 'nuff. Not relevant to my point, of course. (06)
> > By contrast, in mereology, the sum of Bill and Bill+Chuck is just
> > Bill+Chuck; likewise, the sum of Bill's left arm and Bill is just
> > Bill. In set theory, as you note, you get the distinct entities
> > {Bill, {Bill, Chuck}} and {BillsLeftArm, Bill}. But in mereology
> > and set theory alike, the sum/set of Bill and Chuck is a third
> > thing distinct from Bill and Chuck.
>
> I agree with this, (07)
Oh, well, then, great! (Somehow I thought you didn't agree...like when
you said "No" above. :-) (08)
-chris (09)
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