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Re: [ontolog-forum] Visual Complexity

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Chris Menzel <cmenzel@xxxxxxxx>
Date: Thu, 8 Feb 2007 04:09:48 -0600
Message-id: <20070208100948.GB82844@xxxxxxxx>
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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