[Top] [All Lists]

Re: [ontolog-forum] Visual Complexity

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Thu, 08 Feb 2007 01:52:57 -0500
Message-id: <45CAC8C9.4080609@xxxxxxxxxxx>
Chris,    (01)

I was just trying to express, not very clearly, that there
is just one mereological totality of Bill + Chuck:    (02)

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.    (03)

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.    (04)

The crucial issue is how many potential "entities" exist.    (05)

 > And in mereology you have Bill, Chuck, and Bill+Chuck.    (06)

No.  The totality consists of just the sum of Bill & Chuck.    (07)

If you want to count the total number of distinguishable
"entities", you have to include all the possible ways of
extracting and combining some parts of Bill plus some
parts of Chuck.  (I apologize to Bill & Chuck for the
gory images this discussion might conjure up, but you
don't have to do the extraction physically -- you can
identify the slices without actually cutting them).    (08)

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.    (09)

With mereology, there is no clear answer to how many
parts there are if you have a continuous area or solid.
All you can say is that with one method of dividing you
get N parts and with another method you get M parts.    (010)

But with set theory, you create a new entity with each
"CONS" -- to use a LISP term.  In fact, that is one of
the crucial measures of LISP space allocation -- how
many CONSes are used in a given construction.    (011)

 > 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.    (012)

I agree with this, but I think that the crucial difference
between mereology and set theory shows up when you start
dividing things.  Set theory starts with zero or more
urelements and builds more entities from there.  Mereology
never goes beyond a given totality, but it may subdivide
it very far, especially if that totality is continuous.    (013)

John    (014)

Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (015)

<Prev in Thread] Current Thread [Next in Thread>