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Re: [ontolog-forum] Visual Complexity

To: Chris Menzel <cmenzel@xxxxxxxx>, "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Thu, 08 Feb 2007 09:13:01 -0500
Message-id: <45CB2FED.1060108@xxxxxxxxxxx>
Chris,    (01)

Yes, we do agree about the technical details.    (02)

 > Oh, well, then, great! (Somehow I thought you didn't
 > agree...like when you said "No" above.    (03)

Sorry, I should have said "but".  I agreed with the
point, but wanted to state a contrasting view:    (04)

I think it's useful to view mereology and set theory as
contrasting approaches to related issues:  mereology
starts with a given whole, which it can break down
into parts in various ways.  It can never give you
anything new that wasn't already in the pot.    (05)

But set theory starts with zero or more urelements,
from which it can build up infinities of new entities.    (06)

That difference makes it possible to use set theory
to build up all of mathematics.  But if you start
with mereology, as Lesniewski did, you need some
generating mechanism to give you the building blocks.    (07)

One approach, which I like very much, is to start
with the successor function for building up the
integers.  That gives you the raw material, from
which you can construct representations of all
sorts of structures.  That's roughly the approach
Lesniewski was taking before WW II broke out.    (08)

It's also compatible with Kronecker's remark:
"Die ganzen Zahlen hat der liebe Gott gemacht,
alles andere ist Menschenwerk."    (09)

John    (010)

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