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Re: [ontolog-forum] What is the role of an upper level ontology?

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Mon, 20 May 2013 14:36:26 -0400
Message-id: <519A6D2A.2050005@xxxxxxxxxxx>
Pat and Pat,    (01)

> Mereology (which was originally conceived as an alternative
> to set theory, a foundational theory for mathematics) thinks
> of the world as made up of lumps of anonymous stuff, and the
> basic relation between these lumps is parthood.    (02)

I agree.  But I just wanted to add a note about motivation.    (03)

The term 'mereology' was introduced by Stanisław Leśniewski, who
was not happy with the option of constructing infinities out of
nothing but the empty set: { }, {{ }}, {{ }, { }}, {{ }, {{ }}}...    (04)

Leśniewski used a very simple version of mereology that could not
be used to construct a model of the integers (or anything else).
Instead, he maintained that the generating mechanism (such as
the successor function) should be kept separate from whatever
theory is used to contain the collections of things generated.    (05)

That separation is a healthy exercise that keeps the theory of
collections distinct from the mechanisms for generating the
things (or stuff) that goes into those collections.    (06)

> If we have a physical object (e.g. me) and at some time t a neutrino is
> passing through that object (me) so that it is enclosed within the convex
> hull of the physical object, does it follow that the neutrino is part of me
> at that time?    (07)

It's unfortunate that Leśniewski chose the Greek word 'meros' (part) as
the root for the name he chose.  The basic operator of mereology should
be kept separate from the word 'part' in English and other languages.    (08)

My recommendation is to treat the many versions of mereology as abstract
mathematical theories and to treat the English word 'part' as a highly
polysemous term.  Some senses of 'part' might be related to the operator
of some versions of mereology.  As Ingvar Johansson said,    (09)

> Ontology construction with parthood relations is not applied formal-
> axiomatic mereology. It is ontology construction in which, sometimes,
> formal-axiomatic mereology can be applied.    (010)

Quotation from http://hem.passagen.se/ijohansson/information5.pdf    (011)

John    (012)

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