Re: Sets, plurals, and mereology
Pat Hayes <hayes@sumex-aim.stanford.edu>
Date: Wed, May 13, 1992 1:10:19 AM PST
From: Pat Hayes <hayes@sumex-aim.stanford.edu>
To: interlingua@ISI.EDU
Subject: Re: Sets, plurals, and mereology
Cc: cg@cs.umn.edu, sowa@watson.ibm.com, franconi@irst.it
Message-id: <Mailstrom.B45.7419.9528.hayes@sumex-aim.stanford.edu>
In-Reply-To: Your message <199205121557.AA27322@venera.isi.edu> of Tue, 12
May 92 11:52:12 EDT
Content-Type: TEXT/plain; charset=US-ASCII
A few quick comments on Sowa on mereology. I agree with John that mereology is
in many ways more intuitive than set theory, but it has some peculiarities of
its
own. For example, mereology makes no distinction between nouns and adjectives:
there
are no 'things' in mereology, only parts of the universal plenum which have
certain
properties. "Book" and "red" are exactly the same kind of entity. Maybe John's
rebarbative notation has a way of making this distinction, but if it does then
it goes beyond mereology
and must be resting on some other ontological perspective.
I will follow his numbering.
4. True, but notice that this also means that all collectives are similarly
flattened. Thus in
mereology, the collection of shoals of fish and the collection of fish are
indistinguishable, and indeed are similarly indistinguishable from the
collection of all fish flesh. Its all just the fishy part of the universe.
Notice also that this means that there is no way that any mathematical modelling
can be done
in mereology.
5. Apparently this kind of distinction can be made in Sowa graphs: then they
must have their
feet on something firmer than mereology, since this distinction is invisible
there. It does not
"keep coming up" in set theory "whether you need it or not": its a distinction
that can be made if you wish to pay attention to it.
6. What you call them IS relevant to the extent that it guides and claims your
intuitions. This is
especially important when you claim to be capturing natural meaning.
7. Russel's paradox indeed does not arise in mereology. This however does not by
any means establish the consistency of mereology. To do so would require some
formal account of how expressions in mereology acquired meaning, and this would
need at least a model theory, and that needs set theory. This is precisely where
mereology has failed to excite the imaginations of most philosophers, I think.
10. This is a very confusing essay. If Sowa's graphs are thought of as a
formalism of some kind, then the distinction between upper and lower case
symbols is of no deep significance: he is simply distinguishing between two
different formal notations. But sometimes he seems to be placing his graphs on a
par with a natural language, so that their symbols (and presumably their syntax)
have no technical meaning at all. In this case, we could simplify things
tremendously by just having the English and the predicate calculus translations
and removing these graphs from the picture altogether.
Pat Hayes