RE: SUO: Re: RE: Logic and Ontology
John,
I am not sure that everyone would accept your characterisation of a set as
changing over time as the only one. People working in the Quine, Lewis,
Heller tradition would treat the member as 4D, include all the members (at
all times) and so the set is unchanging. I suspect that Matthew belongs to
this school. Of course, there are others who take the view you describe
below. I note both these views in Chs. 5 & 7 my book (Business Objects).
For my money, the difference between property and set (among other things)
is a difference between a proof-theoretic and model-theoretic feel. I think
of there being a mechanism to determine whether something has a property -
whereas I think of a set as being the sum of its members.
However, I expect there are a large number of different views in play here.
Regards,
Chris
-----Original Message-----
From: owner-standard-upper-ontology@majordomo.ieee.org
[mailto:owner-standard-upper-ontology@majordomo.ieee.org]On Behalf Of John
F. Sowa
Sent: 08 March 2002 18:31
To: Seth Russell
Cc: West, Matthew R SITI-ITPSIE; Standard-Upper-Ontology (E-mail)
Subject: Re: SUO: Re: RE: Logic and Ontology
Seth et al.,
The difference between set membership and a monadic predicate
(i.e., a property) is irrelevant if you are dealing with a single
fixed model of the world that is not changing over time.
In that case, there is one fixed universe of discourse, and
a predicate such as P(x) is true of some object x if and only if
x happens to be a member of the set of things for which P is true.
However, if you are talking about hypothetical things, plans for
the future, or comparisons of the state of the world at different
points in time, then the distinction is very important.
For example, let the predicate P(x) mean "x is a Boeing 777 airplane".
Today, the set of all x's for which P(x) is true is an existing
set of things in the world. But for many years, engineers at Boeing
were talking about (and defining) the predicate P when no such
things existed. They were happily defining the predicate P (in terms
of computerized diagrams, simulations, etc.) even though the actual
set was empty.
Bottom line: If you have a fixed set of things, you don't have to
worry about the distinction. But when you are talking about changes,
hypotheses, plans, intentions, etc., the distinction is very important.
John Sowa