SUO: Logic and Ontology
Dear Colleagues,
I was recently sent a copy of Axiomathes, and noticed a paper
with the above title.
Cocchiarella, Nino B.; "Logic and Ontology", Axiomathes 12: 117-150, 2001
The part of the paper that interested me was the different
interpretations that could be made of predication, depending on
whether your basic ontology is based on nominalism, conceptualism,
or realism (or some graduation between).
One of these, attributed to Quine, sems to coincide with my own
interpretation of predication, and I repeat it here.
"Quine's understanding of his ontology as platonistic and of sets
as universals is based on a rather involuted argument, the essentials
of which are as follows: if we were to adopt platonism as a theory of
universals as represented by higher order logic in which predicate
as well as individual variables can be bound, then
1. predicate quantifiers can be given a referential ontological
interpretation only if predicates are (mis)construed as singular
terms (i.e. terms that can occupy the argument or subject positions
of predicates); and
2. assuming extensionality,
3. predicates, as singular terms, can only denote sets, which
4. must then also be the universals that are the values of the
predicate variables in predicate positions; and therefore
5. predication must be the same as membership, in which case
6. we might as well replace predicate variables by individual
variables (thereby accepting nominalism's exclusion of bound
predicate variables) and take sets as values of the individual
variables, arriving thereby at
7. a first order theory of membership (set theory) which
8. is platonist because it has abstract entities as values of
its one type of variable.
Thus beginning with higher order logic with bound predicate
variables as a version of platonism, we arrive at the nominalist
position to recognise only quantification with respect to
individual variables (or the subject positions of predicates)
but with individual variables that can have abstract sets as
their values, which are therefore really universals (i.e.
entities that have a predicable nature)"
Well I'm sure there are some bits of that that have gone over
my head, but the bottom line is that predication = membership
is a possible interpretation of predication, which is the
interpretation I would wish to make. However, other parts of the
paper make it clear that there are other possible interpretations.
I suspect some of these are the interpretation of predication
some others (probably not in the 4D camp) would wish to make here.
The bottom line here as far as I can see is that without stating
a particular meaning for predication, KIF is ambiguous. Or perhaps
I should say that when you use KIF, you need to state the meaning
of predication you are using.
It strikes me that using different interpretations of predication
adds to the difficulties of integrating ontologies with different
ontologies of logic. This is obviously inconvenient, but in the
end I would rather build on rock than on sand.
Matthew West
Principal Consultant
Shell Information Technology International Limited
Shell Centre, London SE1 7NA, United Kingdom
Tel: +44 20 7934 4490 Other Tel: +44 7796 336538
Email: matthew.r.west@is.shell.com
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