Aldo and Chris, (01)
Your examples add further support for the points I keep repeating: (02)
1. Make a sharp distinction between the subject matter of the ontology
and the metalanguage used to talk about the ontology. (03)
2. Restrict the metalanguage to the barest minimum you need to talk
about the logic. The only terms needed for the metalanguage are
those that refer to the syntactic features of the logic. (04)
AG
> being an individual or a class is a technical problem of using
> a logical representation language in the most efficient way with
> respect to a given problem. (05)
That is a choice of ontology. If you want to talk about individuals,
define a monadic predicate isIndividual(x), which is true iff x
is an individual. If you want to talk about classes, define a
predicate isClass(x), which is true iff x is a class. (06)
AG
> ZF set theory defines natural numbers as sets! (07)
If you want to define an ontology for natural numbers that uses ZF set
theory, then specify predicates isNumber(x) and isSet(x) and the axiom (08)
(Ax)(isNumber(x) -> isSet(x)). (09)
Those are object-level statements in the logic, not metalevel statements
about the ontology. (010)
AG
> the ability of having an intuition of the difference between individuals
> and classes (in context) is given by our evolved cognitive abilities,
> such as the containment schema, or something comparable. (011)
If you want to define an ontology that maps to and from your intuitions,
then use your chosen logic to specify whatever predicates you need. (012)
CP
> If you choose to make that distinction, then you may then want to tighten up
> what kind of things cannot have members, and argue that these must all be
> concrete (a kind of abstract object nominalism) - another choice. (013)
You can make any choices you want. But they should all be object-level
axioms and definitions that specify any predicates you need: (014)
isConcrete(x), isAbstract(x)... (015)
No debate needed. If there's any question, check the specifications. (016)
John (017)
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