Alex, (01)
> in axiomatic theory there is a small group of initial entities
> (predicates, constants, functions) we may say mutually defined
> by axioms. (02)
That is true of most mathematical theories. That means that the
*total* number of "initial entities" or "so-called primitives"
is equal to the average number for any particular theory times
the total number of theories involved in an ontology. (03)
> And for example in NBG set theory: there is only one initial
> entity - binary predicate 'in'. (04)
That's fine for starters. But as you add more axioms, you define
more and more structure relationally, not by closed-form definitions. (05)
And mathematical theories are the *simplest* kinds of ontological
theories imaginable. For anything in the real world, there are no
such things as necessary and sufficient conditions. For example,
what is the definition of 'dog', 'house', 'river', 'mother',
'friend', 'spouse', 'food', 'knife', 'breath', 'hand', 'eating',
'drinking', 'walking', 'running', 'skipping', 'giving', 'keeping',
'marrying', 'fighting', etc? Can you state necessary and sufficient
conditions for any of those terms? (06)
Children learn those terms long before they begin first grade, but
nobody ever teaches them by necessary and sufficient conditions.
How is it possible for children to learn and use those terms so
successfully so quickly, while all our great philosophers and
linguists find it so difficult to define them? (07)
John (08)
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