Re: [ontolog-forum] Re Foundation ontology, CYC, and Mapping

["John F. Sowa" <sowa@xxxxxxxxxxx>]

Chris,    (01)

CM> Whoa, combinatory logic is way stronger than ordinary FOL.
 > (I suspect you have in mind syntactically (and historically)
 > related systems like the predicate functor calculi of Quine
 > and Schönfinkel that do away with the apparatus of quantifiers
 > and variables.) ...    (02)

Yes.  I agree that combinatory logic in its full glory goes
far beyond the bounds of FOL.  I was indeed thinking of the
use of combinators for eliminating quantifiers and variables.    (03)

In any case, simplicity is not a simple notion that can be
characterized in any simple way.  Reducing the number of axioms
and primitives can sometimes make a system simpler.  But if you
go too far, the overall structure can become more complex.    (04)

For example, all the operators of Boolean algebra can be
defined in terms of just one: either Nand or Nor.  Those
definitions are actually useful for reducing the number of
transistors in logic circuits.    (05)

But the definitions of the most common operators, such as
And, Or, and Not become more complex.  When you combine a
Boolean algebra based on Nand or Nor with the quantifiers,
it can obscure rather than clarify many relationships.    (06)

John    (07)


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