Gordon,
It finally struck me that you are apparently taking "undefined primitive
term" too seriously and broadly. In Peano's system, 'number', 'successor'
and 'one' are undefined primitives within the axioms, but they are
explicitly chosen to fit number theory. Neither the selection of terms
nor their interrelationships are arbitrary for specific mathematical
calculi.
Logic is usually accepted as a given. But I recall the late E. John
Lemmon noting that a particular proof in modal logic required
Aristotelian assumptions rather than the usual universal quantifier.
Subalternation is valid in syllogistic, but not in contemporary
functional logics.
Dave (ASA)
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Received on Sat Oct 11 16:32:57 2008
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