ONT Re: Logic Of Relatives
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LOR. Discussion Note 26
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HC = Howard Callaway
HC: But on the other hand, it is not customary to think of "&" as
a relation among statements or sentences -- as, for instance,
logical implication is considered a logical relation between
statements or sentences.
Actually, it is the custom in many quarters to treat all of the
boolean operations, logical connectives, propositional relations,
or whatever you want to call them, as "equal citizens", having each
their "functional" (f : B^k -> B) and their "relational" (L c B^(k+1))
interpretations and applications. From this vantage, the interpretive
distinction that is commonly regarded as that between "assertion" and
mere "contemplation" is tantamount to a "pragmatic" difference between
computing the values of a function on a given domain of arguments and
computing the inverse of a function as to its prospective true value.
This is the logical analogue of the way that our mathematical models
of reality have long been working, unsuspected and undisturbed by
most philosophers of science, I might add. If only the logical
side of the ledger were to be developed rather more fully than
it is at present, we might wake one of these days to find our
logical accounts of reality, finally, at long last, after an
overweaningly longish adolescence, beginning to come of age.
Jon Awbrey
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