[FOM] Is there a compendium of examples of the "power" of deductive logic?
Richard Haney
rfhaney at yahoo.com
Fri Dec 9 22:39:44 EST 2005
Does anyone know of a compendium of examples of the "power" of
deductive logic? By the "power" of logic, I mean the capability of
logic to convince in application to matters of empirical phenomena.
Convincing through deductive logic is at the heart -- a crucial aspect
-- of both mathematics and the philosophy of logic generally.
Of course, convincing is in one sense a subjective phenomenon, but
behaviorists/pragmatists could probably identify some objectively
observable behavior to use for suitable definition(s), and such
behavioristic definitions may include reports of being convinced as
well as other behavior that might seem to contradict such reports.
Most uses of deductive logic that come to mind in applications to the
empirical world seem to be exploratory in nature. That is, it seems
that the most common use of deductive logic (outside of its restriction
to abstract mathematics) is to make *tentative* inferences and then to
verify those inferences by empirical means. And it seems that such
inferences are tentative primarily because the premises typically are
not entirely "precise" or may be somewhat dubious in particular
instances.
So I am wondering about the possibility of stunning examples that can
serve as paradigms for the power of logic in empirical applications.
In other words I am looking for empirical evidence that demonstrates
unequivocally that deductive logic is indeed worthy of study.
The closest things that come to mind are the theorems of elementary
geometry. I suppose that theorems concerning discrete and finite
phenomena -- e.g., finite groups, graph theory -- would probably also
qualify as "stunning" examples.
If this seems like a "stupid" question, please excuse the audacity.
Most of my formal education in mathematics and the natural sciences
(especially physics) seems to have been fairly doctrinaire and dogmatic
in nature, with extremely little attention to matters of thorough
empirical verification. But it also seems that dogmatism is probably
the number one impediment to advancement in the sciences, and I have a
habit of only tentatively trusting dogmas and doctrines at best.
Richard Haney
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