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Many people think of logic as cut and dried and settled, and so
it is if you think only of the classical first order logic that
was essentially given by Russell and Whitehead. But unless one takes
a very parochial view of logic, there are many alternatives, which
I am grouping under the title of "deviant logic". They
include the logic of strict implication (C.I.Lewis), various modal
logics, various forms of intensional logic, temporal logic, many
valued logic, probabilistic logic, nonmonotonic logic, deontic logic,
and within mathematics itself, intuitionistic logic. One of the
more recent variants is paraconsistent logic, which comes in a variety
of forms, and allows us to treat inconsistent sets of premises sensibly.
Each of these logics has a rational and a purpose, and many of
them are closely related. To explore them, even in the reltively
superficial way that is open to us, will give some idea of the power
and generality of the logical way of doing things.
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Useful secondary sources:
Brian Chellas, Modal Logic, Cambridge University Press,
1995
Graham Priest, Introduction to Non-Classical Logic, Cambridge
Press, 2001.
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