John Corcoran

  Information-theoretic logic and transformation-theoretic logic


There is a symbiotic relationship between science and logic.  The
rational activities of the scientists provide the content of logic.
Logic, after assimilating and codifying that content, provides science
with an account of its logical foundations.  But when logic turns its
foundational probings back on itself, it discovers problems it can not
now solve.  The opposition between information-theoretic and
transformation-theoretic approaches to the foundations of logic raises
profound ontic and epistemic issues concerning the grounding of two
complementary logical activities: that of determining that a given
conclusion is a consequence of, or is implied by, given premises; and
that of determining that a given conclusion is independent of, or is
not implied by, given premises.  Ironically, the two contradictory
approaches grow naturally from the two complementary logical
activities.  This expository paper, accessible to a broad audience of
philosophers, mathematicians, scientists and humanists, provides clear
descriptions of the two approaches.