Thursday, November 21, 1996, 4:00pm
102 Bradley Hall
Professor Catherine Womack
Re-Solving the Tension Between Plausible and
Demonstrative Reasoning in Mathematics
Abstract.Philosopher and mathematician Georg Polya argued that our
reliance on what he calls "demonstrative reasoning" (deductive reasoning)
in mathematics requires reliance on "plausible reasoning" (inductive
methods). IN this paper I examine the various tasks that mathematicians
are required to do (e.g. finding problems to solve, deciding whether a
conjecture might be true, finding a proof of the conjecture, confirming
that the proof is correct). I argue that, in addition to using plausible
reasoning to discover new mathematical conjectures, mathematicians
also use plausible reasoning to *justify* the correctness of their proofs.
I then suggest ways of extending the use of plausible reasoning to include
inductive methods as equally legitimate as classical deductive proof
Tea. High tea will be served at 3:30pm in the Lounge.
Emmy's. Certain refreshments will be available at the Emmy's after the
Hostess.Marcia Groszek is the hostess. Anybody who is interested in
having dinner with the speaker should contact Marcia at 646-2313.