Doron Zeilberger, Rutgers Experimental Mathematics Seminar, February 25, 2016
See part 2 at vimeo.com/156974932
Abstract: The so-called Law of the Excluded Middle is completely illegitimate for so-called "infinite" sets, leading to so much scholastic drivel, and making a large part of modern mathematics (in particular all those "undecidability" results) utterly meaningless, except as a (usually utterly boring) game with "axioms". But even when restricted to finite sets it leads to paradoxical, unsatisfying conclusions (e.g. Prisoner's dilemma).