HARVARD/MIT LOGIC SEMINAR
Epistemic and Ontological Problems Concerning Mathematics
Haim Gaifman (Columbia University)
Tuesday, April 30, 2013, at 4:15 PM
Fong Auditorium (Boylston Hall 110), Harvard University
Abstract. Philosophy of mathematics is confronted with two major questions: (i) How do we come to know mathematical propositions? (ii) What is the nature of mathematical truth? Attempts to give satisfactory answers to one of the questions have resulted in unsatisfactory accounts regarding the other. I shall outline an approach intended to do justice to both questions. This is an ongoing work.
YESHIVA MATH/PHIL CLUB
The theory of infinite games, with examples, including infinite chess
Joel David Hamkins (CUNY)
Tuesday, April 30, 2013 5:45 pm
Furst Hall, Amsterdam Ave. & 185th Street, Yeshiva University
Abstract. I will give a general introduction to the theory of infinite games, suitable for mathematicians and philosophers. What does it mean to play an infinitely long game? What does it mean to have a winning strategy for such a game? Is there any reason to think that every game should have a winning strategy for one player or another? Could there be a game, such that neither player has a way to force a win? Must every computable game have a computable winning strategy? I will present several game paradoxes and example infinitary games, including an infinitary version of the game of Nim, and several examples from infinite chess.