Logic, Probability & Games
Professor Parikh received all his degrees from Harvard, a bachelor's degree with highest honors in Physics and Masters and Doctors in Mathematics. He is a three time winner of a prize in the Putnam mathematical competition. Prior to coming to CUNY, he has taught at Stanford, Boston University, NYU, Bristol, and Panjab Universities and has had research positions at MIT and IBM. He has made fundamental contributions to Formal Languages, Logic of Programs, Non-standard Analysis, the Theory of Proofs and more recently in Game Theory and Social Software, a field founded by him which has been a theme of four international conferences.
A collaborator for the course will be Professor Haim Gaifman of Columbia University who has also made fundamental contributions to Logic and Philosophy. Professor Gaifman is a mathematician and philosopher who received his Ph.D. under Alfred Tarski (on infinite Boolean algebras). He worked on a broad spectrum in mathematical logic (mostly set theory and models of Peano arithmetic), foundations of probability, as well as theoretical computer science and the philosophy of language. Before moving to Columbia in 1990, he was professor of mathematics at the Hebrew University of Jerusalem, where he also directed the program in History and Philosophy of Science.
The course will concentrate on three fundamental areas. 1) The Foundations of Probability, referring back to the work of Kolmogorov, Ramssey, de Finetti and Savage. 2) Epistemic Reasoning, referring back to the work of Halpern et al, the CUNY school with work by Parikh as well as students like Plaza, Pacuit, Krasucki, and the Amsterdam school led by Johan van Benthem, Alexandru Baltag and Sonja Smets. 3) The third area will be Game theory and Social Software, concentrating on communication and cheap talk, an area which began with the philosopher Paul Grice but which has seen extensive development by game theorists and linguists.
There will be no exams for the course but a student may wish to present a paper. It is expected that there will be distinguished speakers from outside and some of the meetings will take place at Columbia University with its beautiful campus.