Formal Philosophy

Logic at Columbia University

Ramanujam: Reasoning in games that change during play

by Yang Liu

Reasoning in games that change during play
R. Ramanujam (Institute of Mathematical Sciences, India)
4:00 – 6:00 PM, Friday, June 2, 2014
Room 4421, CUNY GC

Abstract. We consider large games, in which the number of players is so large that outcomes are determined not by strategy profiles, but by distributions. In the model we study, a society player monitors choice distributions and intervenes periodically, leading to game changes. Rationality of individual players and that of the society player are mutually interdependent in such games. We discuss stability issues, and mention applications to infrastructure problems.

Pacuit: Knowledge-Theoretic Aspects of Strategic Voting

by Yang Liu

Knowledge-Theoretic Aspects of Strategic Voting
Eric Pacuit (University of Maryland)
4:15 – 6:15 PM, Friday, May 9, 2014
Room 3309, CUNY GC

Abstract. It has long been noted that a voter can sometimes achieve a preferred election outcome by misrepresenting his or her actual preferences. In fact, the classic Gibbard-Sattherthwaite Theorem shows that under very mild conditions, every voting method that is not a dictatorship is susceptible to manipulation by a single voter. One standard response to this important theorem is to note that a voter must possess information about the other voters’ preferences in order for the voter to decide to vote strategically. This seems to limit the “applicability” of the theorem. In this talk, I will survey some recent literature that aims at making this observation precise. This includes models of voting under uncertainty (about other voters’ preferences) and models that take into account how voters may response to poll information.

Leitgeb: The Humean Thesis on Belief

by Yang Liu

The Humean Thesis on Belief
Hannes Leitgeb (Ludwig Maximilian University of Munich)
4:15 pm, May 2nd, 2014
716 Philosophy Hall, Columbia University

Abstract.  I am going to make precise, and assess, the following thesis on (all-or-nothing) belief and degrees of belief: It is rational to believe a proposition just in case it is rational to have a stably high degree of belief in it.I will start with some historical remarks, which are going to motivate calling this postulate the “Humean thesis on belief”. Once the thesis has been formulated in formal terms, it is possible to derive conclusions from it. Three of its consequences I will highlight in particular: doxastic logic; an instance of what is sometimes called the Lockean thesis on belief; and a simple qualitative decision theory.

Egan: Three Grades of Self-Involvement

by Ignacio Ojea

Three Grades of Self-Involvement
Andy Egan (Rutgers University)
4:10-6:00 PM, April 3rd, 2014
716 Philosophy Hall, Columbia University

Reception will follow

Ahmed: Causal Decision Theory and Intrapersonal Nash Equilibria

by Yang Liu

Causal Decision Theory and Intrapersonal Nash Equilibria
Arif Ahmed (University of Cambridge)
4:15 PM, April 4th, 2014
716 Philosophy Hall, Columbia University

Abstract.  Most philosophers today prefer ‘Causal Decision Theory’ to Bayesian or other non-Causal Decision Theories. What explains this is the fact that in certain Newcomb-like cases, only Causal theories recommend an option on which you would have done better, whatever the state of the world had been. But if so, there are cases of sequential choice in which the same difficulty arises for Causal Decision Theory. Worse: under further light assumptions the Causal Theory faces a money pump in these cases. It may be illuminating to consider rational sequential choice as an intrapersonal game between one’s stages, and if time permits I will do this. In that light the difficulty for Causal Decision Theory appears to be that it allows, but its non-causal rivals do not allow, for Nash equilibria in such games that are Pareto inefficient.

Ojea: Evaluation Games for Many Valued Logics

by Ignacio Ojea

Evaluation Games for many valued logics
Ignacio Ojea (Columbia University)
4:15 PM, March 28th, 2014
Room 3305, CUNY Graduate Center

Abstract.  Evaluation Games for classical logic are well known. Following early applications of games in model theory, by Ehrenfeucht and Fraisse, Hintikka and Parikh independently proposed a game-theoretic approach as a way of defining the classical semantics. A great deal of the game theoretic approach has been more recently studied by van Bentham. The original idea was to define the truth-value of a wff, in a given model, in terms of the existence of a strategy for one of the players (the “Verifier” and “Falsifier”) in a certain two-person game. These games can be also viewed in terms of pay-offs. Recently I suggested a natural extension of these games to the case of many valued logics, where the notion of a Nash equilibrium plays a crucial role.