Formal Philosophy

Logic at Columbia University

Category: Events

Beziau : Round Squares are No Contradictions

by Yang Liu

Round Squares are No Contradictions
Jean-Yves Beziau (Federal University of Rio de Janeiro and UC San Diego)
4:10pm, Friday, April 24, 716 Philosophy Hall, Columbia University

Abstract. When talking about contradictions many people think of a round square as a typical example. We will explain in this talk that this is the result of a confusion between two notions of oppositions: contradiction and contrariety. The distinction goes back to Aristotle but it seems that up to now it has not been firmly implemented in the mind of many rational animals nor in their languages.According to the square of opposition, two propositions are contradictory iff they cannot be true and cannot be false together and they are contrary iff they cannot be true together but can be false together. The propositions “X is a square” and “X is a circle” cannot be true together according to the standard definitions of these geometrical objects, but they can be false together: X can be a triangle, something which is neither a square, nor a circle. A round square is a contrariety, not a contradiction. Aristotle insisted that there were two different kinds of oppositions, from this distinction grew a theory of oppositions that was later on shaped in a diagram by Apuleius and Boethius.It is easy to find examples of contrarieties, but not so of contradictions. Many pairs of famous oppositions are rather contraries: black and white (think of the rainbow), right and left (think of the center), day and night (think of dawn or twilight, happy and sad (think of insensibility), noise and silence (think of music), etc. Examples of “real” contradictions are generally from mathematics: odd and even, curved and straight, one and many, finite and infinite. We can indeed wonder if there are any contradictions in (non-mathematical) reality or if it is just an abstraction of our mind expressed through classical negation according to which p and ¬p is a contradiction.

Bjorndahl: Language Based Games

by Yang Liu

Language Based Games
Adam Bjorndahl (Carnegie Mellon University)
10:30 AM to 12:30 PM, Friday, March 20, 2015
Room 7395, CUNY Graduate Center

Abstract: We introduce a generalization of classical game theory wherein each player has a fixed “language of preference”: a player can prefer one state of the world to another if and only if they can describe the difference between the two in this language. The expressiveness of the language therefore plays a crucial role in determining the parameters of the game. By choosing appropriately rich languages, this framework can capture classical games as well as various generalizations thereof (e.g., psychological games, reference-dependent preferences, and Bayesian games). On the other hand, coarseness in the language—cases where there are fewer descriptions than there are actual differences to describe—offers insight into some long-standing puzzles of human decision-making.

The Allais paradox, for instance, can be resolved simply and intuitively using a language with coarse beliefs: that is, by assuming that probabilities are represented not on a continuum, but discretely, using finitely-many “levels” of likelihood (e.g., “no chance”, “slight chance”, “unlikely”, “likely”, etc.). Many standard solution concepts from classical game theory can be imported into the language-based framework by taking their epistemic characterizations as definitional. In this way, we obtain natural generalizations of Nash equilibrium, correlated equilibrium, and rationalizability. We show that there are language-based games that admit no Nash equilibria using a simple example where one player wishes to surprise her opponent. By contrast, the existence of rationalizable strategies can be proved under mild conditions. This is joint work with Joe Halpern and Rafael Pass.

Gruszczyńsk: Methods of constructing points from regions of space

by Yang Liu

Rafał Gruszczyńsk (Nicolaus Copernicus University, Toruń) will give an informal, non-colloquium talk this Friday, Nov. 21, at 2pm, in the seminar room (Philosophy 716). The title of the talk is “Methods of constructing points from regions of space”. Everybody is invited. The talk should be of special interest to colleagues and students working in logic, ontology, the philosophy of mathematics, and the philosophy of space and time.

Workshop on Pragmatics, Relevance and Game Theory

by Yang Liu

Workshop on Pragmatics, Relevance and Game Theory
CUNY Graduate Center, Rm. 9207
October 14 and 15, 2014

Preliminary list of speakers:
Deirdre Wilson (UCL)
Laurence Horn (Yale)
Kent Bach (SFSU)
Robyn Carston (UCL)
Ariel Rubinstein (NYU and Tel Aviv)

Michael Devitt
Stephen Neale
Rohit Parikh

Marilynn Johnson (CUNY)
Ignacio Ojea (Columbia)
Todd Stambaugh (CUNY)
Cagil Tasdemir (CUNY)

Program here.

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.