Ahmed: Causal Decision Theory and Intrapersonal Nash Equilibria

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.

The Inaugural Meeting of the Columbia-CUNY Joint Workshop in Logic, Probability, and Games

The Value of Ignorance and Objective Probabilities
Haim Gaifman (Columbia)
2:00-3:00 PM, October 18th, 2013
Rm. 4419, CUNY GC

Abstract. There are many cases in which knowledge has negative value and a rational agent may be willing to pay for not being informed. Such cases can be classified into those which are essentially of the single-agent kind and those where the negative value of information derives from social interactions, the existence of certain institution, as well as from legal considerations. In the single-agent case the standard examples involve situations in which knowing has in itself a value, besides its instrumental cognitive value for achieving goals. But in certain puzzling examples knowing is still a cognitive instrument and yet it seems to be an obstacle. Some of these cases touch on foundational issues concerning the meaning of objective probabilities. Ellsberg’s paradox involves an example of this kind. I shall focus on some of these problems in the later part of the talk.

Knowledge is Power, and so is Communication
Rohit Parikh (CUNY)
3:00-4:00 PM, October 18th, 2013
Rm. 4419, CUNY GC

Abstract. The BDI theory says that people’s actions are influenced by two factors, what they believe and what they want. Thus we can influence people’s actions by what we choose to tell them or by the knowledge that we withhold. Shakespeare’s Beatrice-Benedick case in Much Ado about Nothing is an old example. Currently we often use Kripke structures to represent knowledge (and belief). So we will address the following issues: a) How can we bring about a state of knowledge, represented by a Kripke structure, not only about facts, but also about the knowledge of others, among a group of agents? b) What kind of a theory of action under uncertainty can we use to predict how people will act under various states of knowledge? c) How can A say something credible to B when their interests (their payoff matrices) are in partial conflict? When can B trust A not to lie about this matter?

Hájek: Staying Regular?

Staying Regular?
Alan Hájek (Australian National University)
Thursday, April 4, 2013, 4:00 – 5:30 PM
716 Philosophy Hall, Columbia University

‘Regularity’ conditions provide nice bridges between the various ‘box’/‘diamond’ modalities and various notions of probability. Schematically, they have the form:

If X is possible, then the probability of X is positive

(or equivalents). Of special interest are the conditions we get when ‘possible’ is understood doxastically (i.e. in terms of binary belief), and ‘probability’ is understood subjectively (i.e. in terms of degrees of belief). I characterize these senses of ‘regularity’—one for each agent—in terms of a certain internal harmony of the agent’s probability space  <Ω, F, P>. I distinguish three grades of probabilistic involvement. A set of possibilities may be recognized by such a probability space by being a subset of Ω; by being an element of F; and by receiving positive probability from P. These are non-decreasingly committal ways in which the agent may countenance a proposition. An agent’s space is regular if these three grades collapse into one.

I briefly review several of the main arguments for regularity as a rationality norm, due especially to Lewis and Skyrms. There are two ways an agent could violate this norm: by assigning probability zero to some doxastic possibility, and by not assigning probability at all to some doxastic possibility (a probability gap). Authors such as Williamson have argued for the rationality of the former kind of violation, and I give an argument of my own. So I think that the second and third grades of probabilistic involvement may come apart for a rational agent. I then argue for the latter kind of violation: the first and second grades may also come apart for such an agent.

Both kinds of violations of regularity have serious consequences for traditional Bayesian epistemology. I consider especially their ramifications for:

  • conditional probability
  • conditionalization
  • probabilistic independence
  • decision theory

van Benthem: Logic in Games

Logic in Games
Johan van Benthem (Amsterdam/Stanford)
Thursday, November 15, 2012, 4:10 – 6:00 PM
716 Philosophy Hall, Columbia University

Abstract. In recent decades, logic has been applied in the foundations of game theory, and this makes sense as a capping stone for the philosophical logic tradition of studying various dimensions of information-driven agency. But at the same time, the core notions of logic themselves can be cast as games, and a thriving theory has sprung up around this perspective, especially at interfaces with computer science. I will compare these two perspectives of logic of games versus logic as games, discuss some results about their connections, and raise the question what this contrast tells us about logic.

Reception to follow

Scott: Lambda Calculus Then and Now

Lambda Calculus: Then and Now
Dana Scott (CMU and Berkeley)
November 9th (Friday), 5PM, 716 Philosophy Hall, Columbia University

Abstract. A very fast development in the early 1930’s following Hilbert’s codification of Mathematical Logic led to the Incompleteness Theorems, Computable Functions, Undecidability Theorems, and the general formulation of Recursive Function Theory. The so called Lambda Calculus played a key role. The history of these developments will be traced, and the much later place of Lambda Calculus in Mathematics and Programming Language Theory will be outlined.

A map of the Columbia campus and directions to the payday lenders room can be found here.

Formal Philosophy Reading Group #13

The next meeting of the formal philosophy reading group will take place on Monday (April 30) 7:10 – 9:00 PM in room 720 Philosophy Hall, Columbia University. Mr. Li, Zhanglv will discuss briefly the base-rate fallacy. Prof. Gaifman will continue his presentation on objective probabilities and conditionalization.

Light refreshments will be served. Hope to see you all there!