### Philosophy of Probability Workshop

March 25, 2015

Marie Mount 1310, University of Maryland, College Park

### Schedule

09:30–10:10 Mathias Frisch: Predictivism and Old Evidence: A Critical Look at Climate Model Tuning
10:10–10:50 Max Bialek: Measuring (Meta-)Physical Limits to Induction
10:50–11:30 David Etlin: Affective Beliefs, Cognitive Desires

10 Minute Break

11:40–12:20 Michael Dascal: Quantum Thinking about Game Theory
12:20–13:00 Jessica Pfiefer: Abstraction and Probabilities in Evolutionary Theory

50 Minute Lunch Break

13:50–14:30 Aleks Knoks: Closed-World Assumption and Probabilistic Reasoning
14:30–15:10 Branden Fitelson: Two Approaches to Belief Revision

10 Minute Break

15:20–16:00 Eric Pacuit: Learning from Deliberation in Games

10 Minute Break

Colloquium Talk (in Marie Mount 1310):
16:10–18:00 Alan Hájek: Deliberation Welcomes Prediction

18:00–18:45 Reception (in the Department Lounge, Skinner)

19:45 Dinner (Ethiopian in DC, restaurant to be determined)

### Abstracts

Branden Fitelson and Ted Shear
Two Approaches to Belief Revision

In this paper, we compare and contrast two approaches to belief revision: a broadly Bayesian approach (based on epistemic utility theory)m and the traditional (logic-based) AGM approach. Our discussion will focus on the most interesting (and surprising) points of (dis)agreement between the two approaches.

Jessica Pfiefer
Abstraction and Probabilities in Evolutionary Theory

There are explanatory reasons to abstract from features of an organism’s environment, even though these features are causally relevant to evolutionary outcomes. This has been touted as one of the main reasons biologists invoke probabilities in understanding evolutionary processes (e.g., Sober 1984, Matthen 2009). In the paper, I argue that there are different modes of abstraction, and these different modes affect how we think about the probabilities involved in quantifying fitness. This in turn helps situate the recent debate between the statisticalists and causalists about selection and makes clear why certain criticisms of the statisticalists miss their mark. However, it also clarifies how we can and ought to think about selection causally. One interesting result of such a causal view is that random drift will not be purely (or perhaps even primarily) a function of population size. This has important implications, not only for how we think about and model selection and drift, but also for how biologists might study these processes experimentally.

Max Bialek
Measuring (Meta-)Physical Limits to Induction

Induction seems to work in our world. (It has so far!) But remembering Hume leaves us worrying that at any moment nature will be unkind to our inductive efforts and, say, turn emeralds blue, stop the sun from rising, or switch off gravity. A world where emeralds suddenly turn blue probably isn’t that bad of a world. It’s plausible that most of the inductive inferences we like to make will be unaffected by the change. In contrast, our lives would be in intellectual (not to mention physical) ruin if gravity was switched off. The blue emeralds world seems more friendly to induction than the stopped gravity world. The aim of this talk is to propose a quantification of that induction (un)friendliness of a possible world. To do so I reconstruct Shannon’s (1948) uniqueness theorem for entropy as a measure of uncertainty, with assumptions being newly motivated by their fit to the aim of measuring induction unfriendliness.

Mathias Frisch
Predictivism and Old Evidence: A Critical Look at Climate Model Tuning

Many climate scientists have made claims that may suggest that evidence used in tuning or calibrating a climate model cannot be used to evaluate the model. By contrast, the philosophers Katie Steele and Charlotte Werndl have argued that, at least within the context of Bayesian confirmation theory, tuning is simply an instance of hypothesis testing. In this paper I argue for a weak predictivism and in support of a nuanced reading of climate scientists' concerns about tuning: there are cases, model-tuning among them, in which predictive successes are more highly confirmatory of a model than accommodation of evidence.

Alan Alan Hájek
Deliberation Welcomes Prediction

A number of prominent authors—Levi, Spohn, Gilboa, Seidenfeld, and Price among them—hold that rational agents cannot assign subjective probabilities to their options while deliberating about which they will choose. This has been called the “deliberation crowds out prediction” thesis. The thesis, if true, has important ramifications for many aspects of Bayesian epistemology, decision theory, and game theory. The stakes are high.

The thesis is not true—or so I maintain. After some scene-setting, I will precisify and rebut several of the main arguments for the thesis. I will defend the rationality of assigning probabilities to options while deliberating about them. Deliberation welcomes prediction.

Michael Dascal

This paper is the first part of a project that begins by reformulating game theory using quantum mechanics. The motivation for this reformulation is that quantum mechanics is built to take into account probability distributions over probability distributions through the density matrix. In the context of game theory (as well as decision theory), this translates into a formal system that can directly deal with ignorance about probability distributions, such as mixed strategies. After introducing the basics of quantum mechanics, the reformulation is presented with particular attention to steps that may seem odd or difficult. From here, some preliminary plans for further research are discussed, including a comprehensive treatment of quantum games meant to unify existing approaches in the literature, an investigation into decision-making with imprecise probabilities, and the identification of deliberation processes with quantum dynamical operators within the system.

David Etlin
Affective Beliefs, Cognitive Desires

The central point in Lewis's argument against Desire as Belief is shown to depend on the thesis that if you desire something then you believe it is good. The converse thesis, that if you believe something is good then you desire it, establishes enough of the controversial value invariance thesis that dropping the latter as a background assumption does not suffice to save Desire as Belief, given Jeffrey's evidential decision theory. Causal decision theory does not support any version of the invariance assumption, and I defend it as an analysis of desire.

Aleks Knoks
Closed-World Assumption and Probabilistic Reasoning

Identification of the so-called closed-world assumption'' is one of the results that the field of Logic and AI can justifiably be proud of. What this principle says is, roughly, that (in certain domains) one can assume that all the propositions that are not explicitly specified to be true can be taken to be false. It seems to account for our reasoning in a certain class of everyday situations, it has been used to explain psychological data (e.g., the suppression effect), and it has interesting connections to Kahneman's [1] explanation of the overconfidence bias. In my talk I will survey the explanatory benefits of the closed-world assumption and argue that a successful probabilistic model of reasoning would need to identify principles that are similar to it.

[1] Kahneman, D. (2011). Thinking Fast and Slow. New York: Farrar, Straus and Giroux.

Eric Pacuit
Learning from Deliberation in Games

There is now a growing body of literature that analyzes games in terms of the "process of deliberation" that leads the players to select their component of a rational outcome (the classic reference here is Skyrms 1990). Although the details of the various models of deliberation in games are different, they share a common line of thought: The rational outcomes of a game are arrived at through a process in which each player settles on an optimal choice given her evolving beliefs about her own choices and the choices of her opponents. The goal is not to develop a formal account of the players’ practical reasoning in game situations. Rather, it is to describe deliberation in terms of a sequence of belief changes about what the players are doing or what their opponents may be thinking. The central question is: What are the update mechanisms that match different game-theoretic analyses? The general conclusion is that the rational outcomes of a game depends not only on the structure of the game, but also on the players’ initial beliefs, which dynamical rule is being used by the players to update their inclinations (in general, different players may be using different rules), and what exactly is commonly known about the process of deliberation.

I will offer a critical analysis of the different models of deliberation and discuss the implications for a theory of rational choice in strategic situations.