Probability and Rationality 2017

For 2018-19:

Please contact me if you can't find the reading materials.

Lecture slides on Blackboard. Contact me if you don't have access.

You should come to class with (at least) two questions regarding the readings (at least one philosophical question and at least one formal/technical question). And, you should always be prepared to discuss the readings in class. The starred reading is essential.

More readings:

1. Probability Calculus and Introduction

Do exercise sheet attached below. Look at the rest of my lecture slides for expectation. Don't be worried if you're struggling with it! We'll go through this stuff again.

Hacking, An Introduction to Probability and InductiveLogic, chs 4-6 [very friendly introduction]

Skyrms Choice and Chance ch. VI

Strevens Notes on Baysean Confirmation Theory, just the start of it

Hajek SEP Interpretations of Probability sections 1&2

2. Interpretations of Probability

* Hajek SEP Interpretations of Probability - Don't worry about 3.1&3.2; section 3.3 is what we'll cover in a lot of detail in the rest of the course so don't worry that section; I'd prefer you to read the Physical Probability stuff (in 3.4,3.5 and 3.6.) as I think it's important to see that.

Strevens Probability and Chance

Propensity: Gillies Varieties of Propensity - Look here for Humphrey's paradox discussion as we were talking about in seminars.

Frequentism: Hajek. “Mises Redux. Redux.”

Pettigrew Probability in Bloomsbury Companion to Philosophical Logic

Popper. Propensity interpretation of probability

3. Dutch Book Theorem

* Vineberg, Susan (2001) ‘The Notion of Consistency for Partial Belief’ Philosophical Studies 102: 281-296.

Jeffrey Subjective Probability the Real Thing. ch.1 Probability Primer.

Vineberg, Susan (2011) ‘Dutch Book arguments’ Stanford Encyclopedia of Philosophy, Zalta, Edward N. (ed.)

Armendt, Brad (1993) ‘Dutch Books, Additivity, and Utility Theory’ Philosophical Topics 21(1):1-20

Howson, Colin (1997) ‘The Logic of Induction’ Philosophy of Science 62(2):268-90.

Hájek, Alan (2005) ‘Scotching Dutch Books’ Philosophical Perspectives 19:140-151.

Anna Mahtani (2015) ‘Dutch Books, Coherence, and Logical Consistency’ Noûs 49(3):522-537.

4. Accuracy

* Joyce, James M. (1998) ‘A Non-Pragmatic Vindication of Probabilism’ Philosophy of Science 65(4):575-603.

Maher, Patrick (2002) ‘Joyce’s Argument for Probabilism’ Philosophy of Science 69(1):73-81.

Easwaran, Kenneth and Branden Fitelson (2012) ‘An ‘evidentialist’ worry about Joyce’s argument for Probabilism’ Dialectica 66(3):425-433.

Pettigrew, Richard (2013) ‘Accuracy and Evidence’ Dialectica 67(4): 579-96.

Pettigrew, Richard ‘Epistemic Utility Arguments for Probabilism’ SEP

Pettigrew, Richard ‘Introduction’ to Accuracy and the Laws of Credence

5. Decision theory

(readings changed for Friday's class. New version:)

* Stanford Encyclopedia "Decision Theory" Steele and Steffanson; focus on sections 1 and 2. Section 3 is also worth a look at.

Titelbaum Chapter 7 gives an overview of stuff later in the course. Focus on material up to end of section 7.2.2, the rest we'll recover.

Also would be good if you can read: Weatherson chapter 8. on blackboard.

Joyce (1999) The Foundations of Causal Decision Theory ch 1&2.

Von Neumen Morgenstern

Liu, Yang. Elements of Bayesian Decision Theory Chapter II Savage’s Subjectivism. For more technical details of Savage’s system

6. Reading Week

No classes

7. Problems for Expected Utility

* Buahak Risk and Tradeoffs

Stefansson and Bradley What is Risk Aversion?

Savage. Foundations of Statistics. Page 1-40

Kannermahn and Tversky Prospect Theory


8. Act state dependence

* Titelbaum Chapter 7 from 7.2.2 -- a textbook that's good to read.

Also good, though harder: Lewis (1981) "Causal Decision Theory". Sections 1-5

Egan Some Counterexamplesto Causal Decision Theory

Weirich Causal Decision Theory esp. "Objections"


Joyce (1999) The Foundations of Causal Decision Theory

Jeffrey (1983) The Logic of Decision

9. Conditionalisation and Reflection

(readings are all available on blackboard)

* R.A. Briggs (2008) ‘Distorted Reflection’ Philosophical Review 118(1):59-85.

Mahtani, Anna (2008) ‘Diachronic Dutch Book Arguments’ Philosophical Review 121(3):443-450.

van Fraassen, Bas C. (1984) ‘Belief and the Will’ Journal of Philosophy 81(5):235-256

Christensen, David (1991) ‘Clever Bookies and Coherent Beliefs’ Philosophical Review 100(2):229-247

Schoenfield, Miriam ‘Conditionalization Does Not (in general) Maximize Expected Accuracy’

Anna Mahtani ‘Deference, Respect and Intensionality’ Philosophical Studies:1-21.

10. Planning to Conditionalise

Reqd for ugs: Dimitri Gallow "Learning and Value Change".

Reqd for masters: Sophie Horowitz "Immoderately Rational"

Greaves and Wallace "Justifying Conditionalisation"

Following plans

  • Laurie Paul "Diachronic Continence"
  • Michael Bratman "Time, Rationality and Self-Governance"

Peter Brown "Conditionalization and Expected Utility "

Graham Oddie "Conditionalization, Cogency, and Cognitive Value"

11. What are credences?

Eriksson and Hajek (2007) "What are Degrees of Belief"

Zynda Representation Theorems and Realism About Degrees of Belief

Nau De Finetti was Right: Probability Does Not Exist

Konek Comparative Credence. on blackboard. esp. section 3

Savage representation theorem

For more comparative confidence: Suppes 1994 Representation and Invariance of Scientific Structures book; and Fishburn

12. Revision

Other topics


Williamson How probable is an infinite sequence of heads?

Pruss Infinitesimals are too small for countably infinite fair lotteries

Wenmakers and Horsten Fair infinite lotteries

Imprecise probabilities

Joyce "How Probabilities Reflect Evidence"

Bradley SEP Imprecise Probabilities