Philosophy 903: Inductive Reasoning, Fall 2009

This graduate seminar on inductive reasoning meets on Mondays from 4-6pm in Helen C. White Hall room 5181.

For those who are enrolled, your grade will be based on class participation and a final paper. The final paper, approximately 20 pages in length, is due on December 21. Once you have chosen a topic, I suggest looking into some of the supplementary readings below, or at the far more extensive bibliography at http://www.fitelson.org/probability/syllabus.html.

Readings for the course:

Week 1 (9/14), the problem of induction:

Required reading: Stroud, Chapter 3 of Hume. Note that in this chapter page references are to Hume's A Treatise of Human Nature unless otherwise indicated. An "E" indicates a reference to Hume's Enquiries Concerning Human Understanding and Concerning the Principles of Morals.

Supplementary reading: Hume, A Treatise of Human Nature, Book I, Sections II through VI.

Weeks 2 and 3 (9/21 and 9/28), Hempel:

Required reading: Hempel, Studies in the Logic of Confirmation (I), Mind 54 (1945), 1–26.

Hempel, Studies in the Logic of Confirmation (II), Mind 54 (1945), 97–121.

Note that Hempel expresses universal generalization in a quirky way: "All objects are Fs" is rendered by him as "(x)(Fx)".

Supplementary reading: Hempel, "A Purely Syntactical Definition of Confirmation", The Journal of Symbolic Logic 8 (1943), 122–143.

Sober, Chapter 2 of Reconstructing the Past. The particularly relevant portion is Section 2.5.

Hempel, "The White Shoe: No Red Herring", British Journal for the Philosophy of Science 18 (1967), 239–240.

Here's my handout from the Hempel discussions.

Week 4 (10/5), the probability calculus:

This week we'll finish off Hempel, then do an introduction to the probability calculus. For those of you with little prior exposure to probability math, I would recommend reading Appendix 2 of Eells's Probabilistic Causality and the first two sections of Fitelson's "A Decision Procedure for Probability Calculus with Applications".

Here's a handout I'll be distributing in class. It's a list of facts that are useful to have handy when working with probabilities.

Weeks 5 and 6 (10/12 and 10/19), Carnap and objective Bayesianism:

Required reading: Carnap, excerpts from the first edition of Logical Foundations of Probability, plus the Preface to the Second Edition.

Note on Carnap's notation: For Carnap, "L-true" means "logically true, analytic." A script "L" with a subscript is a formal language, and a script "B" (that looks kind of like a number 8) with a subscript is a state description in such a language.

Supplementary reading: Carnap, "On Inductive Logic", Philosophy of Science 12 (1945), 72–97.

If you're interested in more on explication, here are two readings from Schillp's volume The Philosophy of Rudolf Carnap: One by Strawson addressing Carnap's theory of explication, and a reply to Strawson's piece by Carnap.

Here is my handout from class explaining Carnap's regular null confirmation functions.

Week 7 (10/26), grue:

Required reading: Goodman, "A Query on Confirmation", The Journal of Philosophy 43 (1946), 383–385.

Goodman, Chapter III of Fact, Fiction, and Forecast.

Supplementary reading: Quine, "Natural Kinds", reprinted in GRUE! The new riddle of induction, Open Court 1994.

Here is a summary I made of some of the main points about the grue problem from class.

Weeks 8 and 9 (11/2 and 11/9), Ramsey and subjective Bayesianism:

Required reading: Ramsey, "Truth and Probability".

Supplementary reading: Vranas, "Hempel's Raven Paradox: A Lacuna in the Standard Bayesian Solution", British Journal for the Philosophy of Science 55 (2004), 545–560.

Fitelson, "The Paradox of Confirmation", Philosophy Compass 1 (2006), 95–113.

Week 10 (11/16), arguments for probabilism:

Required reading: Hajek, "Arguments for—or against—Probabilism?", British Journal of the Philosophy of Science 59 (2008), 793–819.

This article gets a little hairy in Section 5 (on Joyce's argument)—try to just get a sense of what Joyce's argument is meant to be.

Supplementary reading: Hajek, "Dutch Book Arguments".

Kemeny, "Fair Bets and Inductive Probabilities", The Journal of Symbolic Logic 20 (1955), 263–273. (In which is proven the Converse Dutch Book theorem.)

Schick, "Dutch Bookies and Money Pumps", The Journal of Philosophy 83 (1986), 112–119.

Christensen, "Dutch-Book Arguments Depragmatized: Epistemic Consistency for Partial Believers", The Journal of Philosophy 93 (1996), 450–479.

Joyce, "Accuracy and Coherence: Prospects for an Alethic Epistemology of Partial Belief". This is the Joyce article to which Hajek is responding in our required reading for this week. Joyce also asked me to post this note with his article, noting an error in the statement of one of the principles.

Here is a handout with diagrams explaining portions of Joyce's accuracy argument.

Week 11 (11/23), credences and chances:

Required reading: Lewis, "A Subjectivist's Guide to Objective Chance".

Here is a handout from class to go with the Lewis.

Week 12 (11/30), inferences and formal systems:

Required reading: Harman, Change in View, Chapters 1-3.

Supplementary reading: MacFarlane, "In What Sense (If Any) Is Logic Normative for Thought?".

Broome, "Normative Requirements", Ratio XII (1999), 398–419.

Week 13 (12/7), logical omniscience:

Required reading: Eells, "Problems of Old Evidence", Pacific Philosophical Quarterly 66 (1985), 283–302.

Supplementary Reading: Hacking, "Slightly More Realistic Personal Probability", Philosophy of Science 34 (1967), 311–325.

Garber, "Old Evidence and Logical Omniscience in Bayesian Confirmation Theory", in Testing Scientific Theories, U. of Minnesota Press 1983.

Jeffrey, "Bayesianism with a Human Face", in the same volume.

Week 14 (12/14), the significance of language dependence:

Required reading: Titelbaum, "Not Enough There There: Reasons, Evidence, and Language Independence".