Philosophy 148: Probability and Induction

TOC: [ Prerequisites ] [ Readings ] [ Requirements ] [ Sections ] [ Website ] [ Tentative Schedule ]

Prerequisites
Philosophy 12A (or an equivalent introductory symbolic logic class), plus at least high-school algebra (pre-calculus). And, little or no math phobia.

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Readings
All readings for the course will be posted online, in the "Tentative Schedule" portion of this syllabus page, below. In other words, there are no books to buy for the course. All you will need is a good web browser and a recent copy of Adobe Reader (version 7 or later). All readings will be posted here in either HTML or Adobe PDF format. See the "Tentative Schedule" section for all details about the readings (and reading requirements) for the course.

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Requirements
Students are expected to attend lecture and section regularly and to keep up with readings and exercises. This course will move rather quickly, and much of the material is likely to be new to you, so take care not to fall behind. Grades will be based on the following assignments and exams. See our Assignments & Exams Page for scheduling and content details.

• In-Class Quiz on Logic and The Probability Calculus (10%). After the third week of classes, I will give an in-class quiz on logic and the probability calculus. This will give you an early sense of how you are doing on the first, most technical part of the course.
  
  
• Bi-Weekly Homework Assignments (30%). Every other Thursday (starting in week 2), an assignment will be given. Usually, an assignment will consist of several exercises, problems, and/or short answer questions, each of which should be answerable in a page or two. Homework problems may come from the texts, or from lecture materials. We will drop your lowest HW score.
  
  
• In-Class Mid-Term Exam (30%). Self-explanatory (problems similar in nature to those seen in the homework assignments). More information about the mid-term will be given in class, as the time approaches. The mid-term will be after the 8th week.
  
  
• In–class Final Exam (30%). The (cumulative) final exam will also consist of exercises and problems similar to those seen on the mid-term and the assignments (with perhaps some short essay questions thrown in as well). More information about the final will be given in class, as the time approaches.

You are encouraged to work in groups on the assignments. In fact, you will receive a small amount of extra-credit for working in groups (other extra-credit will be given throughout the semester on the homework assignments and exams). There are rules for working in groups. These rules, which must be followed carefully – on pain of risking plagiarism – can be found at:

http://socrates.berkeley.edu/~fitelson/148/groups.html

Section participation will not be formally graded, but enthusiastic and well–informed participation will be taken into account in borderline cases. I strongly encourage you to be an active participant in sections.

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Sections
Sections, which will meet once per week for 50 minutes, will give you the opportunity to discuss the readings and lectures. Our GSI is Raul Saucedo; his contact information can be found on the course website. The section meeting locations, times, and rosters (when they are determined) will be posted on our sections page.

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Website
Current course information (including section info., lecture notes, class handouts, assignments, announcements, interesting links, and any revisions to the schedule) can be found on the course web site, at:

http://socrates.berkeley.edu/~fitelson/148/

The home page of our website is reserved mainly for announcements. The purpose of the other pages on our website should be self–explanatory. You should keep an eye on the course website, as it will be updated regularly with various content and announcements pertaining to the course. The site also contains many interesting links to philosophical information (and people). The only two computer applications you will need to view/print, etc. the content on our website are: (i) your favorite web browser, and (ii) Adobe Reader (version 7 or later). We also have a bspace site for the course (only for keeping track of grades).

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Tentative Schedule (subject to change – so stay tuned)
All readings will be available below – either in HTML or Adobe PDF format. My lecture notes will be the central source of material for the course. So, be sure to read these carefully, as we go along. I am working on a textbook for this course, but it is not yet ready for prime time. So, in the meantime, we will use the materials that I have cobbled together. These are the most salient existing readings I could find. Nothing out there quite matches my perspective on the field (or the path I will be taking through the material). This makes attending lectures and sections that much more important.

The texts below are sometimes difficult, and will often require careful and repeated reading. My lecture notes will cover much or all of what you'll need. But, I recommend doing as much of the readings as you can. I do not expect you to do all the readings below (this website serves both as a course website, and as a repository of readings in probability and induction). The first reading(s) in each section is (are) the one(s) you should read first. If you have time, have a look at readings further down the list (often these are indented) for each of the topics we discuss in lecture. This schedule is subject to change, so stay tuned…

Unit 1: Deductive Logic (review) and Boolean Algebras

• Propositional Logic (semantics) and Boolean Algebras
  • Appendix 1 of Ellery Eells's Probabilistic Causality [nice short overview of salient matierial]
  • Lecture Notes from my 12A course [approx. lectures 4-10]
  • Chapter 3 of Graeme Forbes's Modern Logic
  • Chapter 1 of Brian Skyrms's Choice and Chance: An Introduction to Inductive Logic
  • Chapter 1 of Ian Hacking's Introduction to Probability and Inductive Logic
  • Suber, Propositional Logic Terms and Symbols
  • Some Boolean Algebra Links: #1, #2, #3, #4, #5
    
• Monadic Predicate Logic (semantics) and Boolean Algebras
  • Lecture Notes from my 12A course [approx. lectures 23-29]
  • Chapter 6 of Graeme Forbes's Modern Logic
  • Suber, Predicate Logic Terms and Symbols
  • Some Boolean Algebra Links: #1, #2, #3, #4, #5

Unit 5: The Paradoxes of Confirmationf6e3c1f0da62660cb33935bec5c98586

• The Paradox of the Ravens
  • Hempel, Studies in the Logic of Confirmation, [pages 9–21]
  • Fitelson, Seminar notes on the ravens
    • Fitelson, The Paradox of Confirmation
  • Hosiasson-Lindenbaum, On Confirmation
  • Earman, Sections on H–D Confirmation, Bayesian Confirmation, and the Ravens Paradox, in Bayes or Bust, MIT Press, 1992.
  • Vranas, Hempel's Raven Paradox: A Lacuna in the Standard Bayesian Solution
  • Quine, Natural Kinds, in GRUE! The new riddle of induction, Open Court, 1994.
  • Howson and Urbach, Section on The Ravens Paradox, in Scientific Reasoning: The Bayesian Approach
  • Earman & Salmon, The Confirmation of Scientific Hypotheses (excerpts), from Introduction to the Philosophy of Science.
  • Earman, Sections on H–D Confirmation, Bayesian Confirmation, and the Ravens Paradox, in Bayes or Bust, MIT Press, 1992.
  • Vranas, Hempel's Raven Paradox: A Lacuna In The Standard Bayesian Solution
  • Maher, Probability Captures the Logic of Scientific Confirmation [sections on the raven paradox]
  • Forster, Hempel, Scheffler, and the Ravens
  • Fitelson and Hawthorne, How Bayesian Confirmation Theory Handles the Paradox of the Ravens
• The Grue Paradox
• Goodman, The New Riddle of Induction, Chapter 3 of Fact, Fiction, and Forecast
• Fitelson, Goodman's `New Riddle'
  • Chapter 4 of Brian Skyrms's Choice and Chance: An Introduction to Inductive Logic
  • Earman & Salmon, The Confirmation of Scientific Hypotheses (excerpts), from Introduction to the Philosophy of Science [just the sections on the paradoxes of confirmation].
  • Sober, No Model, No Inference: A Bayesian Primer on the Grue Problem, in GRUE! The new riddle of induction
  • Maher, Probability Captures the Logic of Scientific Confirmation [sections on the grue paradox]
  • Maher, Confirmation Theory
  • Quine, Natural Kinds, in GRUE! The new riddle of induction, Open Court, 1994.
  • Goodman, A Query on Confirmation
  • Hooker, Goodman, `Grue' and Hempel
  • Stove, The Myth of Formal Logic from The Rationality of Induction
  • Harman, Chapters 1 and 2 of Change in View
  • Macfarlane, Chapters 3 and 7 of What Does it Mean to Say that Logic is Formal?

Unit 6: More Problems from the Confrimation Theory Literature

• The Popper-Miller Challenge to Inductive Logic
  • Popper & Miller, A proof of the impossibility of inductive probability
  • Earman & Salmon, The Confirmation of Scientific Hypotheses (excerpts), from Introduction to the Philosophy of Science [section 2.10.2]
    • Chihara & Gillies, An Interchange on the Popper-Miller Problem
    • Eells, On the Alleged Impossibility of Inductive Probability
• The Problem of Old Evidence
  • Glymour, Why I am Not a Bayesian
  • Earman & Salmon, The Confirmation of Scientific Hypotheses (excerpts), from Introduction to the Philosophy of Science [section 2.10.3]
    • Eells, Bayesian Problems of Old Evidence
    • Howson, The 'Old Evidence' Problem
    • Maher, Subjective and Objective Confirmation
    • Hawthorne, Degree of Belief and Degree of Support: Why Bayesians Need Both Notions
    • Christensen, Measuring Confirmation
    • Garber, Old Evidence and Logical Omniscience in Bayesian Confirmation Theory
    • Jeffrey, Bayesianism with a Human Face
    • Jeffrey, Old News Explained [sections on old evidence from Subjective Probability: The Real Thing]
    • Eells & Fitelson, Measuring Confirmation and Evidence
    • Fitelson, Review of Joyce's The Foundations of Causal Decision Theory
• The Problem of Logical Omniscience
  • Fitelson, Old Evidence, Logical Omniscience & Bayesianism
    • Garber, Old Evidence and Logical Omniscience in Bayesian Confirmation Theory
    • Jeffrey, Bayesianism with a Human Face
    • Eells, Bayesian Problems of Old Evidence
    • Jeffrey, Old News Explained [sections on old evidence from Subjective Probability: The Real Thing]
    • Gaifman, Reasoning with Bounded Resources and Assigning Probabilities to Arithmetical Statements
    • Hacking, Slightly More Realistic Personal Probability
• The "Likelihoodism vs Bayesianism" Debate
  • Royall, Chapter 1 of his Statistical Evidence: A Likelihood Paradigm
  • Fitelson, "Likelihoodism, Bayesianism, and Relational Confirmation"
    • Steel, Bayesian Confirmation Theory and The Likelihood Principle and Must a Bayesian Accept the Likelihood Principle?
    • Rinard, Comments on Steel's Must a Bayesian Accept the Likelihood Principle?
    • Sober, Bayesianism – It's Scope and Limits, in Bayes's Theorem
    • Good, 46656 Varieties of Bayesians & The Bayesian Influence, or How to Sweep Subjectivism under the Carpet, Chapters 3 and 4 of his Good Thinking
    • Joyce, Bayes's Theorem, Stanford Encyclopedia of Philosophy
    • Good, The Bayes/Non-Bayes Compromise: A Brief Review
• The Problem of Irrelevant Conjunction
  • Fitelson, Putting the Irrelevance Back into the Problem of Irrelevant Conjunction
  • Hawthorne & Fitelson, Re-Solving Irrelevant Conjunction with Probabilistic Independence
    • Rinard, Comments on Steel's Must a Bayesian Accept the Likelihood Principle?
    • Maher, Bayesianism and Irrelevant Conjunction
    • Earman, Section on Irrelevant Conjunction in Bayes or Bust?
    • Rosenkrantz, Bayesian Confirmation: Paradise Regained
    • Skyrms, Comments on Some Recent Approaches to Irrelevant Conjunction

Unit 7: Three Psychological Controversies Involving Probability and Confirmation

• The Base Rate Fallacy
  • Odd Question #5 [discussed by Hacking here] from Ian Hacking's Introduction to Probability and Inductive Logic
  • Fitelson, Comments on the Role of Base Rates in Probabilistic Reasoning
    • Koehler, The base rate fallacy reconsidered: Descriptive, normative, and methodological challenges
    • Levi, Illusions About Uncertainty
    • Fitelson, Judgment Under Uncertainty Revisitied: Probability vs Confirmation
    • Sloman et al, Frequency illusions and other fallacies
    • Jonathan et al, Frequency versus probability formats in statistical word problems
    • Vranas, Gigerenzer's normative critique of Kahneman and Tversky
• The Conjunction Fallacy
  • Odd Question #2 [discussed by Hacking here] from Ian Hacking's Introduction to Probability and Inductive Logic
  • Crupi, Fitelson and Tentori, Probability, Confirmation and the `Conjunction Fallacy'
    • Tversky and Kahneman, Extensional Versus Intuitive Reasoning: The Conjunction Fallacy in Probability Judgment
  • Sides, Osherson, Bonini, and Viale, On the Reality of the Conjunction Fallacy
  • Tentori, Bonini, and Osherson, The conjunction fallacy: a misunderstanding about conjunction? and A Different Conjunction Fallacy
  • Crupi, Tentori, Gonzalez, On Bayesian Measures of Evidential Support: Theoretical and Empirical Issues
  • Tentori, Crupi, Bonini, and Osherson, Comparison of Confirmation Measures
  • Eells and Fitelson, Symmetries and Asymmetries in Evidential Support
  • Hertwig and Chase, Many Reasons or Just One: How Response Mode Affects Reasoning in the Conjunction Problem
  • Levi, Illusions About Uncertainty
  • Levi, Jaakko Hintikka
  • Lagnado and Shanks, Probability judgment in hierarchical learning: a conflict between predictiveness and coherence
• The Wason Selection Task
  • Wason & Shapiro, Natural and contrived experience in a reasoning problem
  • Fitelson & Hawthorne, The Wason Task(s) and the Paradox of Confirmation
    • Humberstone, Hempel Meets Wason
    • Nickerson, Hempel's paradox and Wason's selection task: Logical and psychological puzzles of confirmation
    • Oaksford and Chater, A Rational Analysis of the Selection Task as Optimal Data Selection
    • Oaksford and Chater, Rational Explanation of the Selection Task
    • Mckenzie and Mikkelsen, The Psychological Side of Hempel's Paradox of Confirmation

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