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
- Monadic Predicate Logic (semantics) and Boolean Algebras
Unit 2: The Probability Caluclus
- Algebraic Treatment
- Axiomatic Treatment
Unit 3: Theories (or Kinds) of Probability
- Background on Theories of Truth
- Overviews of Theories of Probability
- Pragmatic or Personalistic Theories
- Hájek, Interpretations of Probability, Stanford Encyclopedia of Philosophy [just section on subjective probability]
- Eriksson & Hájek, What are Degrees of Belief?
- Chapters 13 and 14 of Ian Hacking's Introduction to Probability and Inductive Logic
- Schick, Dutch Bookies and Money Pumps
- Skyrms, Coherence
- Kyburg, Chapter 6 of Probability and Inductive Logic [esp. the first few pages]
- Ramsey, Truth and Probability
- Sahlin, Frank Ramsey – just section 4 on Probability and Utility.
- Maher, Inductive Logic and the Justification of Induction, unpublished manuscript
- Christensen, Dutch-Book Arguments Depragmatized: Epistemic Consistency for Partial Believers
- Maher, Depragmatized Dutch Book Arguments
- Zynda, Representation Theorems and Realism about Degrees of Belief
- Kemeny, Fair Bets and Inductive Probabilities
- Hacking, Slightly More Realistic Personal Probability
- Kolodny, Why Have Consistent and Closed Beliefs, or, for that Matter, Probabilistically Coherent Credences?
- Kolodny, How Does Coherence Matter?
- Maher, Bayesian Probability
- van Fraassen, Indifference: The Symmetries of Probability
- Epistemic Theories
- Joyce, The Accuracy of Partial Beliefs [presented at FEW 2004, this is an updated version of his 1998 paper]
- Gibbard, Rational Credence and the Value of Truth
- Arntzenius, Rationality and Self-confidence [comments on Gibbard's "Rational Credence and the Value of Truth"]
- Swanson, Notes on Gibbard's "Rational Credence and the Value of Truth"
- Gibbard, Aiming at Truth Over Time [replies to Arntzenius and Swanson]
- Kolodny, Why Have Consistent and Closed Beliefs, or, for that Matter, Probabilistically Coherent Credences?
- Kolodny, How Does Coherence Matter?
- Maher, Joyce’s Argument for Probabilism
- Fallis, Attitudes Toward Epistemic Risk and the Value of Experiments
- van Fraassen, Indifference: The Symmetries of Probability
- Ramsey, Truth and Probability
- Logical or Inductive Theories
- Frequency Theories
- Objective Chance / Propensity Theories
Unit 4: Confirmation Theory — Four (Formal) Approaches
- Deductive Approaches
to Confirmation
- Probabilistic Approaches to Confirmation
- Fitelson, Inductive Logic
- Fitelson, Seminar notes comparing four theories of confirmation
- Chapter 2 of Brian Skyrms's Choice and Chance: An Introduction to Inductive Logic
- Salmon, Confirmation and Relevance
- Earman & Salmon, The Confirmation of Scientific Hypotheses (excerpts), from Introduction to the Philosophy of Science [section 2.9]
- Carnap, preface, sections 11–12, sections 43–45, and sections 87–88, from Logical Foundations of Probability (2ed)
- Popper, Degree of Confirmation
- Kemeny and Oppenheim, Degree of Factual Support
- Kyburg, Chapters 5 and 13 of Probability and Inductive Logic
- Maher, Probability Captures the Logic of Scientific Confirmation
- Maher, The Concept of Inductive Probability
- Maher, Probabilities for Multiple Properties
- Maher, Confirmation Theory
- Fine, Logical (Conditional) Probability
- Carnap, On Inductive Logic
- Hesse, Analogy and Confirmation Theory
- Michalos, The Popper-Carnap Controversy
Unit 5: The Paradoxes of Confirmation
- The Paradox of the Ravens
- Hempel, Studies in the Logic of Confirmation, [pages 9–21]
- Fitelson, Seminar notes on the ravens
- 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
- 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
- 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
Unit 7: Three Psychological Controversies Involving Probability and Confirmation
- The Base Rate Fallacy
- 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'
- 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
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