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Profile: Branden Fitelson (University of California, Berkeley)
  1. Branden Fitelson, Dempster-Shafer Functions as Metalinguistic Probability Functions.
    Let Ln be a sentential language with n atomic sentences {A1, . . . , An}. Let Sn = {s1, . . . , s2n} be the set of 2n state descriptions of Ln, in the following, canonical lexicographical truth-table order: State Description A1 A2 · · · An−1 An T T T T T s1 = A1 & A2 & · · · &An−1 & An T T T T F s1 = A1 & A2 & · · · (...)
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  2. Branden Fitelson, Epistemological Critiques of ‘Classical’ Logic: Two Case Studies.
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  3. Branden Fitelson, “Survey” of Formal Epistemology: Some Propaganda and an Example.
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  4. Branden Fitelson, Accuracy & Coherence.
    This talk is (mainly) about the relationship two types of epistemic norms: accuracy norms and coherence norms. A simple example that everyone will be familiar with.
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  5. Branden Fitelson, Accuracy & Coherence II.
    Comparative. Let C be the full set of S’s comparative judgments over B × B. The innaccuracy of C at a world w is given by the number of incorrect judgments in C at w.
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  6. Branden Fitelson, Accuracy & Coherence III.
    In this talk, I will explain why only one of Miller’s two types of language-dependence-of-verisimilitude problems is a (potential) threat to the sorts of accuracy-dominance approaches to coherence that I’ve been discussing.
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  7. Branden Fitelson, A Concise Analysis of Popper's Qualitative Theory of Verisimilitude.
    Popper [3] offers a qualitative definition of the relation “p q” = “p is (strictly) closer to the truth than (i.e., strictly more verisimilar than) q”, using the notions of truth (in the actual world) and classical logical consequence ( ), as follows.
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  8. Branden Fitelson, A Historical Introduction to Confirmation Theory.
    Here’s what Nicod [23] said about instantial confirmation: Consider the formula or the law: A entails B. How can a particular proposition, or more briefly, a fact, affect its probability? If this fact consists of the presence of B in a case of A, it is favourable to the law . . . on the contrary, if it consists of the absence of B in a case of A, it is unfavourable to this law.
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  9. Branden Fitelson, Bayes's Theorem.
    This is a high quality, concise collection of articles on the foundations of probability and statistics. Its editor, Richard Swinburne, has collected five papers by contemporary leaders in the field, written a pretty thorough and even-handed introductory essay, and placed a very clean and accessible version of Reverend Thomas Bayes’s famous essay (“An Essay Towards the Solving a Problem in the Doctrine of Chances”) at the end, as an Appendix (with a brief historical introduction by the noted statistician G.A. Barnard). (...)
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  10. Branden Fitelson, Comments on Presting's “Computability and Newcomb's Problem”.
    • What’s essential to Newcomb’s problem? 1. You must choose between two particular acts: A1 = you take just the opaque box; A2 = you take both boxes, where the two states of nature are: S 1 = there’s $1M in the opaque box, S2 = there’s $0 in the opaque box.
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  11. Branden Fitelson, Comparative Probability, Comparative Confirmation, and the “Conjunction Fallacy”.
    In the first edition of LFP, Carnap [2] undertakes a precise probabilistic explication of the concept of confirmation. This is where modern confirmation theory was born (in sin). Carnap was interested mainly in quantitative confirmation (which he took to be fundamental). But, he also gave (derivative) qualitative and comparative explications: • Qualitative. E inductively supports H. • Comparative. E supports H more strongly than E supports H . • Quantitative. E inductively supports H to degree r . Carnap begins by (...)
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  12. Branden Fitelson, Decermber 30, 2005.
    Slide #0 (Title). Before I get underway, I’d like to quickly thank a few people. First, Jonathan Vogel and John MacFarlane for working behind the scenes to make this thing happen. And, of course, David Christensen for chairing, and Patrick Maher and Jim Joyce for participating. I especially want to thank Patrick for his terrific feedback on my work this term, which has helped me to get much clearer on my project. Before we get started, does everyone have a handout? (...)
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  13. Branden Fitelson, Goodman's “Grue” Argument in Historical Perspective.
    The talk is mainly defensive. I won’t offer positive accounts of the “paradoxical” cases I will discuss (but, see “Extras”). I’ll begin with Harman’s defense of classical deductive logic against certain (epistemological) “relevantist” arguments.
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  14. Branden Fitelson, Judgment Under Uncertainty Revisited: Probability Vs Confirmation.
    Carnap [1] aims to provide a formal explication of an informal concept (relation) he calls “confirmation”. He clarifies “E confirms H” in various ways, including: (∗) E provides some positive evidential support for H. His formal explication of “E confirms H” (in [1]) is: (1) E confirms H iff Pr(H | E) > r, where Pr is a suitable (“logical”) probability function, and r is a threshold value.
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  15. Branden Fitelson, Knowledge From Falsehood.
    It is useful to note how (CC) differs from closure: (C) If S comes to believe q solely on the basis of competent deduction from p and S knows that p, then S knows that q. I won’t be discussing (C) today, but here is a useful contrast.
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  16. Branden Fitelson, Knowledge From Non-Knowledge.
    The Naive View (TNV) of Inferential Knowledge (slogan): (TNV) Inferential knowledge requires known relevant premises. One key aspect of (TNV) is “counter-closure” [9, 10].
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  17. Branden Fitelson, Language Dependence in Philosophy of Science and Formal Epistemology.
    Suppose we have two false hypotheses H1 and H2. Sometimes, we would like to be able to say that H1 is closer to the truth than H2 (e.g., Newton’s hypothesis vs. Ptolemy’s).
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  18. Branden Fitelson, Overview of Finite Propositional Boolean Algebras I.
    of monadic or relational predicate calculus (Fa, Gb, Rab, Hcd, etc.). • The Boolean Algebra BL set-up by such a language will be such that: – BL will have 2 n states (corresponding to the state descriptions of L) – BL will contain 2 2n propositions, in total. ∗ This is because each proposition p in BL is equivalent to a disjunction of state descriptions. Thus, each subset of the set of..
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  19. Branden Fitelson, Probabilistic Coherence From a Logical Point of View.
    – Foundation: Probabilistic Confirmation (c) from a Logical POV ∗ cph, eq as a “relevant” quantitative generalization of pe  hq ∗ cph, eq, so understood, is not Prpe  hq or Prph | eq, etc. ∗ cph, eq is something akin (ordinally) to the likelihood ratio..
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  20. Branden Fitelson, Remarks on Probability and “Intelligent Design”.
    There are various non-contrastive questions that one can ask about a single hypothesis H and a body of evidence E: What is the probability of H, given E [Pr(H | E)]? What is the likelihood of H on E [Pr(E | H)]? Does E support/counter-support H? Should we accept/reject H in light of E? There are also contrastive questions concerning pairs of alternative hypotheses H1 vs H2 and a body of evidence E: Is H1 more probable than H2, given E? (...)
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  21. Branden Fitelson, Some Recent Fallacies of Approximation in Bayesian Confirmation Theory.
    • Several recent Bayesian discussions make use of “approximation” – Earman on the Quantitative Old Evidence Problem – Vranas on Quantitative Approaches to the Ravens Paradox – Dorling’s Quantitative Approach to Duhem–Quine – Strevens’s Quantitative Approach to Duhem–Quine – rThere are also examples not involving confirmation: E.g.
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  22. Branden Fitelson, Some Remarks on the Model Selection Problem.
    We’ll adopt a simple framework today. Our assumptions: A model (M) is a family of hypotheses. A hypothesis (H) is a curve plus an associated error term . For simplicity, we’ll assume a common N (0, 1) Gaussian.
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  23. Branden Fitelson, The Central Thesis as Involving “Inference to the Best Explanation”.
    • Two competing explanations (independence of S i favors R over CB): (CB) there is a coherence bias in a’s S -formation process.
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  24. Branden Fitelson, Two Technical Corrections to My Coherence Measure.
    Note: This is not an ad hoc change at all. It’s simply the natural thing say here – if one thinks of F as a generalization of classical logical entailment. The extra complexity I had in my original (incorrect) definition of F was there because I was foolishly trying to encode some non-classical, or “relavant” logical structure in F. I now think this is a mistake, and that I should go with the above, classical account of F. Arguments about relevance (...)
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  25. Branden Fitelson & Kenny Easwaran, Accuracy, Coherence and Evidence.
    Taking Joyce’s (1998; 2009) recent argument(s) for probabilism as our point of departure, we propose a new way of grounding formal, synchronic, epistemic coherence requirements for (opinionated) full belief. Our approach yields principled alternatives to deductive consistency, sheds new light on the preface and lottery paradoxes, and reveals novel conceptual connections between alethic and evidential epistemic norms.
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  26. Branden Fitelson & Daniel Osherson, Remarks on “Random Sequences”.
    We consider how to reach reasonable belief about whether a (possibly idealized) physical process is producing its output randomly. For definiteness, we’ll consider a coin-flipper C which reports a sequence of outcomes of tosses of a coin. C outputs “H” for a heads outcome and “T” for a tails outcome. By C producing its output “randomly,” we mean that the probability of C issuing an H on any given trial is the same as the probability of issuing a T, and (...)
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  27. Branden Fitelson & Daniel Osherson, The Problem: First Pass.
    Intuitively, it seems that S 1 is “more random” or “less regular” than S 2. In other words, it seems more plausible (in some sense) that S 1 (as opposed to S 2) was generated by a random process ( e.g. , by tossing a fair coin eight times, and recording an H for a heads outcome and a T for a tails outcome). We will use the notation x σ 1 ą σ 2y to express the claim that xstring (...)
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  28. Branden Fitelson & Andrew Waterman, A Rejoinder to Strevens.
    By and large, we think Strevens’s [6] is a useful reply to our original critique [2] of his paper on the Quine–Duhem (QD) problem [5]. But, we remain unsatisfied with several aspects of his reply (and his original paper). Ultimately, we do not think he properly addresses our most important worries. In this brief rejoinder, we explain our remaining worries, and we issue a revised challenge for Strevens’s approach to QD.
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  29. Kenneth Harris & Branden Fitelson, Distributivity in Lℵ0 and Other Sentential Logics.
    Certain distributivity results for Lukasiewicz’s infinite-valued logic Lℵ0 are proved axiomatically (for the first time) with the help of the automated reasoning program Otter [16]. In addition, non -distributivity results are established for a wide variety of positive substructural logics by the use of logical matrices discovered with the automated model findingprograms Mace [15] and MaGIC [25].
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  30. Larry Wos & Branden Fitelson, G The Automation of Sound Reasoning and Successful Proof Findin.
    The consideration of careful reasoning can be traced to Aristotle and earlier authors. The possibility of rigorous rules for drawing conclusions can certainly be traced to the Middle Ages when types o f syllogism were studied. Shortly after the introduction of computers, the audacious scientist naturally envisioned the automation of sound reasoning—reasoning in which conclusions that are drawn follow l ogically and inevitably from the given hypotheses. Did the idea spring from the intent to emulate s Sherlock Holmes and Mr. (...)
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  31. Larry Wos, Dolph Ulrich & Branden Fitelson, Vanquishing the XCB Question: The Methodological Discovery of the Last Shortest Single Axiom for the Equivalential Calculus.
    detail a question that, for a quarter of a century, remained open despite intense study by various researchers. Is the formula XC B = e(x e(e(e( ) e( )) z)) a single axiom for the classical equivalential calculus when the rules of inference consist..
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  32. Branden Fitelson, Automated Reasoning in Modal Logics: A Framework with Applications.
    The principle that every truth is possibly necessary can now be shown to entail that every truth is necessary by a chain of elementary inferences in a perspicuous notation unavailable to Hegel. —Williamson [5, p.
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  33. Branden Fitelson, Comments and Criticism Measuring Confirmation and Evidence.
    Bayesian epistemology suggests various ways of measuring the support that a piece of evidence provides a hypothesis. Such measures are defined in terms of a subjective probability assignment, pr, over propositions entertained by an agent. The most standard measure (where “H” stands for “hypothesis” and “E” stands for “evidence”) is.
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  34. Branden Fitelson, Comments on Jill North's “Symmetry and Probability”.
    Jill’s paper contains several distinct threads and arguments. I will focus only on what I see as the main theses of the paper, which involve the justification or grounding of the microcanonical probability distribution of classical statistical mechanics (MCD). I’ll begin by telling the “canonical” story of the MCD (as I see it). Then I will discuss Jill’s proposal. I will describe one worry that I have regarding her proposal, and I will offer a friendly amendment which seems to (...)
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  35. Branden Fitelson, Comments on Jim Franklin's “the Representation of Context: Ideas From Artificial Intelligence”.
    To be honest, I have almost nothing critical to say about Jim’s presentation (and this is quite unusual for a cranky analytic philosopher like me!). What Jim has said is all very sensible, and his examples are very well chosen, etc. So, instead of making critical remarks, I will try to expand a little on one of the themes Jim briefly touched upon in his talk: the contextuality of probability.
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  36. Branden Fitelson, Distributivity in Lℵ0 and Other Sentential Logics.
    Certain distributivity results for Lukasiewicz’s infinite-valued logic Lℵ0..
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  37. Branden Fitelson, Earman on Old Evidence and Measures of Confirmation.
    In Bayes or Bust? John Earman quickly dismisses a possible resolution (or avoidance) of the problem of old evidence. In this note, I argue that his dismissal is premature, and that the proposed resolution (when charitably reconstructed) is reasonable.
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  38. Branden Fitelson, G the Automation of Sound Reasoning and Successful Proof Findin.
    The consideration of careful reasoning can be traced to Aristotle and earlier authors. The possibility of rigorous rules for drawing conclusions can certainly be traced to the Middle Ages when types o f syllogism were studied. Shortly after the introduction of computers, the audacious scientist naturally envisioned the automation of sound reasoning—reasoning in which conclusions that are drawn follow l ogically and inevitably from the given hypotheses. Did the idea spring from the intent to emulate..
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  39. Branden Fitelson, Likelihoods, Counterfactuals, and Tracking.
    Overview Setting the Stage Consistency Redundancy Goodbye ? Conclusion & References Overview Setting the Stage Consistency Redundancy Goodbye ? Conclusion & References..
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  40. Branden Fitelson, MaGIC: Matrix Generator for Implication Connectives.
    The program MaGIC (Matrix Generator for Implication Connectives) is intended as a tool for logical research. It computes small algebras (normally with up to 14 elements) suitable for modelling certain non-classical logics. Along the way, it eliminates from the output any algebra isomorphic to one already generated, thus returning only one from each isomorphism class. Optionally, the user may specify a formula which is to be..
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  41. Branden Fitelson, Notes on Gibbard's Theorem.
    Let L be a sentential (object) language containing atoms ‘A’, ‘B’, . . . , and two logical connectives ‘&’ and ‘→’. In addition to these two logical connectives, L will also contain another binary connective ‘ ’, which is intended to be interpreted as the English indicative. In the meta-language for L , we will have two meta-linguistic operations: ‘ ’ and ‘ ’. ‘ ’ is a binary relation between individual sentences in L . It will be interpreted (...)
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  42. Branden Fitelson, Overview of Presentation.
    • What are the ends of statistical experiment, analysis, and inference? • What are the most effective means for achieving these ends? • Several paradigms for statistics have been developed — each of these presupposes answers to these key “philosophical” questions about statistics.
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  43. Branden Fitelson, Overview of Talk.
    The talk is mainly defensive. I won’t offer positive accounts of the “paradoxical” cases I will discuss (but, see “Extras”).
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  44. Branden Fitelson, Probabilistic Coherence From a Logical Point of View From Confirmation to Coherence I.
    ∗ C pp, qq as a “mutual confirmation” generalization of pp & qq Prpe  hq won’t work Prpp & qq won’t work ∗ C pp, qq, so understood, is not Prpp & qq or Prpq | pq, etc.
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  45. Branden Fitelson, Some Remarks on the “Intelligent Design” Controversy.
    There are various questions that arise in connection with the “intelligent design” (ID) controversy. This introductory section aims to distinguish five of these questions. Later sections are devoted to detailed discussions of each of these five questions. The first (and central) question is the one that has been discussed most frequently in the news lately: (Q1) Should ID be taught in our public schools? It is helpful to break this general “public school curriculum question” into the following two more specific (...)
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  46. Branden Fitelson, The British Journal for the Philosophy of Science.
    The British Journal for the Philosophy of Science 2002 53(4):539-563; doi:10.1093/bjps/53.4.539 © 2002 by British Society for the Philosophy of Science..
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  47. Branden Fitelson, The Jowett Society & the Philosophical Sociey.
    The Jowett Society and the Philosophical Society of the University of Oxford provide a forum for discussion of philosophical issues for all members of the Philosophy Faculty. The Jowett society dates back to the 19th century and was named in honour of Benjamin Jowett..
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  48. Branden Fitelson, Using Mathematica to Understand the Computer Proof of the Robbins Conjecture.
    mathematicians for over 60 years. Amazingly, the Argonne team's automated theorem-proving program EQP took only 8 days to find a proof of it. Unfortunately, the proof found by EQP is quite complex and difficult to follow. Some of the steps of the EQP proof require highly complex and unintuitive substitution strategies. As a result, it is nearly impossible to reconstruct or verify the computer proof of the Robbins conjecture entirely by hand. This is where the unique symbolic capabilities of Mathematica (...)
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  49. Branden Fitelson, Vanquishing the XCB Question: The Methodological Discovery of the Last Shortest Single Axiom for the Equivalential Calculus.
    With the inclusion of an e ective methodology, this article answers in detail a question that, for a quarter of a century, remained open despite intense study by various researchers. Is the formula XCB = e(x e(e(e(x y) e(z y)) z)) a single axiom for the classical equivalential calculus when the rules of inference consist of detachment (modus ponens) and substitution? Where the function e represents equivalence, this calculus can be axiomatized quite naturally with the formulas (x x), e(e(x y) (...)
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  50. Branden Fitelson & Lara Buchak, Advice-Giving and Scoring-Rule-Based Arguments for Probabilism.
    Dutch Book Arguments. B is susceptibility to sure monetary loss (in a certain betting set-up), and F is the formal role played by non-Pr b’s in the DBT and the Converse DBT. Representation Theorem Arguments. B is having preferences that violate some of Savage’s axioms (and/or being unrepresentable as an expected utility maximizer), and F is the formal role played by non-Pr b’s in the RT.
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