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99The 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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171Steps Toward a Computational MetaphysicsJournal of Philosophical Logic 36 (2): 227-247. 2007.In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this paper, we describe what we have discovered when the theory of abstract objects is implemented in PROVER9 (a first-order automated reasoning system which is the successor to OTTER). After reviewing the second-order, axiomatic theory of abstract objects, we show (1) how to represent a fragment of that theory in PRO…Read more
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127Popper [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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84The 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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378How Bayesian Confirmation Theory Handles the Paradox of the RavensIn Ellery Eells & James Fetzer (eds.), The Place of Probability in Science, Springer. pp. 247--275. 2010.The Paradox of the Ravens (a.k.a,, The Paradox of Confirmation) is indeed an old chestnut. A great many things have been written and said about this paradox and its implications for the logic of evidential support. The first part of this paper will provide a brief survey of the early history of the paradox. This will include the original formulation of the paradox and the early responses of Hempel, Goodman, and Quine. The second part of the paper will describe attempts to resolve the paradox wit…Read more
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289Declarations of independenceSynthese 194 (10): 3979-3995. 2017.According to orthodox (Kolmogorovian) probability theory, conditional probabilities are by definition certain ratios of unconditional probabilities. As a result, orthodox conditional probabilities are undefined whenever their antecedents have zero unconditional probability. This has important ramifications for the notion of probabilistic independence. Traditionally, independence is defined in terms of unconditional probabilities (the factorization of the relevant joint unconditional probabilitie…Read more
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1619Monty hall, doomsday and confirmationAnalysis 63 (1). 2003.We give an analysis of the Monty Hall problem purely in terms of confirmation, without making any lottery assumptions about priors. Along the way, we show the Monty Hall problem is structurally identical to the Doomsday Argument.
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129Wason Task(s) and the Paradox of ConfirmationPhilosophical Perspectives 24 (1): 207-241. 2010.The (recent, Bayesian) cognitive science literature on The Wason Task (WT) has been modeled largely after the (not-so-recent, Bayesian) philosophy of science literature on The Paradox of Confirmation (POC). In this paper, we apply some insights from more recent Bayesian approaches to the (POC) to analogous models of (WT). This involves, first, retracing the history of the (POC), and, then, reexamining the (WT) with these historico-philosophical insights in mind.
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39Jill’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. I’ll begin by telling the “canonical” story of the MCD. 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 allay my worry
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177Pollock on probability in epistemology (review)Philosophical Studies 148 (3). 2010.In Thinking and Acting John Pollock offers some criticisms of Bayesian epistemology, and he defends an alternative understanding of the role of probability in epistemology. Here, I defend the Bayesian against some of Pollock's criticisms, and I discuss a potential problem for Pollock's alternative account
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128The Strongest Possible Lewisian Triviality ResultThought: A Journal of Philosophy 4 (2): 69-74. 2015.The strongest possible Lewisian triviality result for the indicative conditional is proven
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11Book ReviewDavid Howie, Interpreting Probability: Controversies and Developments in the Early Twentieth Century. Cambridge: Cambridge University Press , xi + 262 pp., $60.00 cloth (review)Philosophy of Science 70 (3): 643-646. 2003.
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96Let 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 as “single premise entailment” (or “single premise de…Read more
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41• 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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118Accuracy, Language Dependence, and Joyce’s Argument for ProbabilismPhilosophy of Science 79 (1): 167-174. 2012.In this article, I explain how a variant of David Miller's argument concerning the language dependence of the accuracy of predictions can be applied to Joyce's notion of the accuracy of “estimates of numerical truth-values”. This leads to a potential problem for Joyce's accuracy-dominance-based argument for the conclusion that credences should obey the probability calculus.
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18Hacking Ian. An introduction to probability and inductive logic. Cambridge University Press, 2000, xvii+ 302 pp (review)Bulletin of Symbolic Logic 9 (4): 506-508. 2003.
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44• 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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102This 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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41detail 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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165Favoring, Likelihoodism, and Bayesianism (review)Philosophy and Phenomenological Research 83 (3): 666-672. 2011.This (brief) note is about the (evidential) “favoring” relation. Pre-theoretically, favoring is a three-place (epistemic) relation, between an evidential proposition E and two hypotheses H1 and H2. Favoring relations are expressed via locutions of the form: E favors H1 over H2. Strictly speaking, favoring should really be thought of as a four-place relation, between E, H1, H2, and a corpus of background evidence K. But, for present purposes (which won't address issues involving K), I will suppre…Read more
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135Comments and Criticism: Measuring Confirmation and EvidenceJournal of Philosophy 97 (12): 663-672. 2000.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: the difference measure: d(H,E) = pr(H/E) - pr(H).0 This may be called a “positive (probabilistic) relevance measure” of confirmation, since, according to it, a piece…Read more
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37Certain 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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74Let 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 & · · · &An−1 & ¬An T T T F T s3 = A1 & A2 & · · · & ¬An−1 & An T T T F F s4 = A1 & A2 & · · · & ¬An−1 & ¬An..
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17Review of Richard Swinburne (ed.), Bayes's Theorem (review)Notre Dame Philosophical Reviews 2003 (11). 2003.
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33With 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) e(…Read more
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123Contrastive BayesianismIn Martijn Blaauw (ed.), Contrastivism in philosophy, Routledge/taylor & Francis Group. 2013.Bayesianism provides a rich theoretical framework, which lends itself rather naturally to the explication of various “contrastive” and “non-contrastive” concepts. In this (brief) discussion, I will focus on issues involving “contrastivism”, as they arise in some of the recent philosophy of science, epistemology, and cognitive science literature surrounding Bayesian confirmation theory
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79∗ 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.
Boston, MA, United States of America
Areas of Specialization
Metaphysics and Epistemology |
Science, Logic, and Mathematics |
Formal Epistemology |