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32With 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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119Contrastive 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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200Likelihoodism, Bayesianism, and relational confirmationSynthese 156 (3): 473-489. 2007.Likelihoodists and Bayesians seem to have a fundamental disagreement about the proper probabilistic explication of relational (or contrastive) conceptions of evidential support (or confirmation). In this paper, I will survey some recent arguments and results in this area, with an eye toward pinpointing the nexus of the dispute. This will lead, first, to an important shift in the way the debate has been couched, and, second, to an alternative explication of relational support, which is in some se…Read more
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224The plurality of bayesian measures of confirmation and the problem of measure sensitivityPhilosophy of Science 66 (3): 378. 1999.Contemporary Bayesian confirmation theorists measure degree of (incremental) confirmation using a variety of non-equivalent relevance measures. As a result, a great many of the arguments surrounding quantitative Bayesian confirmation theory are implicitly sensitive to choice of measure of confirmation. Such arguments are enthymematic, since they tacitly presuppose that certain relevance measures should be used (for various purposes) rather than other relevance measures that have been proposed an…Read more
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38The 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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398Goodman’s “New Riddle‘Journal of Philosophical Logic 37 (6): 613-643. 2008.First, a brief historical trace of the developments in confirmation theory leading up to Goodman's infamous "grue" paradox is presented. Then, Goodman's argument is analyzed from both Hempelian and Bayesian perspectives. A guiding analogy is drawn between certain arguments against classical deductive logic, and Goodman's "grue" argument against classical inductive logic. The upshot of this analogy is that the "New Riddle" is not as vexing as many commentators have claimed. Specifically, the anal…Read more
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365Accuracy, Coherence and EvidenceOxford Studies in Epistemology 5 61-96. 2015.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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175- In decision theory, an agent is deciding how to value a gamble that results in different outcomes in different states. Each outcome gets a utility value for the agent.
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194Dutch 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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101Introduction to the Special Issue: Probability, Confirmation and FallaciesSynthese 184 (1): 1-1. 2012.
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569Plantinga’s Probability Arguments Against Evolutionary NaturalismPacific Philosophical Quarterly 79 (2). 1998.In Chapter 12 of Warrant and Proper Function, Alvin Plantinga constructs two arguments against evolutionary naturalism, which he construes as a conjunction E&N .The hypothesis E says that “human cognitive faculties arose by way of the mechanisms to which contemporary evolutionary thought directs our attention (p.220).”1 With respect to proposition N , Plantinga (p. 270) says “it isn’t easy to say precisely what naturalism is,” but then adds that “crucial to metaphysical naturalism, of course, is…Read more
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23REVIEWS-An introduction to probability and inductive logicBulletin of Symbolic Logic 9 (4): 506-507. 2003.
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44To 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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19The talk is mainly defensive. I won’t offer positive accounts of the “paradoxical” cases I will discuss (but, see “Extras”).
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53Note: 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 logic need to be handled in a different way (and …Read more
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125Bayesians sometimes cannot ignore even very implausible theories (even ones that have not yet been thought of)Australasian Journal of Logic 6 25-36. 2008.In applying Bayes’s theorem to the history of science, Bayesians sometimes assume – often without argument – that they can safely ignore very implausible theories. This assumption is false, both in that it can seriously distort the history of science as well as the mathematics and the applicability of Bayes’s theorem. There are intuitively very plausible counter-examples. In fact, one can ignore very implausible or unknown theories only if at least one of two conditions is satisfied: (i) one is …Read more
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35Carnap [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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28The 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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248A probabilistic theory of coherenceAnalysis 63 (3). 2003.Let E be a set of n propositions E1, ..., En. We seek a probabilistic measure C(E) of the ‘degree of coherence’ of E. Intuitively, we want C to be a quantitative, probabilistic generalization of the (deductive) logical coherence of E. So, in particular, we require C to satisfy the following..
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77Finding missing proofs with automated reasoningStudia Logica 68 (3): 329-356. 2001.This article features long-sought proofs with intriguing properties (such as the absence of double negation and the avoidance of lemmas that appeared to be indispensable), and it features the automated methods for finding them. The theorems of concern are taken from various areas of logic that include two-valued sentential (or propositional) calculus and infinite-valued sentential calculus. Many of the proofs (in effect) answer questions that had remained open for decades, questions focusing on …Read more
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44There 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 t…Read more
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29Comparative. 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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87Shortest Axiomatizations of Implicational S4 and SNotre Dame Journal of Formal Logic 43 (3): 169-179. 2002.Shortest possible axiomatizations for the implicational fragments of the modal logics S4 and S5 are reported. Among these axiomatizations is included a shortest single axiom for implicational S4—which to our knowledge is the first reported single axiom for that system—and several new shortest single axioms for implicational S5. A variety of automated reasoning strategies were essential to our discoveries
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25Review of Richard Jeffrey, Subjective Probability: The Real Thing (review)Notre Dame Philosophical Reviews 2005 (10). 2005.
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106Think of confirmation in the context of the Ravens Paradox this way. The likelihood ratio measure of incremental confirmation gives us, for an observed Black Raven and for an observed non-Black non-Raven, respectively, the following “full” likelihood ratios
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7David Howie: Interpreting Probability: Controversies and Developments in the Early Twentieth Century (review)Philosophy of Science 70 (3): 643-646. 2003.
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Metaphysics and Epistemology |
Science, Logic, and Mathematics |
Formal Epistemology |