-
126Bayesians 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
-
19The talk is mainly defensive. I won’t offer positive accounts of the “paradoxical” cases I will discuss (but, see “Extras”).
-
251A 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..
-
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
-
31The 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..
-
30Comparative. 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
-
90Shortest 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
-
79Finding 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
-
45There 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
-
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
-
8David Howie: Interpreting Probability: Controversies and Developments in the Early Twentieth Century (review)Philosophy of Science 70 (3): 643-646. 2003.
-
25Review of Richard Jeffrey, Subjective Probability: The Real Thing (review)Notre Dame Philosophical Reviews 2005 (10). 2005.
-
92Wayne, Horwich, and evidential diversityPhilosophy of Science 63 (4): 652-660. 1996.Wayne (1995) critiques the Bayesian explication of the confirmational significance of evidential diversity (CSED) offered by Horwich (1982). Presently, I argue that Wayne’s reconstruction of Horwich’s account of CSED is uncharitable. As a result, Wayne’s criticisms ultimately present no real problem for Horwich. I try to provide a more faithful and charitable rendition of Horwich’s account of CSED. Unfortunately, even when Horwich’s approach is charitably reconstructed, it is still not completely s…Read more
-
583 Contrastive BayesiansimIn Martijn Blaauw (ed.), Contrastivism in philosophy, Routledge/taylor & Francis Group. pp. 39--64. 2013.
-
46– 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..
-
86Knowledge, Scepticism, and Defeat: Themes from Klein (edited book)Springer Verlag. 2019.This is a collection of new essays written in honor of the work of Peter D. Klein, who has had and continues to have a tremendous influence in the development of epistemology. The essays reflect the breadth and depth of Klein’s work by engaging directly with his views and with the views of his interlocutors.
-
33By 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.
-
50Overview Setting the Stage Consistency Redundancy Goodbye ? Conclusion & References Overview Setting the Stage Consistency Redundancy Goodbye ? Conclusion & References..
-
312The paradox of confirmationPhilosophy Compass 1 (1). 2006.Hempel first introduced the paradox of confirmation in (Hempel 1937). Since then, a very extensive literature on the paradox has evolved (Vranas 2004). Much of this literature can be seen as responding to Hempel’s subsequent discussions and analyses of the paradox in (Hempel 1945). Recently, it was noted that Hempel’s intuitive (and plausible) resolution of the paradox was inconsistent with his official theory of confirmation (Fitelson & Hawthorne 2006). In this article, we will try to explain h…Read more
-
114A decision procedure for probability calculus with applicationsReview of Symbolic Logic 1 (1): 111-125. 2008.(new version: 10/30/07). Click here to download the companion Mathematica 6 notebook that goes along with this paper.
-
19The 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 emul…Read more
-
8Solutions to Some Open Problems from SlaneyAustralasian Journal of Logic 13 (4). 2016.In response to a paper by Harris & Fitelson, Slaney states several open questions concerning possible strategies for proving distributivity in a wide class of positive sentential logics. In this note, I provide answers to all of Slaney's open questions. The result is a better understanding of the class of positive logics in which distributivity holds.
-
82The philosophical significance of Stein’s paradoxEuropean Journal for Philosophy of Science 7 (3): 411-433. 2017.Charles Stein discovered a paradox in 1955 that many statisticians think is of fundamental importance. Here we explore its philosophical implications. We outline the nature of Stein’s result and of subsequent work on shrinkage estimators; then we describe how these results are related to Bayesianism and to model selection criteria like AIC. We also discuss their bearing on scientific realism and instrumentalism. We argue that results concerning shrinkage estimators underwrite a surprising form o…Read more
-
692Evidence of evidence is not (necessarily) evidenceAnalysis 72 (1): 85-88. 2012.In this note, I consider various precisifications of the slogan ‘evidence of evidence is evidence’. I provide counter-examples to each of these precisifications (assuming an epistemic probabilistic relevance notion of ‘evidential support’)
-
152Studies in Bayesian Confirmation TheoryDissertation, University of Wisconsin, Madison. 2001.According to Bayesian confirmation theory, evidence E (incrementally) confirms (or supports) a hypothesis H (roughly) just in case E and H are positively probabilistically correlated (under an appropriate probability function Pr). There are many logically equivalent ways of saying that E and H are correlated under Pr. Surprisingly, this leads to a plethora of non-equivalent quantitative measures of the degree to which E confirms H (under Pr). In fact, many non-equivalent Bayesian measures of the…Read more
-
119A bayesian account of independent evidence with applicationsProceedings of the Philosophy of Science Association 2001 (3). 2001.outlined. This account is partly inspired by the work of C.S. Peirce. When we want to consider how degree of confirmation varies with changing I show that a large class of quantitative Bayesian measures of con-.
-
94A New Garber-Style Solution to the Problem of Old EvidencePhilosophy of Science 82 (4): 712-717. 2015.In this discussion note, we explain how to relax some of the standard assumptions made in Garber-style solutions to the Problem of Old Evidence. The result is a more general and explanatory Bayesian approach
-
44• 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.
-
164Putting the irrelevance back into the problem of irrelevant conjunctionPhilosophy of Science 69 (4): 611-622. 2002.Naive deductive accounts of confirmation have the undesirable consequence that if E confirms H, then E also confirms the conjunction H & X, for any X—even if X is utterly irrelevant to H (and E). Bayesian accounts of confirmation also have this property (in the case of deductive evidence). Several Bayesians have attempted to soften the impact of this fact by arguing that—according to Bayesian accounts of confirmation— E will confirm the conjunction H & X less strongly than E confirms H (again, i…Read more
Boston, MA, United States of America
Areas of Specialization
Metaphysics and Epistemology |
Science, Logic, and Mathematics |
Formal Epistemology |