-
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
-
691Evidence 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
-
320Probability, confirmation, and the conjunction fallacyThinking and Reasoning 14 (2). 2007.The conjunction fallacy has been a key topic in debates on the rationality of human reasoning and its limitations. Despite extensive inquiry, however, the attempt to provide a satisfactory account of the phenomenon has proved challenging. Here we elaborate the suggestion (first discussed by Sides, Osherson, Bonini, & Viale, 2002) that in standard conjunction problems the fallacious probability judgements observed experimentally are typically guided by sound assessments of _confirmation_ relation…Read more
-
176The Wason 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, re-examining the (WT) with these historico-philosophical insights in mind
-
47This 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 sta…Read more
-
285ProbabilityIn Sahotra Sarkar & Jessica Pfeifer (eds.), The Philosophy of Science: An Encyclopedia, Routledge. 2005.There are two central questions concerning probability. First, what are its formal features? That is a mathematical question, to which there is a standard, widely (though not universally) agreed upon answer. This answer is reviewed in the next section. Second, what sorts of things are probabilities---what, that is, is the subject matter of probability theory? This is a philosophical question, and while the mathematical theory of probability certainly bears on it, the answer must come from elsewh…Read more
-
33Axiomatic proofs through automated reasoningBulletin of the Section of Logic 29 (3): 125-36. 2000.
-
100It 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
-
119Teaching & learning guide for: The paradox of confirmationPhilosophy Compass 3 (5): 1103-1105. 2008.
-
39In 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
-
29We’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
-
149Discussion: Re‐solving irrelevant conjunction with probabilistic independencePhilosophy of Science 71 (4): 505-514. 2004.Naive deductivist 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 completely irrelevant to E and H. Bayesian accounts of confirmation may appear to have the same problem. In a recent article in this journal Fitelson (2002) argued that existing Bayesian attempts to resolve of this problem are inadequate in several important respects. Fitelson then proposes a new‐and‐improved Bayesian account that over…Read more
-
24Certain distributivity results for Lukasiewicz’s infinite-valued logic Lℵ0..
-
22Remarks on "Random Sequences"Australasian Journal of Logic 12 (1). 2015.We show that standard statistical tests for randomness of finite sequences are language-dependent in an inductively pernicious way.
-
188Symmetries and asymmetries in evidential supportPhilosophical Studies 107 (2). 2002.Several forms of symmetry in degrees of evidential support areconsidered. Some of these symmetries are shown not to hold in general. This has implications for the adequacy of many measures of degree ofevidential support that have been proposed and defended in the philosophical literature.
-
441What is the “Equal Weight View'?Episteme 6 (3): 280-293. 2009.In this paper, we investigate various possible (Bayesian) precisifications of the (somewhat vague) statements of “the equal weight view” (EWV) that have appeared in the recent literature on disagreement. We will show that the renditions of (EWV) that immediately suggest themselves are untenable from a Bayesian point of view. In the end, we will propose some tenable (but not necessarily desirable) interpretations of (EWV). Our aim here will not be to defend any particular Bayesian precisification…Read more
-
149Comparative Bayesian Confirmation and the Quine–Duhem Problem: A Rejoinder to StrevensBritish Journal for the Philosophy of Science 58 (2): 333-338. 2007.By and large, we think is a useful reply to our original critique of his article on the Quine–Duhem problem. But, we remain unsatisfied with several aspects of his reply. 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.
-
219Probabilistic measures of causal strengthIn Phyllis McKay Illari Federica Russo (ed.), Causality in the Sciences, Oxford University Press. pp. 600--627. 2011.
-
213Too Odd (Not) to Be True? A Reply to OlssonBritish Journal for the Philosophy of Science 53 (4): 539-563. 2002.Corroborating Testimony, Probability and Surprise’, Erik J. Olsson ascribes to L. Jonathan Cohen the claims that if two witnesses provide us with the same information, then the less probable the information is, the more confident we may be that the information is true (C), and the stronger the information is corroborated (C*). We question whether Cohen intends anything like claims (C) and (C*). Furthermore, he discusses the concurrence of witness reports within a context of independent witnesses…Read more
Boston, MA, United States of America
Areas of Specialization
Metaphysics and Epistemology |
Science, Logic, and Mathematics |
Formal Epistemology |