
Dutch book argumentsIn Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, The Metaphysics Research Lab. 2014.

36Mathematical explanation and indispensabilityTheoria : An International Journal for Theory, History and Fundations of Science 33 (2): 233247. 2018.This paper discusses Baker’s Enhanced Indispensability Argument for mathematical realism on the basis of the indispensable role mathematics plays in scientific explanations of physical facts, along with various responses to it. I argue that there is an analogue of causal explanation for mathematics which, of several basic types of explanation, holds the most promise for use in the EIA. I consider a plausible case where mathematics plays an explanatory role in this sense, but argue that such use …Read more

7Is Indispensability Still a Problem for Fictionalism?In Gerhard Preyer (ed.), Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism, Ontos. pp. 132144. 2008.

18The Curve Fitting Problem: A Bayesian ApproachPhilosophy of Science 63 (S3). 1996.In the curve fitting problem two conflicting desiderata, simplicity and goodnessoffit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodnessoffit. Using Bayes’ theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory’s goodnessoffit. We justify the use of prior probability and show how to calculate the likelihood of a f…Read more

17Coherence and Epistemic RationalityThe Paideia Archive: Twentieth World Congress of Philosophy 45 256261. 1998.This paper addresses the question of whether probabilistic coherence is a requirement of rationality. The concept of probabilistic coherence is examined and compared with the familiar notion of consistency for simple beliefs. Several reasons are given for thinking rationality does not require coherence. Finally, it is argued that incoherence does not necessarily involve fallacious reasoning.

30Mathematical explanation and indispensabilityTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 33 (2): 233247. 2018.This paper discusses Baker’s Enhanced Indispensability Argument for mathematical realism on the basis of the indispensable role mathematics plays in scientific explanations of physical facts, along with various responses to it. I argue that there is an analogue of causal explanation for mathematics which, of several basic types of explanation, holds the most promise for use in the EIA. I consider a plausible case where mathematics plays an explanatory role in this sense, but argue that such use …Read more

15Paul Weirich, Decision Space: Multidimensional Utility Analysis. Cambridge: Cambridge University Press , 286 pp., $85.00 (review)Philosophy of Science 72 (3): 503506. 2005.

Conditionalization and Rational Belief ChangeDissertation, University of California, Berkeley. 1992.I give a critique of the widely held Bayesian position that rational beliefs change by conditionalization. The conditionalization rules are intended to describe, in terms of probabilities, how degrees of belief should change in response to new information. First, I discuss the Simple Rule of Conditionalization, which states that when the probability of the proposition e changes to one the new probability of the proposition A is equal to the old probability of A given e . I then discuss Richard J…Read more

21Defending the axioms: On the philosophical foundations of set theory * by Penelope MaddyAnalysis 72 (3): 635637. 2012.

75Eliminative induction and bayesian confirmation theoryCanadian Journal of Philosophy 26 (2): 25766. 1996.In his recent book The Advancement of Science, Philip Kitcher endorses eliminative induction, or the view that confirmation of hypotheses proceeds by the elimination of alternatives. My intention here is to critically examine Kitcher's eliminativist view of confirmation, and his rejection of the widely held Bayesian position, according to which an hypothesis H is confirmed by evidence E just in case the probability of H conditional on E is greater than the simple unconditional probability of H […Read more

Science, Error Statistics, and Arguing from Error CommentaryPoznan Studies in the Philosophy of the Sciences and the Humanities 71 95111. 2000.

100Dutch books, dutch strategies and what they show about rationalityPhilosophical Studies 86 (2): 185201. 1997.

30Is Indispensability Still a Problem for Fictionalism?ProtoSociology 25 128139. 2008.For quite some time the indispensability arguments of Quine and Putnam were considered a formidable obstacle to anyone who would reject the existence of mathematical objects. Various attempts to respond to the indispensability arguments were developed, most notably by Chihara and Field. Field tried to defend mathematical fictionalism, according to which the existential assertions of mathematics are false, by showing that the mathematics used in applications is in fact dispensable. Chihara sugges…Read more

15The Logical Status of Conditionalization and its Role in ConfirmationPoznan Studies in the Philosophy of the Sciences and the Humanities 71 7794. 2000.

194Review of P. Maddy, Defending the Axioms: On the Philosophical Foundations of Set Theory (review)Analysis 72 (3): 635637. 2012.

167More Precisely: The Math You Need to Do Philosophy. By Eric SteinhartMetaphilosophy 42 (12): 161165. 2011.

159Confirmation and the indispensability of mathematics to sciencePhilosophy of Science 63 (3): 263. 1996.Quine and Putnam argued for mathematical realism on the basis of the indispensability of mathematics to science. They claimed that the mathematics that is used in physical theories is confirmed along with those theories and that scientific realism entails mathematical realism. I argue here that current theories of confirmation suggest that mathematics does not receive empirical support simply in virtue of being a part of well confirmed scientific theories and that the reasons for adopting a real…Read more
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