• Dutch book arguments
    In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, The Metaphysics Research Lab. 2014.
  •  36
    Mathematical explanation and indispensability
    Theoria : An International Journal for Theory, History and Fundations of Science 33 (2): 233-247. 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
  •  18
    The Curve Fitting Problem: A Bayesian Approach
    with Prasanta S. Bandyopadhayay and Robert J. Boik
    Philosophy of Science 63 (S3). 1996.
    In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. 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 goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a f…Read more
  •  17
    Coherence and Epistemic Rationality
    The Paideia Archive: Twentieth World Congress of Philosophy 45 256-261. 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.
  •  30
    Mathematical explanation and indispensability
    Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 33 (2): 233-247. 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
  • Conditionalization and Rational Belief Change
    Dissertation, 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
  •  22
    Philosophy of Mathematics (review)
    Philosophical Books 45 (3): 277-282. 2004.
  •  93
    Dutch book arguments
    Stanford Encyclopedia of Philosophy. 2011.
  •  75
    Eliminative induction and bayesian confirmation theory
    Canadian Journal of Philosophy 26 (2): 257-66. 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 Commentary
    Poznan Studies in the Philosophy of the Sciences and the Humanities 71 95-111. 2000.
  •  30
    Is Indispensability Still a Problem for Fictionalism?
    ProtoSociology 25 128-139. 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
  •  34
    Book review Decision Space (review)
    Philosophy of Science 72 (3): 503-506. 2005.
  •  15
    The Logical Status of Conditionalization and its Role in Confirmation
    Poznan Studies in the Philosophy of the Sciences and the Humanities 71 77-94. 2000.
  •  167
  •  159
    Confirmation and the indispensability of mathematics to science
    Philosophy 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