Papers
Please quote unpublished work only with permission. Comments welcome!
"Maddy and Mathematics: Naturalism or Not, " The British Journal for the Philosophy of Science (2007) 58: 423-450
Abstract: Penelope Maddy advances a purportedly naturalistic account of mathematical methodology which might be taken to answer the question 'What justifies axioms of set theory?' I argue that her account fails both to adequately answer this question and to be naturalistic. Further, the way in which it fails to answer the question deprives it of an analog to one of the chief attractions of naturalism. Naturalism is attractive to naturalists and non-naturalists alike because it explains the reliability of scientific practice. Maddy's account, on the other hand, appears to be unable to similarly explain the reliability of mathematical practice without violating one of its central tenets. (Link is to published version.)
"Kitcher and the Obsessive Unifier," Philosophy and Phenomenological Research (2008) 77: 493-506
Abstract: Philip Kitcher's account of scientific progress incorporates a conception of explanatory unification that invites the so-called 'obsessive unifier' worry, to wit, that in our drive to unify the phenomena we might impose artificial structure on the world and consequently produce an incorrect view of how things, in fact, are. I argue that Kitcher's attempt to address this worry is unsatisfactory because it relies on an ability to choose between rival patterns of explanation which itself rests on the relevant choice having already been made. I also suggest a way of answering the worry that Kitcher is not likely to endorse.
"Kitcher, Mathematics, and Naturalism," Australasian Journal of Philosophy (2008) 86: 481-497
Abstract: This paper argues that Philip Kitcher's epistemology of mathematics, codified in his Naturalistic Constructivism, is not naturalistic on Kitcher's own conception of naturalism. Kitcher's conception of naturalism is committed to (i) explaining the correctness of belief-regulating norms and (ii) a realist notion of truth. Naturalistic Constructivism is unable to simultaneously meet both of these commitments.
"On Naturalizing the Epistemology of Mathematics," Pacific Philosophical Quarterly (2009) 90: 63-97
Abstract: In this paper, I consider an argument for the claim that any satisfactory epistemology of mathematics will violate core tenets of naturalism, i.e., that mathematics cannot be naturalized. I find little reason for optimism that the argument can be effectively answered.
"Concept Grounding and Knowledge of Set Theory," Philosophia (2010) 38: 179-193
Abstract: C. S. Jenkins has recently proposed an account of arithmetical knowledge designed to be realist, empiricist, and apriorist: realist in that what's the case in arithmetic doesn't rely on us being any particular way; empiricist in that arithmetic knowledge crucially depends on the senses; and apriorist in that it accommodates the time-honored judgment that there is something special about arithmetical knowledge, something we have historically labeled with 'a priori'. I'm here concerned with the prospects for extending Jenkins's account beyond arithmetic--in particular, to set theory. After setting out the central elements of Jenkins's account and entertaining challenges to extending it to set theory, I conclude that a satisfactory such extension is unlikely.
"A Euthyphronic Problem for Kitcher's Epistemology of Science," Southern Journal of Philosophy (2009) 47: 205-223
Abstract: Philip Kitcher has advanced an epistemology of science which purports to be naturalistic. For Kitcher, this entails that his epistemology of science must explain the correctness of belief-regulating norms while endorsing a realist notion of truth. This paper concerns whether or not Kitcher's epistemology of science is naturalistic on these terms. I find that it is not, but that by supplementing the account we can secure its naturalistic standing.
"Nominalism and Causal Theories of Reference," SATS--Nordic Journal of Philosophy (2010) 10: 51-68
Abstract: According to contemporary nominalism, there are no abstracta. A common way of arguing against the existence of abstracta deploys a causal theory of reference. In short, we have no good reason to believe in what we cannot refer to and, since reference is causal and abstracta are causally isolated, we cannot refer to abstracta. In this paper, I examine just how far this sort of argument takes nominalism.
''Anti-Luck Epistemologies and Necessary Truths'' (with Jon Cogburn), Philosophia (2011) 39: 547-561.
Abstract: That believing truly as a matter of luck does not generally constitute knowing has become epistemic commonplace. Accounts of knowledge incorporating this anti-luck idea frequently rely on one or another of a safety or sensitivity condition. Sensitivity-based accounts of knowledge have a well-known problem with necessary truths, to wit, that any believed necessary truth trivially counts as knowledge on such accounts. In this paper, we argue that safety-based accounts similarly trivialize knowledge of necessary truths and that two ways of responding to this problem for safety, issuing from work by Williamson and Pritchard, are of dubious success.
''Strong, Therefore Sensitive: Misgivings about DeRose's Contextualism'' (with Jon Cogburn), Grazer Philosophische Studien (2012) 85: 237-253
Abstract: According to an influential contextualist solution to skepticism advanced by Keith DeRose, denials of skeptical hypotheses are, in most contexts, strong yet insensitive. The strength of such denials allows for knowledge of them, thus undermining skepticism, while the insensitivity of such denials explains our intuition that we do not know them. In this paper we argue that, under some well-motivated conditions, a negated skeptical hypothesis is strong only if it is sensitive. We also consider how a natural response on behalf of DeRose appears to be equally available to his primary rival (viz., the sensitivity theorist)
''Safety and the True-True Problem'' (with Jon Cogburn), Pacific Philosophical Quarterly, (2013) 94: 246–267
Abstract: Standard accounts of semantics for counterfactuals confront the true–true problem: when the antecedent and consequent of a counterfactual are both actually true, the counterfactual is automatically true. This problem presents a challenge to safety-based accounts of knowledge. In this paper, drawing on work by Angelika Kratzer, Alan Penczek, and Duncan Pritchard, we propose a revised understanding of semantics for counterfactuals utilizing machinery from generalized quantifier theory which enables safety theorists to meet the challenge of the true–true problem.
''On the Current Status of Quinean Naturalism,'' in Philosophical Methodology: The Armchair or the Laboratory?, edited by Matthew C. Haug (Routledge, 2013)
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