•  2
    Naturalism and Mathematics
    In Kelly James Clark (ed.), The Blackwell Companion to Naturalism, Wiley. 2016.
    In this chapter, I consider some problems with naturalizing mathematics. More specifically, I consider how the two leading kinds of approach to naturalizing mathematics, to wit, Quinean indispensability‐based approaches and Maddy's Second Philosophical approach, seem to run afoul of constraints that any satisfactory naturalistic mathematics must meet. I then suggest that the failure of these kinds of approach to meet the relevant constraints indicates a general problem with naturalistic mathemat…Read more
  •  16
    Pritchard’s Epistemology and Necessary Truths
    Erkenntnis 1-21. forthcoming.
    Duncan Pritchard has argued that his basis-relative anti-luck construal of a safety condition on knowing avoids the problem with necessary truths that safety conditions are often thought to have, viz., that beliefs the contents of which are necessarily true are trivially safe. He has further argued that adding an ability condition to truth, belief, and his anti-luck safety conditions yields an adequate account of knowledge. In this paper, we argue that not only does Pritchard’s anti-luck safety …Read more
  •  47
    Kitcher, Mathematics, and Apriority
    Erkenntnis 84 (3): 687-702. 2019.
    Philip Kitcher has argued against the apriority of mathematical knowledge in a number of places. His arguments rely on a conception of mathematical knowledge as embedded in a historical tradition and the claim that this sort of embedding compromises apriority. In this paper, I argue that tradition dependence of mathematical knowledge does not compromise its apriority. I further identify the factors which appear to lead Kitcher to argue as he does.
  •  83
  •  104
    Safety and the True–True Problem
    Pacific Philosophical Quarterly 94 (2): 246-267. 2013.
    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 enable…Read more
  •  27
    Kitcher and the Obsessive Unifier
    Philosophy and Phenomenological Research 77 (2): 493-506. 2008.
  •  638
    Strong, therefore sensitive: Misgivings about derose’s contextualism
    Grazer Philosophische Studien 85 (1): 237-253. 2012.
    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…Read more
  •  1442
    Anti-Luck Epistemologies and Necessary Truths
    Philosophia 39 (3): 547-561. 2011.
    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 knowledg…Read more
  •  125
    Kitcher, mathematics, and naturalism
    Australasian Journal of Philosophy 86 (3). 2008.
    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.
  •  176
    A Euthyphronic Problem for Kitcher’s Epistemology of Science
    Southern Journal of Philosophy 47 (2): 205-223. 2009.
    Philip Kitcher has advanced an epistemology of science that 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.
  •  102
    Concept grounding and knowledge of set theory
    Philosophia 38 (1): 179-193. 2010.
    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 pr…Read more
  •  148
    Maddy and Mathematics: Naturalism or Not
    British Journal for the Philosophy of Science 58 (3): 423-450. 2007.
    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 nonnaturalists alike because it explains the reliability of s…Read more
  •  222
    On Naturalizing the Epistemology of Mathematics
    Pacific Philosophical Quarterly 90 (1): 63-97. 2009.
    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.
  •  116
    Kitcher and the obsessive unifier
    Philosophy and Phenomenological Research 77 (2): 493-506. 2008.
    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 t…Read more