•  353
    Replies to Rosen, Leiter, and Dutilh Novaes
    Philosophy and Phenomenological Research 107 (3): 817-837. 2023.
    Gideon Rosen, Brian Leiter, and Catarina Dutilh Novaes raise deep questions about the arguments in Morality and Mathematics (M&M). Their objections bear on practical deliberation, the formulation of mathematical pluralism, the problem of universals, the argument from moral disagreement, moral ‘perception’, the contingency of our mathematical practices, and the purpose of proof. In this response, I address their objections, and the broader issues that they raise.
  •  385
    Observation and Intuition
    with Avner Ash
    In Carolin Antos, Neil Barton & Venturi Giorgio (eds.), Palgrave Companion to the Philosophy of Set Theory, . forthcoming.
    The motivating question of this paper is: ‘How are our beliefs in the theorems of mathematics justified?’ This is distinguished from the question ‘How are our mathematical beliefs reliably true?’ We examine an influential answer, outlined by Russell, championed by Gödel, and developed by those searching for new axioms to settle undecidables, that our mathematical beliefs are justified by ‘intuitions’, as our scientific beliefs are justified by observations. On this view, axioms are analogous …Read more
  •  300
    Platonism, Nominalism, and Semantic Appearances
    Logique Et Analyse. forthcoming.
    It is widely assumed that platonism with respect to a discourse of metaphysical interest, such as fictional or mathematical discourse, affords a better account of the semantic appearances than nominalism, other things being equal. Of course, other things may not be equal. For example, platonism is supposed to come at the cost of a plausible epistemology and ontology. But the hedged claim is often treated as a background assumption. It is motivated by the intuitively stronger one that the pla…Read more
  •  1226
    What is Logical Monism?
    In Christopher Peacocke & Paul Boghossian (eds.), Normative Realism, Oxford University Press. forthcoming.
    Logical monism is the view that there is ‘One True Logic’. This is the default position, against which pluralists react. If there were not ‘One True Logic’, it is hard to see how there could be one true theory of anything. A theory is closed under a logic! But what is logical monism? In this article, I consider semantic, logical, modal, scientific, and metaphysical proposals. I argue that, on no ‘factualist’ analysis (according to which ‘there is One True Logic’ expresses a factual claim, …Read more
  •  432
    Mathematics and Metaphilosophy
    Cambridge University Press. 2022.
    This book discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the challenge to explain the (defeasible) justification of our mathematical beliefs (‘the justificatory challenge’), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the challenge to explain their reliability (‘the reliability challenge’), arises to the extent that we could have easily had different beliefs. The book show…Read more
  •  540
    Modal Pluralism and Higher‐Order Logic
    with William McCarthy
    Philosophical Perspectives 36 (1): 31-58. 2022.
    In this article, we discuss a simple argument that modal metaphysics is misconceived, and responses to it. Unlike Quine's, this argument begins with the simple observation that there are different candidate interpretations of the predicate ‘could have been the case’. This is analogous to the observation that there are different candidate interpretations of the predicate ‘is a member of’. The argument then infers that the search for metaphysical necessities is misguided in much the way the ‘set-t…Read more
  •  109
    Modal Objectivity
    Noûs 53 (2): 266-295. 2017.
    It is widely agreed that the intelligibility of modal metaphysics has been vindicated. Quine's arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators.2 But even if modal metaphysics is intelligible, it could be misconceived. It could be that metaphysical necessity is not absolute necessity – the strictest real notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every real sense. If…Read more
  •  550
    From Non-Usability to Non-Factualism
    Analysis 81 (4): 747-758. 2022.
    Holly Smith has done more than anyone to explore and defend the importance of usability for moral theories. In Making Morality Work, she develops a moral theory that is almost universally usable. But not quite. In this article, I argue that no moral theory is universally usable, in the sense that is most immediately relevant to action, even by agents who know all the normative facts. There is no moral theory knowledge of which suffices to settle deliberation about what to do. However, this …Read more
  •  453
    Addiction and Agency
    In Matt King & Joshua May (eds.), Agency in Mental Disorder: Philosophical Dimensions, Oxford University Press. 2022.
    Addicts are often portrayed as compelled by their addiction and thus as a paradigm of unfree action and mitigated blame. This chapter argues that our best scientific theories of addiction reveal that, psychologically, addicts are not categorically different from non-addicts. There is no pairing of contemporary accounts of addiction and of prominent theories of moral responsibility that can justify our intuitions about the mitigation of addicts but not non-addicts. Two conclusions are advanced. F…Read more
  •  1509
    Justification and Explanation in Mathematics and Morality
    Oxford Studies in Metaethics 10. 2015.
    In his influential book, The Nature of Morality, Gilbert Harman writes: “In explaining the observations that support a physical theory, scientists typically appeal to mathematical principles. On the other hand, one never seems to need to appeal in this way to moral principles.” What is the epistemological relevance of this contrast, if genuine? This chapter argues that ethicists and philosophers of mathematics have misunderstood it. They have confused what the chapter calls the justificatory cha…Read more
  •  708
    I discuss methodology in epistemology. I argue that settling the facts, even the epistemic facts, fails to settle the questions of intellectual policy at the center of our epistemic lives. An upshot is that the standard methodology of analyzing concepts like knowledge, justification, rationality, and so on is misconceived. More generally, any epistemic method that seeks to issue in intellectual policy by settling the facts, whether by way of abductive theorizing or empirical investigation, no…Read more
  •  814
    Realism, Objectivity, and Evaluation
    In David Kaspar (ed.), Explorations in Ethics, Palgrave-macmillan. 2020.
    I discuss Benacerraf's epistemological challenge for realism about areas like mathematics, metalogic, and modality, and describe the pluralist response to it. I explain why normative pluralism is peculiarly unsatisfactory, and use this explanation to formulate a radicalization of Moore's Open Question Argument. According to the argument, the facts -- even the normative facts -- fail to settle the practical questions at the center of our normative lives. One lesson is that the concepts of real…Read more
  •  386
    Modal Security
    with Dan Baras
    Philosophy and Phenomenological Research 102 (1): 162-183. 2021.
    Modal Security is an increasingly discussed proposed necessary condition on undermining defeat. Modal Security says, roughly, that if evidence undermines (rather than rebuts) one’s belief, then one gets reason to doubt the belief's safety or sensitivity. The primary interest of the principle is that it seems to entail that influential epistemological arguments, including Evolutionary Debunking Arguments against moral realism and the Benacerraf-Field Challenge for mathematical realism, are unso…Read more
  •  454
    Undermining Belief in Consciousness
    Journal of Consciousness Studies 26 (9-10): 34-47. 2019.
    Does consciousness exist? In “The Meta-Problem of Consciousness” (MPC) David Chalmers sketches an argument for illusionism, i.e., the view that it does not. The key premise is that it would be a coincidence if our beliefs about consciousness were true, given that the explanation of those beliefs is independent of their truth. In this article, I clarify and assess this argument. I argue that our beliefs about consciousness are peculiarly invulnerable to undermining, whether or not their conte…Read more
  •  643
    The ethics–mathematics analogy
    Philosophy Compass 15 (1). 2019.
    Ethics and mathematics have long invited comparisons. On the one hand, both ethical and mathematical propositions can appear to be knowable a priori, if knowable at all. On the other hand, mathematical propositions seem to admit of proof, and to enter into empirical scientific theories, in a way that ethical propositions do not. In this article, I discuss apparent similarities and differences between ethical (i.e., moral) and mathematical knowledge, realistically construed -- i.e., construed …Read more
  •  1039
    Objectivity and Evaluation
    In Christopher Cowie & Richard Rowland (eds.), Companions in Guilt Arguments in Metaethics, . forthcoming.
    I this article, I introduce the notion of pluralism about an area, and use it to argue that the questions at the center of our normative lives are not settled by the facts -- even the normative facts. One upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension. Another is that the concept of objectivity, not realism, should take center stage.
  •  946
    Morality and Mathematics
    Oxford University Press. 2020.
    To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better…Read more
  •  1802
    Metaphysical and absolute possibility
    Synthese 198 (Suppl 8): 1861-1872. 2019.
    It is widely alleged that metaphysical possibility is “absolute” possibility Conceivability and possibility, Clarendon, Oxford, 2002, p 16; Stalnaker, in: Stalnaker Ways a world might be: metaphysical and anti-metaphysical essays, Oxford University Press, Oxford, 2003, pp 201–215; Williamson in Can J Philos 46:453–492, 2016). Kripke calls metaphysical necessity “necessity in the highest degree”. Van Inwagen claims that if P is metaphysically possible, then it is possible “tout court. Possible si…Read more
  •  1306
    Set-theoretic pluralism and the Benacerraf problem
    Philosophical Studies 177 (7): 2013-2030. 2020.
    Set-theoretic pluralism is an increasingly influential position in the philosophy of set theory (Balaguer [1998], Linksy and Zalta [1995], Hamkins [2012]). There is considerable room for debate about how best to formulate set-theoretic pluralism, and even about whether the view is coherent. But there is widespread agreement as to what there is to recommend the view (given that it can be formulated coherently). Unlike set-theoretic universalism, set-theoretic pluralism affords an answer to Ben…Read more
  • It is sometimes alleged that “the reliability challenge” to moral realism is equally compelling against mathematical realism. This allegation is of interest. The reliability challenge to moral realism is increasingly taken to be the most serious challenge to moral realism. However, the specific considerations that are said to motivate it – such as considerations of rational dubitability and evolutionary influence – are widely held not to motivate an analogous challenge to mathematical realism…Read more
  •  1278
    Modal Objectivity
    Noûs 53 266-295. 2019.
    It is widely agreed that the intelligibility of modal metaphysics has been vindicated. Quine's arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators.2 But even if modal metaphysics is intelligible, it could be misconceived. It could be that metaphysical necessity is not absolute necessity – the strictest real notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every real sense. If…Read more
  •  1860
    What is Absolute Undecidability?†
    Noûs 47 (3): 467-481. 2012.
    It is often supposed that, unlike typical axioms of mathematics, the Continuum Hypothesis (CH) is indeterminate. This position is normally defended on the ground that the CH is undecidable in a way that typical axioms are not. Call this kind of undecidability “absolute undecidability”. In this paper, I seek to understand what absolute undecidability could be such that one might hope to establish that (a) CH is absolutely undecidable, (b) typical axioms are not absolutely undecidable, and (c) if …Read more
  •  610
    Morality and Mathematics: The Evolutionary Challenge
    Ethics 122 (2): 313-340. 2012.
    It is commonly suggested that evolutionary considerations generate an epistemological challenge for moral realism. At first approximation, the challenge for the moral realist is to explain our having many true moral beliefs, given that those beliefs are the products of evolutionary forces that would be indifferent to the moral truth. An important question surrounding this challenge is the extent to which it generalizes. In particular, it is of interest whether the Evolutionary Challenge for m…Read more
  •  200
    A disagrees with B with respect to a proposition, p, flawlessly just in case A believes p and B believes not-p, or vice versa, though neither A nor B is guilty of a cognitive shortcoming – i.e. roughly, neither A nor B is being irrational, lacking evidence relevant to p, conceptually incompetent, insufficiently imaginative, etc
  •  1937
    What is the Benacerraf Problem?
    In Fabrice Pataut Jody Azzouni, Paul Benacerraf Justin Clarke-Doane, Jacques Dubucs Sébastien Gandon, Brice Halimi Jon Perez Laraudogoitia, Mary Leng Ana Leon-Mejia, Antonio Leon-Sanchez Marco Panza, Fabrice Pataut Philippe de Rouilhan & Andrea Sereni Stuart Shapiro (eds.), New Perspectives on the Philosophy of Paul Benacerraf: Truth, Objects, Infinity (Fabrice Pataut, Editor), Springer. 2017.
    In "Mathematical Truth", Paul Benacerraf articulated an epistemological problem for mathematical realism. His formulation of the problem relied on a causal theory of knowledge which is now widely rejected. But it is generally agreed that Benacerraf was onto a genuine problem for mathematical realism nevertheless. Hartry Field describes it as the problem of explaining the reliability of our mathematical beliefs, realistically construed. In this paper, I argue that the Benacerraf Problem canno…Read more
  •  194
    Multiple reductions revisited
    Philosophia Mathematica 16 (2): 244-255. 2008.
    Paul Benacerraf's argument from multiple reductions consists of a general argument against realism about the natural numbers (the view that numbers are objects), and a limited argument against reductionism about them (the view that numbers are identical with prima facie distinct entities). There is a widely recognized and severe difficulty with the former argument, but no comparably recognized such difficulty with the latter. Even so, reductionism in mathematics continues to thrive. In this pape…Read more
  •  32
    Introduction
    Review of Symbolic Logic 5 (3): 379-379. 2012.
  •  1496
    Debunking and Dispensability
    In Uri D. Leibowitz & Neil Sinclair (eds.), Explanation in Ethics and Mathematics: Debunking and Dispensability, Oxford University Press. 2016.
    In his précis of a recent book, Richard Joyce writes, “My contention…is that…any epistemological benefit-of-the-doubt that might have been extended to moral beliefs…will be neutralized by the availability of an empirically confirmed moral genealogy that nowhere…presupposes their truth.” Such reasoning – falling under the heading “Genealogical Debunking Arguments” – is now commonplace. But how might “the availability of an empirically confirmed moral genealogy that nowhere… presupposes” the truth…Read more