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 shows that mathematical facts are not, in general, empirically accessible, contra Quine, (...) and that they cannot be dispensed with, contra Field. However, it argues that they might be so plentiful that our knowledge of them is intelligible. The book concludes with a complementary ‘pluralism’ about modality, logic and normative theory, highlighting its revisionary implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap’s pragmatism, transposed to the key of realism. (shrink)

I argue that certain species of belief, such as mathematical, logical, and normative beliefs, are insulated from a form of Harman-style debunking argument whereas moral beliefs, the primary target of such arguments, are not. Harman-style arguments have been misunderstood as attempts to directly undermine our moral beliefs. They are rather best given as burden-shifting arguments, concluding that we need additional reasons to maintain our moral beliefs. If we understand them this way, then we can see why moral beliefs are vulnerable (...) to such arguments while mathematical, logical, and normative beliefs are not—the very construction of Harman-style skeptical arguments requires the truth of significant fragments of our mathematical, logical, and normative beliefs, but requires no such thing of our moral beliefs. Given this property, Harman-style skeptical arguments against logical, mathematical, and normative beliefs are self-effacing; doubting these beliefs on the basis of such arguments results in the loss of our reasons for doubt. But we can cleanly doubt the truth of morality. (shrink)

In the introduction to his Realism, mathematics and modality, and in earlier papers included in that collection, Hartry Field offered an epistemological challenge to platonism in the philosophy of mathematics. Justin Clarke-Doane Truth, objects, infinity: New perspectives on the philosophy of Paul Benacerraf, 2016) argues that Field’s challenge is an illusion: it does not pose a genuine problem for platonism. My aim is to show that Clarke-Doane’s argument relies on a misunderstanding of Field’s challenge.

Scanlon’s Being Realistic about Reasons (BRR) is a beautiful book – sleek, sophisticated, and programmatic. One of its key aims is to demystify knowledge of normative and mathematical truths. In this article, I develop an epistemological problem that Scanlon fails to explicitly address. I argue that his “metaphysical pluralism” can be understood as a response to that problem. However, it resolves the problem only if it undercuts the objectivity of normative and mathematical inquiry.

A key question for research on the evolutionary origins of morality concerns just what the target of an evolutionary explanation of morality should be. Some researchers focus on behaviors, others on systems of norms, yet others on moral emotions. Richard Joyce (2006) offers an evolutionary explanation for the trait of making moral judgments. Here, I defend Joyce’s account of moral judgment against two objections from Stephen Stich (2008). Stich’s first objection concerns the supposed universality of moral judgments as Joyce conceives (...) of them. I respond by undermining the empirical evidence upon which this objection is based. Stich’s second objection concerns the extent of the moral domain, which he takes to include far more than the considerations of harm and fairness central to Joyce’s account. In response, I outline several strategies for reconciling Stich’s observations with Joyce’s account. (shrink)

While Richard Joyce’s moral skepticism might seem to be an extreme metaethical view, it is actually far more moderate than it might first appear. By articulating four challenges facing his approach to moral skepticism, I argue that Joyce’s moderation is, in fact, a theoretical liability. First, the fact that Joyce is not skeptical about normativity in general makes it possible to develop close approximations to morality, lending support to moderate moral revisionism over moral error theory. Second, Joyce relies on strong, (...) contentious conceptual and empirical claims in support of his views. Third, Joyce’s evolutionary debunking argument threatens to backfire, generalizing to all normative judgments. Finally, Joyce fails to offer an adequate account of the normativity of desire. Each of these four challenges can be either sidestepped or embraced by radicalizing and defending a global form of normative skepticism. There are thus several ways in which global normative skepticism appears to be in a more robust dialectical position than Joyce’s moral skepticism. Furthermore, I argue, Joyce’s arguments against global normative skepticism are unconvincing. While this discussion is framed in terms of Joyce’s work, its arguments will apply to other moral skeptics who are not also global normative skeptics. The result is an invitation for Joyce and other moral skeptics to leave these problems behind and join the radical camp. (shrink)

Evolutionary debunking arguments purport to undercut the justification of our moral judgments by showing why a tendency to make moral judgments would evolve regardless of the truth of those judgments. Machery and Mallon (2010. Evolution of morality. In J.M. Doris and The Moral Psychology Research Group (Eds.), The Moral Psychology Handbook (pp. 3-46). Oxford: Oxford University Press) have recently tried to disarm these arguments by showing that moral cognition – in the sense that is relevant to debunking – is not (...) the product of natural selection. Specifically, they present a barrage of increasingly influential challenges against reciprocity-based approaches to moral nativism. In the present paper I defend the nativist account of moral cognition against these criticisms, thereby bolstering the skeptical conclusions of evolutionary debunking arguments. However, Machery and Mallon's critique does successfully highlight several vulnerabilities in Richard Joyce's approach to debunking, suggesting several ways in which it can be revised toward generating a more robust version of the argument. (shrink)

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 as independent of human mind and languages. (...) I argue that some are are merely apparent, while others are of little consequence. There is a difference between the cases. But it is not an epistemological difference per se. The difference, surprisingly, is that ethical knowledge, if it is practical, cannot fail to be objective in a way that mathematical knowledge can. One upshot of the discussion is radicalization of Moore’s Open Question Argument. Another is that the concepts of realism and objectivity, which are widely identified, are actually in tension. (shrink)