There is a long tradition comparing moral knowledge to mathematical knowledge. In this paper, I discuss apparent similarities and differences between knowledge in the two areas, realistically conceived. I argue that many of these are only apparent, while others are less philosophically significant than might be thought. The picture that emerges is surprising. There are definitely differences between epistemological arguments in the two areas. However, these differences, if anything, increase the plausibility of moral realism as compared to mathematical realism. It (...) is hard to see how one might argue, on epistemological grounds, for moral antirealism while maintaining commitment to mathematical realism. But it may be possible to do the opposite. (shrink)

I give an account of what makes an event a coincidence. -/- I start by critically discussing a couple of other approaches to the notion of coincidence -- particularly that of Lando (2017) -- before developing my own view. The central idea of my view is that the correct understanding of coincidences is closely related to our understanding of the correct 'level' or 'grain' of explanation. Coincidences have a kind of explanatory deficiency — if they did not have this deficiency (...) they would not be coincidences. This deficiency, I claim, is the same explanatory deficiency as when we give low-level explanations of special science phenomena. Such explanations are typically too specific and not robust enough. I claim that there is this same badness in purported explanations of coincidences. -/- I cash out this idea sketching an account of explanatory goodness — an account of what makes explanations better or worse -- and using that to give a more precise account of coincidences. (shrink)

In this paper, I will attempt to develop and defend a common form of intuitive resistance to the companions in guilt argument. I will argue that one can reasonably believe there are promising solutions to the access problem for mathematical realism that don’t translate to moral realism. In particular, I will suggest that the structuralist project of accounting for mathematical knowledge in terms of some form of logical knowledge offers significant hope of success while no analogous approach offers such hope (...) for moral realism. (shrink)

The official model of explanation proposed by the logical empiricists, the covering law model, is subject to familiar objections. The goal of the present paper is to explore an unofficial view of explanation which logical empiricists have sometimes suggested, the view of explanation as unification. I try to show that this view can be developed so as to provide insight into major episodes in the history of science, and that it can overcome some of the most serious difficulties besetting the (...) covering law model. (shrink)

Since Benacerraf’s “Mathematical Truth” a number of epistemological challenges have been launched against mathematical platonism. I first argue that these challenges fail because they unduely assimilate mathematics to empirical science. Then I develop an improved challenge which is immune to this criticism. Very roughly, what I demand is an account of how people’s mathematical beliefs are responsive to the truth of these beliefs. Finally I argue that if we employ a semantic truth-predicate rather than just a deflationary one, there surprisingly (...) turns out to be logical space for a response to the improved challenge where no such space appeared to exist. (shrink)

Although all mathematical truths are necessary, mathematicians take certain combinations of mathematical truths to be ‘coincidental’, ‘accidental’, or ‘fortuitous’. The notion of a ‘ mathematical coincidence’ has so far failed to receive sufficient attention from philosophers. I argue that a mathematical coincidence is not merely an unforeseen or surprising mathematical result, and that being a misleading combination of mathematical facts is neither necessary nor sufficient for qualifying as a mathematical coincidence. I argue that although the components of a mathematical coincidence (...) may possess a common explainer, they have no common explanation ; that two mathematical facts have a unified explanation makes their truth non-coincidental. I suggest that any motivation we may have for thinking that there are mathematical coincidences should also motivate us to think that there are mathematical explanations, since the notion of a mathematical coincidence can be understood only in terms of the notion of a mathematical explanation. I also argue that the notion of a mathematical coincidence plays an important role in scientific explanation. When two phenomenological laws of nature are similar, despite concerning physically distinct processes, it may be that any correct scientific explanation of their similarity proceeds by revealing their similarity to be no mathematical coincidence. (shrink)

According to the traditional view of the causal structure of a coincidence, the several parts of a coincidence are produced by independent causes. I argue that the traditional view is mistaken; even the several parts of a coincidence may have a common cause. This has important implications for how we think about the relationship between causation and causal explanation—and in particular, for why coincidences cannot be explained.

Metaethical—or, more generally, metanormative— realism faces a serious epistemological challenge. Realists owe us—very roughly speaking—an account of how it is that we can have epistemic access to the normative truths about which they are realists. This much is, it seems, uncontroversial among metaethicists, myself included. But this is as far as the agreement goes, for it is not clear—nor uncontroversial—how best to understand the challenge, what the best realist way of coping with it is, and how successful this attempt is. (...) In this paper I try, first, to present the challenge in its strongest version, and second, to show how realists—indeed, robust realists—can cope with it. The strongest version of the challenge is, I argue, that of explaining the correlation between our normative beliefs and the independent normative truths. And I suggest an evolutionary explanation as a way of solving it. (shrink)

Hartry Field has argued that mathematical realism is epistemologically problematic, because the realist is unable to explain the supposed reliability of our mathematical beliefs. In some of his discussions of this point, Field backs up his argument by saying that our purely mathematical beliefs do not ‘counterfactually depend on the facts’. I argue that counterfactual dependence is irrelevant in this context; it does nothing to bolster Field's argument.