One of the key supposed 'platitudes' of contemporary epistemology is the claim that knowledge excludes luck. One can see the attraction of such a claim, in that knowledge is something that one can take credit for - it is an achievement of sorts - and yet luck undermines genuine achievement. The problem, however, is that luck seems to be an all-pervasive feature of our epistemic enterprises, which tempts us to think that either scepticism is true and that we don't know (...) very much, or else that luck is compatible with knowledge after all. In this book, Duncan Pritchard argues that we do not need to choose between these two austere alternatives, since a closer examination of what is involved in the notion of epistemic luck reveals varieties of luck that are compatible with knowledge possession and varieties that aren't. Moreover, Pritchard shows that a more nuanced understanding of the relationship between luck and knowledge can cast light on many of the most central topics in contemporary epistemology. These topics include: the externalism/internalism distinction; virtue epistemology; the problem of scepticism; metaepistemological scepticism; modal epistemology; and the problem of moral luck. All epistemologists will need to come to terms with Pritchard's original and incisive contribution. (shrink)

The modal account of luck is the predominant account of luck in epistemology and ethics. In the first half of this paper, I discuss three possible interpretations of the modal account and raise objections to each. I then raise an objection to all plausible versions of the modal account, that is, that whether an event is lucky or the extent to which it is a matter of luck will depend on what initial conditions or features of the event one holds (...) constant across nearby possible worlds. However, there is often reasonable disagreement about what the relevant initial conditions of an event are, and the modal account of luck has no means of determining which description of the event is correct. As such, the modal account is subject to a kind of reference class problem, and the view cannot actually tell us the extent to which certain events are a matter of luck. (shrink)

Cantor’s theory of cardinal numbers offers a way to generalize arithmetic from finite sets to infinite sets using the notion of one-to-one association between two sets. As is well known, all countable infinite sets have the same ‘size’ in this account, namely that of the cardinality of the natural numbers. However, throughout the history of reflections on infinity another powerful intuition has played a major role: if a collectionAis properly included in a collectionBthen the ‘size’ ofAshould be less than the (...) ‘size’ ofB(part–whole principle). This second intuition was not developed mathematically in a satisfactory way until quite recently. In this article I begin by reviewing the contributions of some thinkers who argued in favor of the assignment of different sizes to infinite collections of natural numbers (Thabit ibn Qurra, Grosseteste, Maignan, Bolzano). Then, I review some recent mathematical developments that generalize the part–whole principle to infinite sets in a coherent fashion (Katz, Benci, Di Nasso, Forti). Finally, I show how these new developments are important for a proper evaluation of a number of positions in philosophy of mathematics which argue either for the inevitability of the Cantorian notion of infinite number (Gödel) or for the rational nature of the Cantorian generalization as opposed to that, based on the part–whole principle, envisaged by Bolzano (Kitcher). (shrink)

The modal account of luck is the predominant account of luck in epistemology and ethics. In the first half of this paper, I discuss three possible interpretations of the modal account and raise objections to each. I then raise an objection to all plausible versions of the modal account, that is, that whether an event is lucky or the extent to which it is a matter of luck will depend on what initial conditions or features of the event one holds (...) constant across nearby possible worlds. However, there is often reasonable disagreement about what the relevant initial conditions of an event are, and the modal account of luck has no means of determining which description of the event is correct. As such, the modal account is subject to a kind of reference class problem, and the view cannot actually tell us the extent to which certain events are a matter of luck. (shrink)