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.

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 scientific practice. Maddy's (...) account, on the other hand, appears to be unable to similarly explain the reliability of mathematical practice without violating one of its central tenets. (shrink)

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 condition have a problem (...) with necessary truths, adding an ability condition is of no help. Indeed, the same sort of case that precipitates Pritchard’s introduction of an ability condition shows the inadequacy of his completed anti-luck account of knowledge. Moreover, reconstruing safety as an anti-risk condition as Pritchard has recently done does not fix the problem we’ve identified. We conclude by entertaining a radical suggestion to the effect that the failures of safety-based accounts of modal knowledge are due to failures of doxastic success rather than failures to satisfy an anti-luck (or anti-risk) condition. Accepting this radical suggestion makes available the view that there is, after all, no special problem between safety and necessary truths. (shrink)

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.

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 knowledge of necessary truths and that two ways of responding (...) to this problem for safety, issuing from work by Williamson and Pritchard, are of dubious success. (shrink)

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.

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 mathematics meeting these constraints, and thus with the project of naturalizing mathematics (...) itself. (shrink)

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 prospects for extending Jenkins’s account beyond arithmetic—in (...) particular, to set theory. After setting out the central elements of Jenkins’s account and entertaining challenges to extending it to set theory, I conclude that a satisfactory such extension is unlikely. (shrink)

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 the relevant choice having (...) already been made. I also suggest a way of answering the worry that Kitcher is not likely to endorse. (shrink)

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.

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 enables safety theorists to meet the challenge of the true–true problem.

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 a natural response on behalf (...) of DeRose appears to be equally available to his primary rival (viz., the sensitivity theorist). (shrink)

In a characteristically provocative judgement Sir Ronald Syme has declared: ‘It is not easy to go against a document. Nevertheless, the worse posture is obduracy against the testimony of a precise and lucid writer’. The writer is Ovid, the document one employed by Frontinus, and the context, the death-date of Messalla Corvinus, a subject of scholarly dispute since Scaliger's day. Largely on the basis of two passages in Ovid , Syme rejects the apparent testimony of Frontinus and Jerome that Messalla (...) died in a.d. 12 or 13, in favour of a date in a.d. 8, before Ovid's departure for exile. Issues beyond the death-date of Messalla are involved. Thus Syme wishes, as a corollary, to ante-date the year of Livy's death by five years from a.d. 17 to a.d. 12.3 Further, Syme's characterization of Ovid as ‘a precise and lucid writer’ seems to have more general implications. His arguments merit close scrutiny. (shrink)

11 essays by leading Whitehead scholars re-examinae Whitehead's Barbour-Page lectures, published as the book Symbolism: Its Meaning and Effect in 1927, to give you exciting insights into the contemporary implications of Whitehead's symbolism in an era of new scientific, cultural and technological developments.

What is the legacy of Theory after the deaths of so many of its leading lights, from Jacques Derrida to Roland Barthes? Bringing together reflections by leading contemporary scholars, Dead Theory explores the afterlives of the work of the great theorists and the current state of Theory today. Considering the work of thinkers such as Derrida, Deleuze, and Levinas, the book explores the ways in which Theory has long been haunted by death and how it might endure for the (...) future."--Page 4 of cover. (shrink)

Another title in the reissued Oxford Classic Texts in the Physical Sciences series, Jeffrey's Theory of Probability, first published in 1939, was the first to develop a fundamental theory of scientific inference based on the ideas of Bayesian statistics. His ideas were way ahead of their time and it is only in the past ten years that the subject of Bayes' factors has been significantly developed and extended. Until recently the two schools of statistics were distinctly different and set apart. (...) Recent work has changed all that and today's graduate students and researchers all require an understanding of Bayesian ideas. This book is their starting point. (shrink)

Our chromosomes are full of the dead relics of genes. DNA analysis is beginning to unravel the origin and fate of these pseudogenes, and the influence that they may have on genome organization and evolution.

ChickenHawk is a social-dilemma game that distinguishes uncoordinated from coordinated cooperation. In tests with players belonging to a culturally homogeneous population, natural-language “cheap talk” led to efficient coordination, while nonlinguistic signaling yielded uncoordinated altruism. In a subsequent test with players from a moderately more heterogeneous population nearby, the “cheap talk” condition still produced better coordination than other signaling conditions, but at a lower level and with fewer acts of altruism overall. Implications are: (1) without language, even willing cooperators coordinate poorly; (...) (2) given a sufficiently homogeneous social group, language can coordinate cooperation in the face of opportunities for anonymous defection; (3) coordination therefore depends not on merely a general propensity to cooperate but on the overlap of social identities, which are always costly to acquire and maintain. So far as linguistic variation establishes how much social identities overlap, natural-language “cheap talk” is self-insuring, suggesting that linguistic variation is itself adaptive. (shrink)

Peter Singer’s recent appointment to Princeton University created considerable controversy, most of it focused on his proposal for active euthanasia of disabled infants. Singer articulates utilitarian ideas that often appear in public discussions of euthanasia. Drawing on Pope John Paul II’s work on ethics and suffering, I argue that Singer’s utilitarian theory of value is impoverished. After introducing the Pope’s ethic based on the imago dei, I discuss love as self-gift. I show how this concept supports a theory of value (...) in which spiritual goods are preeminent over material goods. I then describe how suffering reveals spiritual goods, discussing how participation in Christ’s suffering can alter our perception of value. I also consider how communal responses to suffering provide opportunities for self-giving. Third, I consider Singer’s proposal for killing infants with hemophilia, arguing that it arbitrarily ignores spiritual goods. I then discuss proposals to kill anencephalic infants, discussing how parental response to their suffering can demonstrate an extraordinary love in seemingly hopeless circumstances. I conclude by calling for a more sustained social response to euthanasia initiatives. (shrink)

The hexameter poems of Theodore Metochites are perhaps the most determinedly baroque of all Byzantine literary productions to have survived. The tortuous constructions of Metochites' prose rhetoric are transmuted into his rather imprecise concept of the hexameter, with a vocabulary that is ostensibly Homeric but in fact ranges over the whole spectrum of Greek literature, with not a few coinages of his own. The twenty poems, in just over 9,000 lines, were written probably towards the end of his period in (...) high office; several clearly date from the period immediately before his fall from power in 1328, with others written in the years between his return from exile to his beloved monastery of the Chora and his death in 1332. The topics treated by Metochites range from solipsistic musings on his youth and the troubles that afflicted his old age to bombastic funerary memorials. Although the poems are preserved in several manuscripts, it has been demonstrated (by Ihor Ševčenko) that Par.Gr. 1776 stands at the head of the tradition. It is in a format similar to that, for example, of another luxury copy of Metochites' own works, Vindob. Phil. Gr. 95, while the corrections to the verses have been shown to be in the hand of Metochites himself. (shrink)

There is a considerable divergence of opinion about the meaning of mathematics, and it is only with hesitation that I, as a theoretical physicist concerned mainly with geophysics, venture to discuss a matter that professional logicians differ about. Nevertheless I am concerned with the problems of the acquirement of knowledge by scientific methods, and the solutions of these problems involve pure mathematics, the validity of which one is usually willing to take for granted. But the logical schools are not so (...) willing, and aim at demonstration. Logic must be true in all possible worlds, and all empirical propositions must be rigorously excluded. A scientist, on the other hand, is interested mainly in empirical propositions, and mathematics is primarily a tool for investigating their relations. The proof of mathematics would therefore have interest for science, provided that the proof is sufficiently general to cover scientific requirements. If it is not, and the subject matter of the proof is restricted so that it fails to cover the scientific use of mathematics, then in its scientific application it is merely an analogy, and we are no better off than we should be if we simply took the validity of mathematics as it stands as a postulate. (shrink)

We are entering an era in which “cultural construction of the body” refers to a literal technological enterprise. This era was anticipated in the 1920s by geneticist J. B. S. Haldane in a lecture which inspired Aldous Huxley's Brave New World. In that lecture, Haldane reinterpreted the Greek myth of Daedalus and the Minotaur as heroic fable. Seventy years later another geneticist, François Jacob, used the same myth as cautionary tale. Here I explain the Minotaur's “genetic” monstrosity in terms of (...) disability and hybridity, using the movie Gattaca to argue that ancient fears of monstrously disabled bodies are being recycled as bioethics. (shrink)

Contrary to received opinion among philosophers, psychologists, and neuroscientists, conscious duality as a principle of brain organization is neither incoherent nor demonstrably false. The present paper begins by reviewing the history of the theory and its anatomical basis and defending it against the claim that it rests upon an arbitrary decision as to what constitutes the biological substratum of mind or person.

Après avoir fait le point sur les divers manuscrits du Digénis Acritas , connus à l'époque byzantine et sur leurs relations, l'auteur tente de discerner lesquels entrent dans la composition de la version escoriale.