How far should our realism extend? For many years philosophers of mathematics and philosophers of ethics have worked independently to address the question of how best to understand the entities apparently referred to by mathematical and ethical talk. But the similarities between their endeavours are not often emphasised. This book provides that emphasis. In particular, it focuses on two types of argumentative strategies that have been deployed in both areas. The first—debunking arguments—aims to put pressure on realism by emphasising the (...) seeming redundancy of mathematical or moral entities when it comes to explaining our judgements. In the moral realm this challenge has been made by Gilbert Harman and Sharon Street; in the mathematical realm it is known as the 'Benacerraf-Field' problem. The second strategy—indispensability arguments—aims to provide support for realism by emphasising the seeming intellectual indispensability of mathematical or moral entities, for example when constructing good explanatory theories. This strategy is associated with Quine and Putnam in mathematics and with Nicholas Sturgeon and David Enoch in ethics. Explanation in Ethics and Mathematics addresses these issues through an explicitly comparative methodology which we call the 'companions in illumination' approach. By considering how argumentative strategies in the philosophy of mathematics might apply to the philosophy of ethics, and vice versa, the papers collected here break new ground in both areas. For good measure, two further companions for illumination are also broached: the philosophy of chance and the philosophy of religion. Collectively, these comparisons light up new questions, arguments, and problems of interest to scholars interested in realism in any area. (shrink)

Moral philosophers are, among other things, in the business of constructing moral theories. And moral theories are, among other things, supposed to explain moral phenomena. Consequently, one’s views about the nature of moral explanation will influence the kinds of moral theories one is willing to countenance. Many moral philosophers are (explicitly or implicitly) committed to a deductive model of explanation. As I see it, this commitment lies at the heart of the current debate between moral particularists and moral generalists. In (...) this paper I argue that we have good reasons to give up this commitment. In fact, I show that an examination of the literature on scientific explanation reveals that we are used to, and comfortable with, non-deductive explanations in almost all areas of inquiry. As a result, I argue that we have reason to believe that moral explanations need not be grounded in exceptionless moral principles. (shrink)

In this essay I offer a new particularist reading of Aristotle’s Nicomachean Ethics. I argue that the interpretation I present not only helps us to resolve some puzzles about Aristotle’s goals and methods, but it also gives rise to a novel account of morality—an account that is both interesting and plausible in its own right. The goal of this paper is, in part, exegetical—that is, to figure out how to best understand the text of the Nicomachean Ethics. But this paper (...) also aims to contribute to the current exciting and controversial debate over particularism. By taking the first steps towards a comprehensive particularist reading of Aristotle’s Ethics I hope to demonstrate that some of the mistrust of particularism is misplaces and that what is, perhaps, the most influential moral theory in the history of philosophy is, arguably, a particularist moral theory. (shrink)

What makes some acts morally right and others morally wrong? Traditionally, philosophers have thought that in order to answer this question we must find and formulate exceptionless moral principles—principles that capture all and only morally right actions. Utilitarianism and Kantianism are paradigmatic examples of such attempts. In recent years, however, there has been a growing interest in a novel approach—Particularism—although its precise content is still a matter of controversy. In this paper I develop and motivate a new formulation of particularism (...) as a research program and I show that my formulation is not vulnerable to the most common objections to particularism. Moreover, I argue that the particularist research program shows enough promise to warrant further exploration. (shrink)

The paper identifies a distinctive feature of friendship. Friendship, it is argued, is a relationship between two people in which each participant values the other and successfully communicates this fact to the other. This feature of friendship, it is claimed, explains why friendship plays a key role in human happiness, why it is praised by philosophers, poets, and novelists, and why we all seek friends. Although the characterization of friendship proposed here differs from other views in the literature, it is (...) shown that it accommodates key insights of other writers on the topic. Thus, in accordance with the Aristotelian strategy the paper employs, it is shown that the account on offer preserves the received opinions on friendship. (shrink)

In this paper I assess the viability of a particularist explanation of moral knowledge. First, I consider two arguments by Sean McKeever and Michael Ridge that purport to show that a generalist, principle-based explanation of practical wisdom—understood as the ability to acquire moral knowledge in a wide range of situations—is superior to a particularist, non-principle-based account. I contend that both arguments are unsuccessful. Then, I propose a particularist-friendly explanation of knowledge of particular moral facts. I argue that when we are (...) careful to keep separate the various explanatory tasks at hand we can see that a particularist-friendly explanation of the fact that Jane knows that A is morally right might not be so difficult to come by. Moreover, I suggest that a particularist approach to explaining knowledge of particular moral facts may go some way towards discharging the challenge of moral scepticism. (shrink)

Monists, pluralists, and particularists disagree about the structure of the best explanation of the rightness (wrongness) of actions. In this paper I argue that the availability of good moral advice gives us reason to prefer particularist theories and pluralist theories to monist theories. First, I identify two distinct roles of moral theorizing—explaining the rightness (wrongness) of actions, and providing moral advice—and I explain how these two roles are related. Next, I explain what monists, pluralists, and particularists disagree about. Finally, I (...) argue that particularists and pluralists are better situated than monists to explain why it is a good idea to think before we act, and that this gives us reason to favor particularism and pluralism over monism. (shrink)

Many of us read Peter Singer ’ s work on our obligations to those in desperate need with our students. Famously, Singer argues that we have a moral obligation to give a significant portion of our assets to famine relief. If my own experience is not atypical, it is quite common for students, upon grasping the implications of Singer ’ s argument, to ask whether Singer gives to famine relief. In response it might be tempting to remind students of the (...) ad hominem fallacy of attacking the person advancing an argument rather than the argument itself. In this paper I argue that the “ ad hominem reply ” to students ’ request for information about Singer is misguided. First I show that biographical facts about the person advancing an argument can constitute indirect evidence for the soundness / unsoundness of the argument. Second, I argue that such facts are relevant because they may reveal that one can discard the argument without thereby incurring moral responsibility for failing to act on its conclusion even if the argument is sound. (shrink)

Descartes claimed that the Cogito is ‘so firm and sure that all the most extravagant suppositions of the sceptics were incapable of shaking it’. This paper aims to demonstrate that this claim is false by presenting a sceptical scenario for the Cogito. It is argued that the story ‘The Circular Ruins’ by J. L. Borges illustrates that one can doubt one’s own existence and that pace Descartes (and many others) the claim ‘I am, I exist, is necessarily true whenever it (...) is put forward by me or conceived in my mind’ is false. (shrink)

What are the consequences, for human moral practice, of an evolutionary understanding of that practice? By ‘moral practice’ we mean the way in which human beings think, talk and debate in moral terms. We suggest that the proper upshot of such considerations is moderate support for anti-realism in ethics.

Are moral properties intellectually indispensable, and, if so, what consequences does this have for our understanding of their nature, and of our talk and knowledge of them? Are mathematical objects intellectually indispensable, and, if so, what consequences does this have for our understanding of their nature, and of our talk and knowledge of them? What similarities are there, if any, in the answers to the first two questions? Can comparison of the two cases shed light on which answers are most (...) plausible in either case? This chapter – the introduction to the volume Explanation in Ethics and Mathematics – elucidates these questions and sketches their history. (shrink)

Evolutionary debunkers claim that evolutionary explanations of moral phenomena lead to sceptical conclusions. The aim of this paper is to show that even if we grant debunkers the speculative claims that evolution provides the best explanation of moral phenomena and that there are no other moral phenomena for which moral facts/properties are indispensable, the sceptical conclusions debunkers seek to establish still do not follow. The problem for debunkers is to link the empirical explanatory claim to the normative conclusion that moral (...) beliefs are unjustified. The paper argues that debunkers face a dilemma, and that neither of the two options available to them supports the sceptical conclusions for which they aim. Consequently, it is claimed, the dialectical force of evolutionary debunking arguments is, at best, exceedingly weak. (shrink)

If one answers the question ‘What is G-ness?’ with a biconditional of the form ‘x is G iff x is F,’ one can ask whether x is G because it is F, or whether x is F because it is G. This question, known as The Euthyphro Question, invites one to choose between one of two options which are presented as mutually exclusive and jointly exhaustive: either x is G because it is F, or x is F because it is (...) G but not both. Each answer has its attractions and difficulties. The _Euthyphro Problem_ is the problem of choosing one rather than the other. This paper argues that holism in the theory of reasons — a view developed by Jonathan Dancy in a different context and for a different purpose — provides a novel and elegant solution to this age-old problem. (shrink)

Purpose: Physicians are often reluctant to discuss “Do Not Resuscitate” orders with patients. Although perceived self-efficacy is a known prerequisite for behavioural change, little is understood about the confidence of physicians regarding DNR discussions.Subjects and methods: A survey of 217 internal medicine attendings and 132 housestaff at two teaching hospitals about their attitudes and confidence regarding DNR discussions.Results: Participants were significantly less confident about their ability to discuss DNR orders than to discuss consent for medical procedures , and this was (...) true for both attendings and housestaff . In a multivariate logistic model of confidence regarding DNR discussions, women were less confident than men ; house officers were less confident than attendings , those who were less confident of their ability to discuss medical procedures were less confident discussing DNR , and those who found talking to patients about DNR orders very difficult reported less confidence than those who did not .Conclusion: We conclude that physicians’ confidence regarding DNR discussions is low compared with their confidence regarding other medical discussions and that confidence varies by sex and perceived difficulty of the task. Efforts to improve DNR discussions should explore the need to tailor educational interventions to fit these characteristics. (shrink)

Combinatorial operations on sets are almost never well defined on Turing degrees, a fact so obvious that counterexamples are worth exhibiting. The case we focus on is the symmetric-difference operator; there are pairs of degrees for which the symmetric-difference operation is well defined. Some examples can be extracted from the literature, e.g. from the existence of nonzero degrees with strong minimal covers. We focus on the case of incomparable r.e. degrees for which the symmetric-difference operation is well defined.

Unfounded—conspiracy and health—beliefs about COVID-19 have accompanied the pandemic worldwide. Here, we examined cross-nationally the structure and correlates of these beliefs with an 8-item scale, using a multigroup confirmatory factor analysis. We obtained a two-factor model of unfounded (conspiracy and health) beliefs with good internal structure (average CFI = 0.98, RMSEA = 0.05, SRMR = 0.04), but a high correlation between the two factors (average latent factor correlation = 0.57). This model was replicable across 50 countries (total N = 13,579), (...) as evidenced by metric invariance between countries (CFI = 0.96, RMSEA = 0.06, SRMS = 0.07) as well as scalar invariance across genders (CFI = 0.98, RMSEA = 0.04, SRMS = 0.03) and educational levels (CFI = 0.98, RMSEA = 0.04, SRMS = 0.03). Also, lower levels of education, more fear of COVID-19, and more cynicism were weakly associated with stronger conspiracy and health beliefs. The study contributes to knowledge about the structure of unfounded beliefs, and reveals the potential relevance of affective (i.e., fear of COVID-19) and cognitive (i.e., cynicism) factors along with demographics, in endorsing such beliefs. In summary, we obtained cross-cultural evidence for the distinctiveness of unfounded conspiracy and health beliefs about COVID-19 in terms of their structure and correlates. (shrink)

We examine how degrees of computably enumerable equivalence relations under computable reduction break down into isomorphism classes. Two ceers are isomorphic if there is a computable permutation of ω which reduces one to the other. As a method of focusing on nontrivial differences in isomorphism classes, we give special attention to weakly precomplete ceers. For any degree, we consider the number of isomorphism types contained in the degree and the number of isomorphism types of weakly precomplete ceers contained in the (...) degree. We show that the number of isomorphism types must be 1 or ω, and it is 1 if and only if the ceer is self-full and has no computable classes. On the other hand, we show that the number of isomorphism types of weakly precomplete ceers contained in the degree can be any member of $[0,\omega ]$. In fact, for any $n \in [0,\omega ]$, there is a degree d and weakly precomplete ceers ${E_1}, \ldots,{E_n}$ in d so that any ceer R in d is isomorphic to ${E_i} \oplus D$ for some $i \le n$ and D a ceer with domain either finite or ω comprised of finitely many computable classes. Thus, up to a trivial equivalence, the degree d splits into exactly n classes.We conclude by answering some lingering open questions from the literature: Gao and Gerdes [11] define the collection of essentially FC ceers to be those which are reducible to a ceer all of whose classes are finite. They show that the index set of essentially FC ceers is ${\rm{\Pi }}_3^0$-hard, though the definition is ${\rm{\Sigma }}_4^0$. We close the gap by showing that the index set is ${\rm{\Sigma }}_4^0$-complete. They also use index sets to show that there is a ceer all of whose classes are computable, but which is not essentially FC, and they ask for an explicit construction, which we provide.Andrews and Sorbi [4] examined strong minimal covers of downwards-closed sets of degrees of ceers. We show that if $\left$ is a uniform c.e. sequence of non universal ceers, then $\left\{ {{ \oplus _{i \le j}}{E_i}|j \in \omega } \right\}$ has infinitely many incomparable strong minimal covers, which we use to answer some open questions from [4].Lastly, we show that there exists an infinite antichain of weakly precomplete ceers. (shrink)

We present some techniques in c.c.c. forcing, and apply them to prove consistency results concerning the isomorphism and embeddability relations on the family of ℵ 1 -dense sets of real numbers. In this direction we continue the work of Baumgartner [2] who proved the axiom BA stating that every two ℵ 1 -dense subsets of R are isomorphic, is consistent. We e.g. prove Con). Let K H , be the set of order types of ℵ 1 -dense homogeneous subsets of (...) R with the relation of embeddability. We prove that for every finite model L , : Con iff L is a distributive lattice. We prove that it is consistent that the Magidor-Malitz language is not countably compact. We deal with the consistency of certain topological partition theorems. E.g. We prove that MA is consistent with the axiom OCA which says: “If X is a second countable space of power ℵ 1 , and { U 0 ,\h.;, U n−1 } is a cover of D ▪ X x X -} x,x> ¦ x ϵ X } consisting of symmetric open sets, then X can be partitioned into { X i \brvbar; i ϵ ω } such that for every i ϵ ω there is l such that D ⊇ U l ”. We also prove that MA+OCA [xrArr] 2 ℵ 0 = ℵ 2. (shrink)

We examine the degree structure $\operatorname {\mathrm {\mathbf {ER}}}$ of equivalence relations on $\omega $ under computable reducibility. We examine when pairs of degrees have a least upper bound. In particular, we show that sufficiently incomparable pairs of degrees do not have a least upper bound but that some incomparable degrees do, and we characterize the degrees which have a least upper bound with every finite equivalence relation. We show that the natural classes of finite, light, and dark degrees are (...) definable in $\operatorname {\mathrm {\mathbf {ER}}}$. We show that every equivalence relation has continuum many self-full strong minimal covers, and that $\mathbf {d}\oplus \mathbf {\operatorname {\mathrm {\mathbf {Id}}}_1}$ needn’t be a strong minimal cover of a self-full degree $\mathbf {d}$. Finally, we show that the theory of the degree structure $\operatorname {\mathrm {\mathbf {ER}}}$ as well as the theories of the substructures of light degrees and of dark degrees are each computably isomorphic with second-order arithmetic. (shrink)

Dans plusieurs passages, Épicure mentionne des durées infraperceptibles saisies par la raison, ce qui conduit à envisager un atomisme du temps, c’est-à-dire l’existence de durées indivisibles ou quanta de temps. Cette hypothèse, nulle part explicite chez Épicure et Lucrèce, a été évoquée par quelques doxographes. L’objet de cet article est de l’étayer et de la préciser, en lisant les textes épicuriens sur le temps à la lumière des trois grandes objections antiatomistes de la Physique. Notre analyse conclut que l’atomisme du (...) temps permet de répondre aux objections d’Aristote, mais doit être limité au seul niveau des atomes, par opposition à celui des agrégats. Il permet alors en effet de justifier l’isotachie des atomes, de rendre concevable la communauté de structure de la grandeur, du mouvement et du temps, et de garantir le caractère fini de la vitesse atomique. Deux lignes argumentatives se superposent : une conception proprement atomiste du mouvement et une reprise des termes de la physique aristotélicienne destinée à mieux en réfuter les objections. (shrink)

Le passage de la Lettre à Hérodote consacré au temps (Hrdt. 72-73) est particulièrement obscur. Épicure y affirme explicitement que le mot temps ne renvoie à aucune préconception (prolepse), en tout cas pas au sens habituel qu’a ce terme pour lui, puisqu’il n’existe aucun contenu commun à toutes nos expériences du temps ; et cependant le mot temps n’est pas vide. Cet article vise à résoudre ce paradoxe. Il éclaircit la nature de la perception du temps épicurien et tente de (...) reconstituer le processus cognitif qui la sous-tend. La perception du temps est idiosyncrasique, car elle porte sur une entité de troisième degré : le temps est en effet, selon la formule attribuée à Épicure par Démétrius Lacon, un « accident d’accidents ». Sa perception implique une combinaison d’intuition et de déduction, d’analogie et d’épilogisme, en deçà de la formation d’une préconception – dont nous expliquons l’impossibilité. Elle concerne toujours les durées en tant que nous les rapportons les unes aux autres, selon un « libre jeu » de l’épilogisme et de l’analogie qui ne donne pas lieu à une préconception, mais rend possible de nommer le temps. (shrink)

The Protein Ontology (PRO) web resource provides an integrative framework for protein-centric exploration and enables specific and precise annotation of proteins and protein complexes based on PRO. Functionalities include: browsing, searching and retrieving, terms, displaying selected terms in OBO or OWL format, and supporting URIs. In addition, the PRO website offers multiple ways for the user to request, submit, or modify terms and/or annotation. We will demonstrate the use of these tools for protein research and annotation.

What is free will? Can it exist in a determined universe? How can we determine who, if anyone, possesses it? Philosophers have been debating these questions for millennia. In recent decades neuroscientists have joined the fray with questions of their own. Which neural mechanisms could enable conscious control of action? What are intentional actions? Do contemporary developments in neuroscience rule out free will or, instead, illuminate how it works? Over the past few years, neuroscientists and philosophers have increasingly come to (...) understand that both fields can make substantive contributions to the free-will debate, so working together is the best path forward to understanding whether, when, and how our choices might be free. We therefore asked leading philosophers and neuroscientists which questions related to free will they would most like the other field to answer. Those experts then voted on the 15 most important questions for each field to answer. This book is a collection of the answers to those questions along with follow-up questions from world experts in the neuroscience and philosophy of free will. These varied perspectives will fascinate, illuminate, and stimulate students from both fields along with anyone who wants to be brought up to date on these profound issues. (shrink)

We investigate the form of mathematical structuralism that acknowledges the existence of structures and their distinctive structural elements. This form of structuralism has been subject to criticisms recently, and our view is that the problems raised are resolved by proper, mathematics-free theoretical foundations. Starting with an axiomatic theory of abstract objects, we identify a mathematical structure as an abstract object encoding the truths of a mathematical theory. From such foundations, we derive consequences that address the main questions and issues that (...) have arisen. Namely, elements of different structures are different. A structure and its elements ontologically depend on each other. There are no haecceities and each element of a structure must be discernible within the theory. These consequences are not developed piecemeal but rather follow from our definitions of basic structuralist concepts. (shrink)

Biological phenomena can be investigated at multiple levels, from the molecular to the cellular to the organismic to the ecological. In typical biology instruction, these levels have been segregated. Yet, it is by examining the connections between such levels that many phenomena in biology, and complex systems in general, are best explained. We describe a computation-based approach that enables students to investigate the connections between different biological levels. Using agent-based, embodied modeling tools, students model the microrules underlying a biological phenomenon (...) and observe the resultant aggregate dynamics. We describe 2 cases in which this approach was used. In both cases, students framed hypotheses, constructed multiagent models that incorporate these hypotheses, and tested these by running their models and observing the outcomes. Contrasting these cases against traditionally used, classical equation-based approaches, we argue that the embodied modeling approach connects more directly to students’ experience, enables extended investigations as well as deeper understanding, and enables “advanced” topics to be productively introduced into the high school curriculum. (shrink)

According to Alix Cohen, Kant defines emotions as ‘feelings’. Although I find her account of Kantian feelings compelling, I provide three reasons to doubt that it is an account of emotions: (1) it is unclear why Cohen identifies emotions with Kantian feelings; (2) some Kantian feelings are not emotions; (3) some Kantian desires may be emotions. I propose, however, that with some qualifications Cohen’s account may be upheld, provided its extra-textual assumptions about emotions are explicated. Against her claim that Kantian (...) feelings have a derived intentionality, I argue that the text is compatible with their being intrinsically intentional. (shrink)

Assuming the existence of a supercompact cardinal and a weakly compact cardinal above it, we provide a generic extension where there are no Aronszajn trees of height ω 2 or ω 3 . On the other hand we show that some large cardinal assumptions are necessary for such a consistency result.

Commentators provide two different accounts of desires in Kant: “feeling-based” accounts stress their connection with feelings, while “action-based” accounts view them as causes of action. I argue that “feeling-based” accounts blur the feeling-desire distinction, while the “action-based” accounts conflict with Kantian desires that do not cause action. On my alternative, Kantian desires are dispositions to action normally directed at producing future objects, and so they differ from the feelings they are connected to, which refer to the way we are affected (...) by objects. This account preserves the feeling-desire distinction, is compatible with desires that do not cause action, and anticipates holistic theories of desire that combine dispositional, hedonic, and evaluative components. (shrink)

Commentators disagree about Kant’s view on the proper treatment of emotions. In contrast to a tendency in this literature to treat them uniformly, I argue that, according to Kant, feelings (but not affects) require cultivation, and inclinations – although they can and perhaps may be cultivated – generally require discipline. The appropriate treatment for emotions depends on their susceptibility to rational constraint and on the threat they pose to rational deliberation. Although I read Kant as recommending that we cultivate certain (...) emotions, I argue that my reading is not vulnerable to Thomason’s recent pertinent objections to such readings. (shrink)