In the mathematics education research literature, there is a growing body of scholarship on how mathematicians practice their craft. The purpose of this chapter is to survey some of this literature and explain how it can contribute to the philosophy of mathematical practice. We first describe how mathematics educators use empirical methodologies to investigate the behaviors of mathematicians and argue that findings from these studies can inform the philosophy of mathematical practice. We then illustrate this by summarizing research on mathematicians’ (...) understandings and mathematicians’ proof reading. (shrink)

This chapter seeks to make a contribution to the growing interest in Nietzsche's relation to traditions of therapy in philosophy that has emerged in recent years. It is in the texts of his middle period that Nietzsche's writing comes closest to being an exercise in philosophical therapeutics, and in this chapter I focus on Dawn from 1881 as a way of exploring this. Dawn is a text that has been admired in recent years for its ethical naturalism and for its (...) anticipation of phenomenology. My interest in the text in this chapter is in the way it revitalises for a modern age ancient philosophical concerns, notably a teaching for mortal souls who wish to be liberated from the fear and anguish of existence, as well as from God, the ‘metaphysical need’, and romantic music, and are able to affirm their mortal conditions of existence. As a general point of inspiration I have adopted Pierre Hadot's insight into the therapeutic ambitions of ancient philosophy which was, he claims, ‘intended to cure mankind's anguish’. This is evident in the teaching of Epicurus which sought to demonstrate the mortality of the soul and whose aim was, ‘to free humans from “the fears of the mind”.’ Similarly, Nietzsche's teaching in Dawn is for mortal souls. In the face of the loss of the dream of the soul's immortality, philosophy for Nietzsche, I shall show, has new consolations to offer in the form of new sublimities. Indeed, for Nietzsche it is by reflecting, with the aid of psychological observation, on what is ‘human, all too human’, that ‘we can lighten the burden of life’. Nietzsche's thinking in Dawn contains a number of proposals and recommendations of tremendous value to philosophical therapeia, including a call for a new honesty about the human ego and human relations, including relations of self and other and love, so as to free us from certain delusions; the search for an authentic mode of existence which appreciates the value of solitude and independence; the importance of having a rich and mature taste in order to eschew the fanatical. After an introduction to Nietzsche's text the chapter is divided into two main parts. In the first main part I explore various aspects of his conception of philosophical therapy, including purification of the higher feelings and liberation from the destructive effects of ‘morality’ and Christianity. In the second main part I explore his conception of ‘the passion of knowledge’, which is the passion that guides modern free spirits as they seek to overcome the need of religion and constraints of ‘morality’, and to access the new sublimities of philosophy. (shrink)

Definite descriptions, I shall argue, have two possible functions. 1] They are used to refer to what a speaker wishes to talk about, but they are also used quite differently. Moreover, a definite description occurring in one and the same sentence may, on different occasions of its use, function in either way. The failure to deal with this duality of function obscures the genuine referring use of definite descriptions. The best known theories of definite descriptions, those of Russell and Strawson, (...) I shall suggest, are both guilty of this. Before discussing this distinction in use, I will mention some features of these theories to which it is especially relevant. (shrink)

This paper uses the knowledge account of assertion (KAA) in defense of epistemological contextualism. Part 1 explores the main problem afflicting contextualism, what I call the "Generality Objection." Part 2 presents and defends both KAA and a powerful new positive argument that it provides for contextualism. Part 3 uses KAA to answer the Generality Objection, and also casts other shadows over the prospects for anti-contextualism.

Consider the following argument written on the board in room 227: 1 = 1. So, the argument on the board in room 227 is not valid. This argument generates a paradox. The aim of this paper is to present a resolution of this paradox and related paradoxes of validity, including a version of the Curry paradox. The proposal stresses the close connections between these validity paradoxes and paradoxes of truth and paradoxes of denotation. So a more general aim is to (...) provide a unified response to semantic paradox. The positive proposal is in part inspired by a brief, tantalizing suggestion of Gödel’s, that the paradoxes might appear “as something analogous to dividing by zero”—so that the concept of validity, for example, is everywhere applicable except for certain singular points or singularities. A second central claim is that ‘valid’ is a context-sensitive predicate. The key notions of this contextual-singularity theory are presented and applied to a variety of cases. Any purported solution to paradox must deal with the phenomenon of revenge, and a response to revenge is outlined. The paper closes with remarks about the accommodation of Tarski’s claim that natural languages are universal. (shrink)

A Curry paradox about truth is generated by the following sentence, written on the board in room 101:If the sentence on the board in room 101 is true then 1 ≠ 1.A Curry paradox about validity is generated by the following argument, written on the board in room 102:The argument on the board in room 102 is valid. Therefore, 1 ≠ 1.Though the sentence and the argument generate Curry paradoxes, they also generate more basic paradoxes, in a sense to be (...) made clear. I argue that if we solve these more basic paradoxes, we have solutions to both kinds of Curry paradox. The positive proposal is in part inspired by a brief remark of Gödel’s, that the paradoxes might appear “as something analogous to dividing by zero”—so that the concepts of truth and validity, for example, are everywhere applicable except for certain singular points or singularities. A second central claim is that 'true' and 'valid' are context-sensitive predicates. This contextual-singularity approach to the Curry paradoxes applies also to other paradoxes of truth, validity, denotation, and predicate-extension. So a more general aim of the paper is to provide a unified response to semantic paradox. (shrink)

In some lottery situations, the probability that your ticket's a loser can get very close to 1. Suppose, for instance, that yours is one of 20 million tickets, only one of which is a winner. Still, it seems that (1) You don't know yours is a loser and (2) You're in no position to flat-out assert that your ticket is a loser. "It's probably a loser," "It's all but certain that it's a loser," or even, "It's quite certain that it's (...) a loser" seem quite alright to say, but, it seems, you're in no position to declare simply, "It's a loser." (1) and (2) are closely related phenomena. In fact, I'll take it as a working hypothesis that the reason "It's a loser" is unassertable is that (a) You don't seem to know that your ticket's a loser, and (b) In flat-out asserting some proposition, you represent yourself as knowing it.1 This working hypothesis will enable me to address these two phenomena together, moving back and forth freely between them. I leave it to those who reject the hypothesis to sort out those considerations which properly apply to the issue of knowledge from those germane to that of assertability. Things are quite different when you report the results of last night's basketball game. Suppose your only source is your morning newspaper, which did not carry a story about the 1 game, but simply listed the score, "Knicks 83, at Bulls 95," under "Yesterday's Results." Now, it doesn't happen very frequently, but, as we all should suspect, newspapers do misreport scores from time to time. On several occasions, my paper has transposed a result, attributing to each team the score of its opponent. In fact, that your paper's got the present result wrong seems quite a bit more probable than that you've won the lottery of the above paragraph. Still, when asked, "Did the Bulls win yesterday?", "Probably" and "In all likelihood" seem quite unnecessary. "Yes, they did," seems just fine.. (shrink)

problems in psychology The three themes of this book are the relation of the brain's structure to psychological function, the problem of how people perceive ...

Contemporary virtue ethics was revolutionized by Alasdair MacIntyre’s reconfiguration using practices as the starting point for understanding virtues. However, MacIntyre has very pointedly excluded the professions of the financial world from the reformulation. He does not count these professions as practices, and further charges that virtue would actually hinder or even rule out one’s pursuit of these professions. This paper addresses three tasks, in regard to the financial profession of investment advising. First, the paper lays out MacIntyre’s soon-to-be-published charges against (...) the investment world, as specified to this profession. Second, it sets forth the role function of investment advising and shows that it does possess internal goods—the crucial aspect of practices disputed by MacIntyre in this case—including goods of production and goods of performance. Third, it demonstrates that this function, and the goods tied to it, cannot be achieved apart from the virtuous pursuit of the profession, thereby showing that MacIntyre’s charges are mistaken. Investment advising is shown to be a virtue-based practice, and the groundwork is laid for showing that other financial professions are so, as well. (shrink)

Qurʾans of the Umayyads: A First Overview. By François Déroche. Leiden Studies in Islam and Society, vol. 1. Leiden: Brill, 2014. Pp. xiii + 155, illus. $71, £55.

This paper offers a brief comment on Jennings’ preceding paper, focusing on the capacity of a republican approach to public health ethics to facilitate reconceptualization of the right to health in situations of limited resources through a relational reading.

Many of our beliefs are acquired online. Online epistemic environments are replete with fake news, fake science, fake photographs and videos, and fake people in the form of trolls and social bots. The purpose of this paper is to investigate the threat that such online fakes pose to the acquisition of knowledge. I argue that fakes can interfere with one or more of the truth, belief, and warrant conditions on knowledge. I devote most of my attention to the effects of (...) online fakes on satisfaction of the warrant condition, as these have received comparatively little attention. I consider three accounts of the conditions under which fakes compromise the warrant condition. I argue for the third of these accounts, according to which the propensity of fakes to exist in an environment threatens warrant acquisition in that environment. Finally, I consider some limitations on the epistemic threat of fakes and suggest some strategies by which this threat can be mitigated. (shrink)

In recent years the 'zombie argument' has come to occupy a central role in the case against physicalist views of consciousness, in large part because of the powerful advocacy it has received from David Chalmers.1 In this paper I seek to neutralize it by showing that a parallel argument can be run for physicalism, an argument turning on the conceivability of what I shall call anti-zombies. I shall argue that the result is a stand-off, and that the zombie argument offers (...) no independent reason to reject physicalism. (shrink)

This paper defends direct activism-the view that it is possible to form beliefs in a causally direct way. In particular, it addresses the charge that direct activism entails voluntarism-the thesis that we can form beliefs at will. It distinguishes weak and strong varieties of voluntarism and argues that, although direct activism may entail the weak variety, it does not entail the strong one. The paper goes on to argue that strong voluntarism is non-contingently false, sketching a new argument for that (...) conclusion. This argument does not tell against the weak form of voluntarism, however, and the final part of the paper argues that weak voluntarism, and consequently direct activism, remains a coherent and defensible position. (shrink)

fits our evidence.[1] I will propose some potential counter-examples to test this evidentialist thesis. My main intention in presenting the “counter-examples” is to better understand Feldman’s evidentialism, and evidentialism in general. How are we to understand what our evidence is, how it works, and how are we to understand the phrase “epistemically ought to believe” such that evidentialism might make sense as a plausible thesis in light of the examples? Of course, we may decide that there’s no such way to (...) understand evidentialism -- that it just isn’t a plausible thesis. I must admit that my suspicions lean in that direction. But the potential counter-examples are put forward, not in a refutational spirit (though I have nothing against good refutations in philosophy), but as an invitation to evidentialists and potential evidentialists to refine and/or explain their thesis in light of the at least apparent problems that the examples highlight. (shrink)

Bringing together leading international scholars within the fields of social and political theory and philosophy, this book explores how we should understand work and its role in our lives and wider society. What challenges are posed by work in our changing economy and the new economic forms that are beginning to emerge, and how can we best address these challenges? In what ways do patterns of working, as well as work technologies, shape people's lives within and outside work, in particular (...) their life opportunities and their social and natural environment? How might we organize-or seek to reorganize-workplaces so that the experience of work better reflects our shared ethical ideals and normative principles? This volume examines these vital questions in a comprehensive and systematic manner in order to provide much needed theoretical insight and practical guidance in reflecting on the nature, problems, and possibilities of work currently. This book will be of interest to undergraduate and postgraduate students and established academics in the areas of contemporary political theory and philosophy, social theory, legal philosophy, labour studies, the sociology of work, practical ethics, critical theory, and political activism. (shrink)

Many common arguments for physicalism begin with the principle that the cosmos is “causally closed.” But how good are the arguments for causal closure itself? I argue that the deductive, a priori arguments on behalf of causal closure tend to beg the question. The extant inductive arguments fare no better. They commit a sampling error or a non-sequitur, or else offer conclusions that remain compatible with causal openness. In short, we have no good arguments that the physical world is causally (...) closed. (shrink)

An Introduction to the Philosophy of Mind provides a lively and accessible introduction to all the main themes and arguments currently being debated in this area. The book examines and criticizes four major theories of mind: Dualism, Mind/Brain Identity, Behaviourism and Functionalism. It argues that while consciousness and our mental lives depend upon physical processes in the brain, they are not reducible to those processes. The differences between mental and physical states, mind/body causality, the problem of other minds, and personal (...) identity are also explored in full. The second edition of this well respected text has been revised to include a new chapter which explores Aristotle’s philosophy of psychology and mind. It also includes new material on the Turing test and has been expanded and updated throughout. The book is designed to help students think for themselves about all the issues identified above, and contains exercises throughout the text to stimulate and challenge the reader. Objectives are clearly set out at the start of every chapter to enable students to check their understanding as they proceed, and each chapter ends with questions to consider. There are discussions of the most cited contemporary writers in the field, so that the reader can gain a rounded perspective of the debates. (shrink)

In this paper I present two new paradoxes, a definability paradox (related to the paradoxes of Berry, Richard and König), and a paradox about extensions (related to Russell’s paradox). However, unlike the familiar definability paradoxes and Russell’s paradox, these new paradoxes involve no self-reference or circularity.

Externalism holds, and internalism denies, that the individuation of many of an individual's mental states (e.g., thoughts about the physical world) depends necessarily on relations that individual bears to the physical and/or social environment. Many philosophers, externalists and internalists alike, believe that introspection yields knowledge of the contents of our thoughts that is direct and authoritative. It is not obvious, however, that the metaphysical claims of externalism are compatible with this epistemological thesis. Some (e.g., Burge, 1988; Falvey and Owens (F&O), (...) 1994) have sought to dispel the worry that there is a conflict, though they admit that if such a conflict exists, it spells trouble for externalism (see, e.g., F&O, 1994, p. 108). Boghossian has argued that there is indeed a conflict between externalism and introspective knowledge of content. Surprisingly, however, he also argues that there is a conflict between internalism and introspective knowledge of content. I will defend Boghossian's claim that there is a conflict between externalism and knowledge of content, but criticize his claim that there is a conflict between internalism and knowledge of content. (shrink)

Academic dishonesty among students is not confined to the dynamics of the classrooms in which it occurs. The institution has a major role in fostering academic integrity. Ways that institutions can have a significant impact on attitudes toward and knowledge about academic integrity as well as reducing the incidence of academic dishonesty are described. These include the content of an effective academic honesty policy, campus-wide programs designed to foster integrity, and the development of a campus-wide ethos that encourages integrity.

According to the Communicative Theory of Emotions, we experience emotions when events occur that are important for our goals and plans. A method of choice for studying these matters is the emotion diary. Emotions configure our cognitive systems and our relationships. Many of our emotions concern our relationships, and empathy is central to our experience of them. We do not always recognize our emotions or the emotions of others, but literary fiction can help improve our skills of recognition and understanding.

Courts are increasingly obliged to adjudicate upon challenges to allocative decisions in healthcare, but their involvement continues to be regarded with unease, imperilling the legitimacy of the judicial role in this context. A central reason for this is that judges are perceived to lack sufficient expertise to determine allocative questions. This article critically appraises the claim of lack of judicial expertise through an examination of the various components of a limit-setting decision. It is argued that the inexpertise argument is weak (...) when compared with other rationales for judicial restraint, such as the procedural unsuitability and lack of constitutional competence of courts. (shrink)

In contrast to political realism's equation of the `political' with domination, Hannah Arendt understood the `political' as a relation of friendship utterly opposed to the use of violence. This article offers a critique of that understanding. It becomes clear that Arendt's challenge to realism, as exemplified by Max Weber, succeeds on account of a dubious redefinition of the `political' that is the reverse image of the one-sided vision of politics she had hoped to contest. Questioning this paradoxical turn leads to (...) a critique of Arendt's separation of violence and power and, consequently, her attempt to insulate a politics of friendship from one of hostility and coercion. However, political realism is not thereby affirmed. What is required, instead, is a view of the `political' that accepts the interwoven-ness of violence and power but also emphasizes the normative ideals of moderation and care. Key Words: Hannah Arendt • enmity • friendship • moderation • the `political' • power • realism • violence • Max Weber. (shrink)

Complexity theory challenges educational philosophy to reconsider accepted paradigms of teaching, learning and educational research. However, though attractive, not least because of its critique of positivism, its affinity to Dewey and Habermas, and its arguments for openness, diversity, relationships, agency and creativity, the theory is not without its difficulties. These are seen to lie in terms of complexity theory's nature, status, methodology, utility and contribution to the philosophy of education, being a descriptive theory that is easily misunderstood as a prescriptive (...) theory, silent on key issues of values and ethics that educational philosophy should embrace, of questionable internal consistency, and of limited ‘added value’ in educational philosophy. The paper sets out key tenets of complexity theory and argues that, though it is useful for educational philosophy, it requires new conceptual tools and mind‐sets to comprehend fully its significance. (shrink)

The contributors to this book draw upon their unique insights and research experience to address fundamental questions, including: What forms does the will take ...

This paper develops an account of consciousness in action. Both consciousness and action are related to knowledge. A voluntary action is defined as a volition, or something intentionally effected by means of such volitions. Volitions are conscious mental acts whose proper function is to make their content true. A mental act is the exercise of a power of mind and a conscious mental act is identical with knowledge of its own phenomenal character. This set of definitions elucidates the relations between (...) consciousness, action and knowledge. (shrink)