This classic and controversial book examines the roots of the idea of virtue, diagnoses the reasons for its absence in modern life, and proposes a path for its recovery.

We will next speak of Liberality. Now this is thought to be the mean state, having for its object-matter Wealth: I mean, the Liberal man is praised not in the circumstances of war, nor in those which constitute the character of perfected self-mastery, nor again in judicial decisions, but in respect of giving and receiving Wealth, chiefly the former. By the term Wealth I mean all those things whose worth is measured by money.

Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to Gauss (...) and Eisenstein, and a sophisticated proof using algebraic number theory, due to Hilbert. Philosophers have yet to look carefully at such explanatory disagreements in mathematics. I do so here. According to the view I defend, there are two important explanatory virtues—depth and transparency—which different proofs (and other potential explanations) possess to different degrees. Although not mutually exclusive in principle, the packages of features associated with the two stand in some tension with one another, so that very deep explanations are rarely transparent, and vice versa. After developing the theory of depth and transparency and applying it to the case of quadratic reciprocity, I draw some morals about the nature of mathematical explanation. (shrink)

Mathematical apriorists usually defend their view by contending that axioms are knowable a priori, and that the rules of inference in mathematics preserve this apriority for derived statements—so that by following the proof of a statement, we can trace the apriority being inherited. The empiricist Philip Kitcher attacked this claim by arguing there is no satisfactory theory that explains how mathematical axioms could be known a priori. I propose that in analyzing Ernest Sosa’s model of intuition as an intellectual virtue, (...) we can construct an “intuition–virtue” that could supply the missing explanation for the apriority of axioms. I first argue that this intuition–virtue qualifies as an a priori warrant according to Kitcher’s account, and then show that it could produce beliefs about mathematical axioms independent of experience. If my argument stands, this paper could provide insight on how virtue epistemology could help defend mathematical apriorism on a larger scale. (shrink)

The paper asks whether diagrams in mathematics are particularly fruitful compared to other types of representations. In order to respond to this question a number of examples of propositions and their proofs are considered. In addition I use part of Peirce’s semiotics to characterise different types of signs used in mathematical reasoning, distinguishing between symbolic expressions and 2-dimensional diagrams. As a starting point I examine a proposal by Macbeth. Macbeth explains how it can be that objects “pop up”, e.g., as (...) a consequence of the constructions made in the diagrams of Euclid, that is, why they are fruitful. It turns out, however, that diagrams are not exclusively fruitful in this sense. By analysing the proofs given in the paper I introduce the notion of a ‘faithful representation’. A faithful representation represents as either an image or as a metaphor. Secondly it represents certain relevant relations. Thirdly manipulations on the representations respect manipulations on the objects they represent, so that new relations may be found. The examples given in the paper illustrate how such representations can be fruitful. These examples include proofs based on both symbolic expressions as well as diagrams and so it seems diagrams are not special when it comes to fruitfulness. Having said this, I do present two features of diagrams that seem to be unique. One consists of the possibility of exhibiting the type of relation in a diagram—or simply showing that a relation exists—as a contrast to stating in words that it exists. The second is the spatial configurations possible when using diagrams, e.g., allowing to show multiple relations in a single diagram. (shrink)

This paper investigates an important aspect of mathematical practice: that proof is required for a finished piece of mathematics. If follows that non-deductive arguments — however convincing — are never sufficient. I explore four aspects of mathematical research that have facilitated the impressive success of the discipline. These I call the Practical Virtues: Permanence, Reliability, Autonomy, and Consensus. I then argue that permitting results to become established on the basis of non-deductive evidence alone would lead to their deterioration. This furnishes (...) us with a partial rational justification for mathematicians strict insistence on proof. (shrink)

Mathematicians often intentionally leave gaps in their proofs. Based on interviews with mathematicians about their refereeing practices, this paper examines the character of intentional gaps in published proofs. We observe that mathematicians’ refereeing practices limit the number of certain intentional gaps in published proofs. The results provide some new perspectives on the traditional philosophical questions of the nature of proof and of what grounds mathematical knowledge.

Mathematicians use the word ‘deep’ to convey a high appreciation of a concept, theorem, or proof. This paper investigates the extent to which the term can be said to have an objective character by examining its first use in mathematics. It was a consequence of Gauss's work on number theory and the agreement among his successors that specific parts of Gauss's work were deep, on grounds that indicate that depth was a structural feature of mathematics for them. In contrast, French (...) mathematicians had a less structural, more problem-oriented approach to mathematics and did not speak of depth so readily. (shrink)

An inclusive vision of mathematics-- its beauty, its humanity, and its power to build virtues that help us all flourish. For mathematician Francis Su, a society without mathematical affection is like a city without museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a diverse audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves personal reflections, puzzles, and stories to (...) show how mathematics meets basic human desires and cultivates virtues essential for human flourishing. Readers will explore mathematical concepts-- and see how mathematical thinking can even fulfill such longings as for love, play, freedom, justice, and community. Some lessons come from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher Jackson's letters to the author appear throughout the book and show how this intellectual pursuit can-- and must-- be open to all. (shrink)

Here the author of How to Solve It explains how to become a "good guesser." Marked by G. Polya's simple, energetic prose and use of clever examples from a wide range of human activities, this two-volume work explores techniques of guessing, inductive reasoning, and reasoning by analogy, and the role they play in the most rigorous of deductive disciplines.

What are the features of a good scientific theory? Samuel Schindler's book revisits this classical question in the philosophy of science and develops new answers to it. Theoretical virtues matter not only for choosing theories 'to work with', but also for what we are justified in believing: only if the theories we possess are good ones can we be confident that our theories' claims about nature are actually correct. Recent debates have focussed rather narrowly on a theory's capacity to predict (...) new phenomena successfully, but Schindler argues that the justification for this focus is thin. He discusses several other theory properties such as testability, accuracy, and consistency, and highlights the importance of simplicity and coherence. Using detailed historical case studies and careful philosophical analysis, Schindler challenges the received view of theoretical virtues and advances arguments for the view that science uncovers reality through theory. (shrink)

What is intellectual humility? In this essay, we aim to answer this question by assessing several contemporary accounts of intellectual humility, developing our own account, offering two reasons for our account, and meeting two objections and solving one puzzle.

Many mathematicians, physicists, and philosophers have suggested that the fact that mathematics—an a priori discipline informed substantially by aesthetic considerations—can be applied to natural science is mysterious. This paper sharpens and responds to a challenge to this effect. I argue that the aesthetic considerations used to evaluate and motivate mathematics are much more closely connected with the physical world than one might presume, and (with reference to case-studies within Galois theory and probabilistic number theory) show that they are correlated with (...) generally recognized theoretical virtues, such as explanatory depth, unifying power, fruitfulness, and importance. (shrink)

This article explores the virtues of generosity and magnificence in Aristotle's Nicomachean Ethics. Generosity involves private individuals giving moderately; magnificence is spending by individuals on a grand scale for public purposes. Inequality, it is argued, grounds and motivates these virtues. For Aristotle, generosity and magnificence are products of inherited wealth, and the generous and the magnificent person seek the noble in their actions rather than the benefit of their recipients. The generous and the magnificent intend to place themselves in a (...) superior position to those who receive their gifts. Moreover, magnificence flows from a great inequality of wealth and requires that the provision of public goods be in private hands. Aristotle. (shrink)

This article explores the virtues of generosity and magnificence in Aristotle’s Nicomachean Ethics. Generosity involves private individuals giving moderately; magnificence is spending by individuals on a grand scale for public purposes. Inequality, it is argued, grounds and motivates these virtues. For Aristotle, generosity and magnificence are products of inherited wealth, and the generous and the magnificent person seek the noble in their actions rather than the benefit of their recipients. The generous and the magnificent intend to place themselves in a (...) superior position to those who receive their gifts.Moreover, magnificence flows from a great inequality of wealth and requires that the provision of public goods be in private hands. Aristotle, this article suggests, means to critique rather than embrace these virtues by pointing to the inequality and privacy at their foundation. The way in which Aristotle’s theory of justice supplements his analysis of generosity and magnificence is also brought to light. (shrink)

Duhem’s concept of “good sense” is central to his philosophy of science, given that it is what allows scientist to decide between competing theories. Scientists must use good sense and have intellectual and moral virtues in order to be neutral arbiters of scientific theories, especially when choosing between empirically adequate theories. I discuss the parallels in Duhem’s views to those of virtue epistemologists, who understand justified belief as that arrived at by a cognitive agent with intellectual and moral virtues, showing (...) how consideration of Duhem as a virtue epistemologist offers insights into his views, as well as providing possible answers to some puzzles about virtue epistemology. The extent to which Duhem holds that the intellectual and moral virtues of the scientist determine scientific knowledge has not been generally noticed. (shrink)

Ernest Sosa presents a new approach to the problems of knowledge and scepticism. He argues for two levels of knowledge, the animal and the reflective, each viewed as a distinctive human accomplishment. Sosa's virtue epistemology illuminates different varieties of scepticism, the nature and status of intuitions, and epistemic normativity.

Ernest Sosa's A Virtue Epistemology, Vol. I is arguably the single-most important monograph to be published in analytic epistemology in the last ten years. Sosa, the first in the field to employ the notion of intellectual virtue – in his ground-breaking ‘The Raft and the Pyramid’– is the leading proponent of reliabilist versions of virtue epistemology. In A Virtue Epistemology, he deftly defends an externalist account of animal knowledge as apt belief, argues for a distinction between animal and reflective knowledge, (...) contends that rational intuition is an intellectual virtue ; and offers responses to dream scepticism, the problem of the criterion and the value problem. Nearly all of these arguments are new, albeit consistent with Sosa's earlier work; that is, consistent with two notable exceptions. First, c ontra Sosa's ‘Replies’ in Ernest Sosa and His Critics, A Virtue Epistemology explicitly contends that safety is not required for animal knowledge. Second, unlike Sosa's Knowledge in Perspective, which arguably construes the intellectual virtues as merely instrumentally valuable, A Virtue Epistemology explicitly contends that the intellectual virtues are instrumentally and constitutively valuable. Best read in conjunction with the above monographs and Epistemic Justification, A Virtue Epistemology is mandatory reading for epistemologists and graduate students in the field. It will rightly set the standard for debates in analytic epistemology for years to come.I will summarize and raise objections to two key conclusions that are unique to A Virtue Epistemology: the ‘kaleidoscope-perceiver’ has animal knowledge but lacks reflective knowledge; unlike the k-perceiver, the ordinary perceiver has reflective knowledge. My objections …. (shrink)

This paper is about the putative theoretical virtue of strength, as it might be used in abductive arguments to the correct logic in the epistemology of logic. It argues for three theses. The first is that the well-defined property of logical strength is neither a virtue nor a vice, so that logically weaker theories are not—all other things being equal—worse or better theories than logically stronger ones. The second thesis is that logical strength does not entail the looser characteristic of (...) scientific strength, and the third is that many modern logics are on a par—or can be made to be on a par—with respect to scientific strength. (shrink)

Since the publication of Edmund Gettier's challenge to the traditional epistemological doctrine of knowledge as justified true belief, Roberts and Wood claim that epistemologists lapsed into despondency and are currently open to novel approaches. One such approach is virtue epistemology, which can be divided into virtues as proper functions or epistemic character traits. The authors propose a notion of regulative epistemology, as opposed to a strict analytic epistemology, based on intellectual virtues that function not as rules or even as skills (...) but as habits of the heart. To that end, they divide the task of clarifying and expounding their notion in the book's two parts.In the first part, Roberts and Wood examine various components that constitute their notion of regulative epistemology. The first are the epistemic goods or goals that drive the epistemic process. What is needed, claim Roberts and Wood, is an enriched notion of these goods rather than the restricted notion of justified true belief. Epistemic agents are more than calculating devices in that …. (shrink)

We investigate how epistemic injustice can manifest itself in mathematical practices. We do this as both a social epistemological and virtue-theoretic investigation of mathematical practices. We delineate the concept both positively—we show that a certain type of folk theorem can be a source of epistemic injustice in mathematics—and negatively by exploring cases where the obstacles to participation in a mathematical practice do not amount to epistemic injustice. Having explored what epistemic injustice in mathematics can amount to, we use the concept (...) to highlight a potential danger of intellectual enculturation. (shrink)

We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, (...) for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of the discipline. (shrink)

This paper is intended to link the notion of bon sens with the Greek notion of noûs, that exposes the role played by the first notion in the thought of Pierre Duhem and explains the concept of noûs in the thought of Aristotle. Later, it attempts to carry out the explanation of the link that can have both notions.

Descartes held that practicing mathematics was important for developing the mental faculties necessary for science and a virtuous life. Otherwise, he maintained that the proper uses of mathematics were extremely limited. This article discusses his reasons which include a theory of education, the metaphysics of matter, and a psychologistic theory of deductive reasoning. It is argued that these reasons cohere with his system of philosophy.

Prominent mathematician William Thurston was praised by other mathematicians for his intellectual generosity. But what does it mean to say Thurston was intellectually generous? And is being intellectually generous beneficial? To answer these questions I turn to virtue epistemology and, in particular, Roberts and Wood's (2007) analysis of intellectual generosity. By appealing to Thurston's own writings and interviewing mathematicians who knew and worked with him, I argue that Roberts and Wood's analysis nicely captures the sense in which he was intellectually (...) generous. I then argue that intellectual generosity is beneficial because it counteracts negative effects of the reward structure of mathematics that can stymie mathematical progress. (shrink)

The paper argues that there is such a thing as luck in acquisition of candidate a priori beliefs and knowledge, and that the possibility of luck in this “armchair” domain shows that definitions of believing by luck that p offered in literature are inadequate, since they mostly rely on the possibility of it being the case that not- p. When p is necessary, such a definition should be supplemented by one pointing to variation in belief, not in the fact believed. (...) Thus the paper suggests a focus upon the agent and her epistemic virtue in the account of epistemic luck in general. (shrink)

It’s often said that set theory provides a foundation for classical mathematics because every classical mathematical object can be modeled as a set and every classical mathematical theorem can be proved from the axioms of set theory. This is obviously a remarkable mathematical fact, but it isn’t obvious what makes it ‘foundational’. This paper begins with a taxonomy of the jobs set theory does that might reasonably be regarded as foundational. It then moves on to category-theoretic and univalent foundations, exploring (...) to what extent they do these same jobs, and to what extent they might do other jobs also reasonably regarded as foundational. (shrink)

What is an epistemological crisis? Consider, first, the situation of ordinary agents who are thrown into such crises. Someone who has believed that he was highly valued by his employers and colleagues is suddenly fired; someone proposed for membership of a club whose members were all, so he believed, close friends is blackballed. Or someone falls in love and needs to know what the loved one really feels; someone falls out of love and needs to know how he or she (...) can possibly have been so mistaken in the other. For all such persons the relationship of seems to is becomes crucial. It is in such situations that ordinary agents who have never learned anything about academic philosophy are apt to rediscover for themselves versions of the other-minds problem and the problem of the justification of induction. They discover, that is, that there is a problem about the rational justification of inferences from premises about the behaviour of other people to conclusions about their thoughts, feelings, and attitudes and of inferences from premises about how individuals have acted in the past to conclusions expressed as generalizations about their behaviour - generalizations which would enable us to make reasonably reliable predications about their future behaviour. What they took to be evidence pointing unambiguously in some one direction now turns out to have been equally susceptible of rival interpretations. Such a discovery is often paralysing, and were we all of us all of the time to have to reckon with the multiplicity of possible interpretations open to us, social life as we know it could scarcely continue. For social life is sustained by the assumption that we are, by and large, able to construe each other's behaviour - that error, deception, self-deception, irony and ambiguity, although omnipresent in social life, are not so pervasive as to render reliable reasoning and reasonable action impossible. But can this assumption in any way be vindicated? (shrink)

Hyde claims that the trickster spirit is necessary for the renewal of culture, and that he lives only in the ‘complex terrain of polytheism’. Fortunately for those of us in monotheistic cultures, Weber gives reasons for thinking that polytheism is making a return, albeit in a new, disenchanted form. The plan of this paper is to elaborate some basic notions from Weber, to explore Hyde’s thesis in more detail and then to take up the question of the plurality of spirits (...) both around and within us and whether the trickster is one of them. Weber has three roles in this argument. First, he theorises rationalisation, disenchantment and bureaucracy; second, he offers an argument that in a certain sense polytheism is returning ; and third, he presents a way to translate the mytho-poetic register in which Hyde works into terms acceptable to social science of a more materialist bent. The claim of the paper is that polytheism as a practical attitude means recognising that there are diverse and contradictory ethical orders built into the world around us and active with our psyches. Weber explains why this is especially difficult for us, and Hyde offers us the hope that we may be tricky enough to cope. (shrink)

Hyde claims that the trickster spirit is necessary for the renewal of culture, and that he lives only in the ‘complex terrain of polytheism’. Fortunately for those of us in monotheistic cultures, Weber gives reasons for thinking that polytheism is making a return, albeit in a new, disenchanted form. The plan of this paper is to elaborate some basic notions from Weber, to explore Hyde’s thesis in more detail and then to take up the question of the plurality of spirits (...) both around and within us and whether the trickster is one of them. Weber has three roles in this argument. First, he theorises rationalisation, disenchantment and bureaucracy; second, he offers an argument that in a certain sense polytheism is returning ; and third, he presents a way to translate the mytho-poetic register in which Hyde works into terms acceptable to social science of a more materialist bent. The claim of the paper is that polytheism as a practical attitude means recognising that there are diverse and contradictory ethical orders built into the world around us and active with our psyches. Weber explains why this is especially difficult for us, and Hyde offers us the hope that we may be tricky enough to cope. (shrink)

David Stump has recently argued that Pierre Duhem can be interpreted as a virtue epistemologist. Stump’s claims have been challenged by Milena Ivanova on the grounds that Duhem’s ‘epistemic aims’ are more modest than those of virtue epistemologists. I challenge Ivanova’s criticism of Stump by arguing that she not distinguish between ‘reliabilist’ and ‘responsibilist’ virtue epistemologies. Once this distinction is drawn, Duhem clearly emerges as a ‘virtue-responsibilist’ in a way that complements Ivanova’s positive proposal that Duhem’s ‘good sense’ reflects a (...) conception of the ‘ideal scientist’. I support my proposal that Duhem is a ‘virtue-responsibilist’ by arguing that his rejection of the possibility of our producing a ‘perfect theory’ reflects the key responsibilist virtue of ‘intellectual humility’.Keywords: David Stump; Good sense; Humility; Milena Ivanova; Pierre Duhem; Virtue epistemology. (shrink)

In this paper, I explore the relationship of virtue, argumentation, and philosophical conduct by considering the role of the specific virtue of intellectual humility in the practice of philosophical argumentation. I have three aims: first, to sketch an account of this virtue; second, to argue that it can be cultivated by engaging in argumentation with others; and third, to problematize this claim by drawing upon recent data from social psychology. My claim is that philosophical argumentation can be conducive to the (...) cultivation of virtues, including humility, but only if it is conceived and practiced in appropriately ‘edifying’ ways. (shrink)

This paper examines Duhem’s concept of good sense as an attempt to support a non rule-governed account of rationality in theory choice. Faced with the underdetermination of theory by evidence thesis and the continuity thesis, Duhem tried to account for the ability of scientists to choose theories that continuously grow to a natural classification. I will examine the concept of good sense and the problems that stem from it. I will also present a recent attempt by David Stump to link (...) good sense to virtue epistemology. I will argue that even though this approach can be useful for the better comprehension of the concept of good sense, there are some substantial differences between virtue epistemologists and Duhem. In the light of this reconstruction of good sense, I will propose a possible way to interpret the concept of good sense, which overcomes the noted problems and fits better with Duhem’s views on scientific method and motivation in developing the concept of good sense. (shrink)

In his response to my, Ian Kidd claims that my argument against Stump’s interpretation of Duhem’s concept of ‘good sense’ is unsound because it ignores an important distinction within virtue epistemology. In light of the distinction between reliabilist and responsibilist virtue epistemology, Kidd argues that Duhem can be seen as supporting the latter, which he further illustrates with a discussion of Duhem’s argument against ‘perfect theory’. I argue that no substantive argument is offered to show that the distinction is relevant (...) and can establish that Duhem’s ‘good sense’ can be understood within responsibilist virtue epistemology. I furthermore demonstrate that Kidd’s attempt to support his contention relies on a crucial misreading of Duhem’s general philosophy of science, and in doing so highlight the importance of understanding ‘good sense’ in its original context, that of theory choice. (shrink)

What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, and ‘beautiful’? By applying empirical methods developed by social psychologists, we demonstrate that mathematicians' appraisals of proofs vary on four dimensions: aesthetics, intricacy, utility, and precision. We pay particular attention to mathematical beauty and show that, contrary to the classical view, beauty and simplicity are almost entirely unrelated in mathematics.

Fricker shows that virtue epistemology provides a general epistemological idiom in which these issues can be forcefully discussed.

This classic work in the philosophy of physical science is an incisive and readable account of the scientific method. Pierre Duhem was one of the great figures in French science, a devoted teacher, and a distinguished scholar of the history and philosophy of science. This book represents his most mature thought on a wide range of topics.

G.H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician... the purest of the pure'. He was also, as C.P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it (...) was like to be a creative artist'. C.P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his idiosyncrasies and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times. (shrink)

A compact, coherent introduction to the study of rational belief, this text provides points of entry to such areas of philosophy as theory of knowledge, methodology of science, and philosophy of language. The book is accessible to all undergraduates and presupposes no philosophical training.

To find "criteria of simplicity" was the goal of David Hilbert's recently discovered twenty-fourth problem on his renowned list of open problems given at the 1900 International Congress of Mathematicians in Paris. At the same time, simplicity and economy of means are powerful impulses in the creation of artworks. This was an inspiration for a conference, titled the same as this volume, that took place at the Graduate Center of the City University of New York in April of 2013. This (...) volume includes selected lectures presented at the conference, and additional contributions offering diverse perspectives from art and architecture, the philosophy and history of mathematics, and current mathematical practice. (shrink)

In the era of information and communication, issues of misinformation and miscommunication are more pressing than ever. _Epistemic injustice - _one of the most important and ground-breaking subjects to have emerged in philosophy in recent years - refers to those forms of unfair treatment that relate to issues of knowledge, understanding, and participation in communicative practices. The Routledge Handbook of Epistemic Injustice is an outstanding reference source to the key topics, problems and debates in this exciting subject. The first collection (...) of its kind, it comprises over thirty chapters by a team of international contributors, divided into five parts: Core Concepts Liberatory Epistemologies and Axes of Oppression Schools of Thought and Subfields within Epistemology Socio-political, Ethical, and Psychological Dimensions of Knowing Case Studies of Epistemic Injustice. As well as fundamental topics such as testimonial and hermeneutic injustice and epistemic trust, the Handbook includes chapters on important issues such as social and virtue epistemology, objectivity and objectification, implicit bias, and gender and race. Also included are chapters on areas in applied ethics and philosophy, such as law, education, and healthcare. The Routledge Handbook of Epistemic Injustice is essential reading for students and researchers in ethics, epistemology, political philosophy, feminist theory, and philosophy of race. It will also be very useful for those in related fields, such as cultural studies, sociology, education and law. (shrink)

Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. For nearly a century, the axioms of set theory have played this role, so the question of how these axioms are properly judged takes on a central importance. Approaching the question from a broadly naturalistic or second-philosophical point of view, Defending the Axioms isolates the appropriate methods for such evaluations and investigates the ontological and epistemological backdrop that makes them appropriate. In the end, a new account of (...) the objectivity of mathematics emerges, one refreshingly free of metaphysical commitments. (shrink)