We perceive smells as perduring complex entities within a distal array that might be conceived of as smellscapes. However, the philosophical orthodoxy of Odor Theories has been to deny that smells are perceived as having a distal location. Recent challenges have been mounted to Odor Theories’ veracity in handling the timescale of olfactory perception, how it individuates odors as a distal entities, and their claim that olfactory perception is not spatial. The paper does not aim to dispute these criticisms. Rather, (...) what will be shown is that Molecular Structure Theory, a refinement of Odor Theory, can be further developed to handle these challenges. The theory is further refined by focusing on distal perception that requires considering the perceptual object as mereologically complex persisting odor against a background scene conceived of as a smellscape. What will be offered is an expansion of Molecular Structure Theory to account for distal smell perception within natural environments. (shrink)

Capital punishment—the legally authorized killing of a criminal offender by an agent of the state for the commission of a crime—stands in special need of moral justification. This is because execution is a particularly severe punishment. Execution is different in kind from monetary and custodial penalties in an obvious way: execution causes the death of an offender. While fines and incarceration set back some of one’s interests, death eliminates the possibility of setting and pursuing ends. While fines and incarceration narrow (...) one’s routes to happiness, death eliminates its possibility. Not surprisingly, there is much debate about the moral permissibility of capital punishment. This entry maps the terrain of this debate. The first section discusses justifications of the death penalty as they appear in major theories of punishment. The second section surveys moral objections to execution that apply to most justifications. The third addresses procedural criticisms, which do not target the morality of execution so much as the justice of its implementation. (shrink)

ABSTRACTIn this paper I investigate how conceptual engineering applies to mathematical concepts in particular. I begin with a discussion of Waismann’s notion of open texture, and compare it to Shapiro’s modern usage of the term. Next I set out the position taken by Lakatos which sees mathematical concepts as dynamic and open to improvement and development, arguing that Waismann’s open texture applies to mathematical concepts too. With the perspective of mathematics as open-textured, I make the case that this allows us (...) to deploy the tools of conceptual engineering in mathematics. I will examine Cappelen’s recent argument that there are no conceptual safe spaces and consider whether mathematics constitutes a counterexample. I argue that it does not, drawing on Haslanger’s distinction between manifest and operative concepts, and applying this in a novel way to set-theoretic foundations. I then set out some of the questions that need to be engaged with to establish mathematics as involving a kind of conceptual engineering. I finish with a case study of how the tools of conceptual engineering will give us a way to progress in the debate between advocates of the Universe view and the Multiverse view in set theory. (shrink)

Derivationists, those wishing to explain the correctness and rigour of informal proofs in terms of associated formal proofs, are generally held to be supported by the success of the project of translating informal proofs into computer-checkable formal counterparts. I argue, however, that this project is a false friend for the derivationists because there are too many different associated formal proofs for each informal proof, leading to a serious worry of overgeneration. I press this worry primarily against Azzouni's derivation-indicator account, but (...) conclude that overgeneration is a major obstacle to a successful account of informal proofs in this direction. (shrink)

Adult number representations can belong to either of two types. One is discrete, language-specific, and culturally-derived; the other is analog and language-independent. Quantitative evidence is presented to demonstrate that analog number representations are adult-like in young children. Five- to 7-year-olds accurately estimated rapidly presented groups of 5--11 items. Groups were presented in random order and random arrangements controlling for overall area. Children's data were qualitatively, and to some degree quantitatively, similar to adult data with one exception: the ratio of the (...) standard deviation of estimates to mean estimates decreased with age. (shrink)

We are immersed within an odorous sea of chemical currents that we parse into individual odors with complex structures. Odors have been posited as determined by the structural relation between the molecules that compose the chemical compounds and their interactions with the receptor site. But, naturally occurring smells are parsed from gaseous odor plumes. To give a comprehensive account of the nature of odors the chemosciences must account for these large distributed entities as well. We offer a focused review of (...) what is known about the perception of odor plumes for olfactory navigation and tracking, which we then connect to what is known about the role odorants play as properties of the plume in determining odor identity with respect to odor quality. We end by motivating our central claim that more research needs to be conducted on the role that odorants play within the odor plume in determining odor identity. (shrink)

What sorts of epistemic virtues are required for effective mathematical practice? Should these be virtues of individual or collective agents? What sorts of corresponding epistemic vices might interfere with mathematical practice? How do these virtues and vices of mathematics relate to the virtue-theoretic terminology used by philosophers? We engage in these foundational questions, and explore how the richness of mathematical practices is enhanced by thinking in terms of virtues and vices, and how the philosophical picture is challenged by the complexity (...) of the case of mathematics. For example, within different social and interpersonal conditions, a trait often classified as a vice might be epistemically productive and vice versa. We illustrate that this occurs in mathematics by discussing Gerovitch’s historical study of the aggressive adversarialism of the Gelfand seminar in post-war Moscow. From this we conclude that virtue epistemologies of mathematics should avoid pre-emptive judgments about the sorts of epistemic character traits that ought to be promoted and criticised. (shrink)

This thesis is about the nature of proofs in mathematics as it is practiced, contrasting the informal proofs found in practice with formal proofs in formal systems. In the first chapter I present a new argument against the Formalist-Reductionist view that informal proofs are justified as rigorous and correct by corresponding to formal counterparts. The second chapter builds on this to reject arguments from Gödel's paradox and incompleteness theorems to the claim that mathematics is inherently inconsistent, basing my objections on (...) the complexities of the process of formalisation. Chapter 3 looks into the relationship between proofs and the development of the mathematical concepts that feature in them. I deploy Waismann's notion of open texture in the case of mathematical concepts, and discuss both Lakatos and Kneebone's dialectical philosophies of mathematics. I then argue that we can apply work from conceptual engineering to the relationship between formal and informal mathematics. The fourth chapter argues for the importance of mathematical knowledge-how and emphasises the primary role of the activity of proving in securing mathematical knowledge. In the final chapter I develop an account of mathematical knowledge based on virtue epistemology, which I argue provides a better view of proofs and mathematical rigour. (shrink)

Extinction is a concept of rapidly growing importance, with the world currently in the sixth mass extinction event and a biodiversity crisis. However, the concept of extinction has itself received surprisingly little attention from philosophers. I will first argue that in practice there is no single unified concept of extinction, but instead that its usage divides between descriptive, epistemic, and declarative concepts. I will then consider the epistemic challenges that arise in ascertaining whether a species has gone extinct, and how (...) these lead to serious limitations on responsibility and accountability for preventing extinctions. I will propose two conceptual engineering changes to our understanding of extinction. Firstly, to use twin epistemic concepts of extinction, corresponding to high and low epistemic demands. Secondly, to explicitly recognize that in many contexts extinction is a thick concept that contains an evaluative component, which therefore motivates explicit ethical considerations such as the use of precautionary principles. (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)

In this paper, I lay out a case for why those objects of aesthetic attention which are principally characterized as natural objects should be understood not statically, as existing in merely a three-dimensional fixed state, but as dynamic, as existing in a space-time context, complete with change, movement, and flux. After this, I explain why this is important, how the dynamic nature of natural objects raises a concern for aesthetically evaluating natural objects, and how that concern may be addressed.

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.1 (2003) 40-53 [Access article in PDF] Aesthetic Experience and Aesthetic Analysis David E. W. Fenner The "raw data" that aesthetics is meant to explain is the aesthetic experience. People have experiences that they class off from other experiences and label, as a class, the aesthetic ones. Aesthetic experience is basic, and allother things aesthetic — aesthetic properties, aesthetic objects, aesthetic attitudes — (...) are secondary in their importance to aesthetic experiences. 1Considering aesthetic experience as the raw data that philosophical aesthetics seeks to explain is a relatively recent phenomenon. This was certainly not the focus in the seventeenth and eighteenth centuries. Aesthetic judgment was the focus of Shaftesbury, Hutcheson, Hume, and Kant: "How do we make meaningful judgments (hopefully real ones) about the aesthetic quality of (certain) objects and events?" But with George Santayana, John Dewey, and Jerome Stolnitz, the focus changes. Now the interest is in the aesthetic experience: what makes those experiences we label "aesthetic" special? Why do we separate those experiences from others?The movement from the Taste Theories to those focused on aesthetic experience is not a movement that is over and done with — far from it. There is still (and I think there will always be) a tension between these two very basic aspects of philosophical aesthetics. And, although I claim that aesthetic experience is the most basic thing that aesthetics studies, I recognize that this is challengeable and only true from a certain temporal viewpoint.I recently taught the most rewarding undergraduate course in aesthetics. The reason that it was so rewarding was that the students carried the class with deep and insightful discussions, and they were not shy about challenging what was coming out of my mouth. One of the challenges that informed our entire semester focused on the tension between experience and judgment. I lectured comfortably about aesthetic experience as our "raw data," and I lectured equally comfortably about how taking an aesthetic view of an object or event meant focusing primarily, if not exclusively, on [End Page 40] what is available to us through simple sensory acquaintanceship with the object. "Aesthetics," I said, "is about the sensuous aspects of our experiences." And so we could, for instance, take an aesthetic view of a Robert Mapplethorpe photograph which precluded our experiences being mired in the themes that the more famous Mapplethorpe photos take as their content. "Mapplethorpe is a great photographer," I argued, "and one can see this if one is willing to focus strictly on what meets your eye when you look at the picture." In short, I held the position that the aesthetic view is the formal one.Without saying more, what I did was conflate two different things. On the one hand, I argued that aesthetic experience is a natural part of life that aesthetics seeks to explore. On the other, I argued that appreciating something aesthetically was to appreciate its formal qualities, those qualities that one could access simply through looking, hearing, touching, for example. But these really are two different things.Aesthetic experiences, if we are to treat them as "raw data," must be explored without pre-conception, prejudice, or limitation. And, truly enough, the vast majority of aesthetic experiences are not focused exclusively, in terms of their contents, on formal or simple-sensory matters. Aesthetic experiences are, first, experiences. They are complex things, having to do with things as tidy as the formal qualities of the object under consideration and with things as messy as whether one had enough sleep the night before, whether one just had a fight with his roommate, whether one is carrying psychological baggage that is brought to consciousness by this particular aesthetic object. Later in this essay, I want to explore some of this complexity.The other side of what was happening in my class, the formal focus on the sensory as the basis for an aesthetic viewing, is not the substance of "aesthetic experience" per se. It is rather the basis of what we might call "aesthetic analysis." Aesthetic analysis has to do with separating out from our... (shrink)

In this paper I shall consider two related avenues of argument that have been used to make the case for the inconsistency of mathematics: firstly, Gödel’s paradox which leads to a contradiction within mathematics and, secondly, the incompatibility of completeness and consistency established by Gödel’s incompleteness theorems. By bringing in considerations from the philosophy of mathematical practice on informal proofs, I suggest that we should add to the two axes of completeness and consistency a third axis of formality and informality. (...) I use this perspective to respond to the arguments for the inconsistency of mathematics made by Beall and Priest, presenting problems with the assumptions needed concerning formalisation, the unity of informal mathematics and the relation between the formal and informal. (shrink)

In this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of surprising and unusual features of this collaborative endeavour that set it apart from smaller-scale pieces of mathematics. These features raise a number of interesting philosophical issues, but have received very little (...) attention. In this paper, we will consider the philosophical tensions that Steingart uncovers, and use them to argue that the best account of the epistemic status of the Classification Theorem will be essentially and ineliminably social. This forms part of the broader argument that in order to understand mathematical proofs, we must appreciate their social aspects. (shrink)

A set A is m-reducible to B if and only if there is a polynomial-time computable function f such that, for all x, x∈ A if and only if f ∈ B. Two sets are: 1-equivalent if and only if each is m-reducible to the other by one-one reductions; p-invertible equivalent if and only if each is m-reducible to the other by one-one, polynomial-time invertible reductions; and p-isomorphic if and only if there is an m-reduction from one set to the (...) other that is one-one, onto, and polynomial-time invertible. In this paper we show the following characterization. Theorem The following are equivalent: P = PSPACE. Every two 1-equivalent sets are p-isomorphic. Every two p-invertible equivalent sets are p-isomorphic. (shrink)

Speculatively, it is suggested that variola virus, the cause of smallpox, evolved from an orthopoxvirus of animals of the central African rain forests (possibly now represented by Tatera poxvirus), some thousands of years ago, and first became established as a virus specific for human beings in the dense populations of the Nile valley perhaps five thousand years ago. By the end of the first millennium of the Christian era, it had spread to all the densely populated parts of the Eurasian (...) continent and along the Mediterranean fringe of north Africa. It became established in Europe during the times of the Crusades. The great voyages of European colonization carried smallpox to the Americas and to Africa south of the Sahara. Transported across the Atlantic by Europeans and their African slaves, it played a major role in the conquest of Mexico and Peru and the European settlement of north America. Variolation, an effective preventive inoculation, was devised as early as the tenth century. In 1798 this practice was supplanted by Jenner's cowpox vaccine. In 1967, when the disease was still endemic in 31 countries and caused ten to fifteen million cases and about two million deaths annually, the World Health Organization embarked on a programme that was to see the disease eradicated globally just over ten years later, and the world was formally declared to be free of smallpox in May 1980. Smallpox is unique — a specifically human disease that emerged from some animal reservoir, spread to become a worldwide, severe and almost universal affliction, and finally underwent the reverse process to emergence, namely global eradication. (shrink)

Nietzsche distinguished between two forces in art: Apollonian, which represents order and reason, and Dionysian, which represents chaos and energy. Economists, Ward argues, have operated for too long under the assumption that their work reflects the scientific, Apollonian principals that inform physics when they simply do not apply to economics: 'constants' in economics stand in for variables, and the core scientific principles of prediction and replication are all but ignored by economists. Ward encourages economists to reintegrate the standard rigor of (...) the scientific method into their work while embracing the fact of the shape-shifting changeability of human beings. Economists can still aspire to scientific standards, as is demonstrated by the success of biology, in which there is considerable Dionysian variability. Economists must avoid the temptation to wish away dynamic complexity and diversity and must recognize, among other things, that the desire to take risks is fundamentally human. The second half of the book takes some first steps toward creating this new Dionysian Economics. (shrink)

A common description of a mathematical proof is as a logically structured sequence of assertions, beginning from accepted premises and proceeding by standard inference rules to a conclusion. Does this description match the language of proofs as mathematicians write them in their research articles? In this chapter, we use methods from corpus linguistics to look at the prevalence of imperatives and instructions in mathematical preprints from the arXiv repository. We find thirteen verbs that are used most often to form imperatives (...) in proofs, and that these show up significantly more often within proofs than in the surrounding mathematical writing. We also show that there are many more verbs used to form a diverse selection of instructions in proofs. These findings are at odds with the view of proofs as sequences of assertions. Instead, we argue in favour of the recipe model of proofs: that proofs are like recipes, giving instructions for mathematical actions to be carried out. (shrink)

LEGO and math are both about what one do with the objects. In LEGO, he/she can build sets following the instructions, or alternatively dump a whole bunch of LEGO on the floor and build whatever he/she like. In math, he/she have a similar freedom to create new things, solve problems, and play around. Geometry makes far greater use of pictures and diagrams than tends to be the case for other areas of mathematics. This chapter focuses on diagrammatic proofs as a (...) key case where proofs guide him/her through a series of actions. If one accepts the LEGO account of diagrammatic proofs then he/she has strongly sided with the geometers against Plato. The main principle of departure from Plato is to focus on mathematical activities. The same thought is meant to apply to LEGO: the particular bricks are only important insofar as they facilitate the things we can practically do with them. (shrink)

Hardly anyone disputes that discrimination can be a grave moral wrong. Yet this consensus masks fundamental disagreements about what makes something discrimination, as well as precisely why acts of discrimination are wrong. Benjamin Eidelson develops systematic answers to those two questions. He claims that discrimination is a form of differential treatment distinguished by its special connection to the differential ascription of some property to different people, and goes on to argue that what makes some cases of discrimination intrinsically wrongful (...) is that they manifest an attitude of disrespect for the personhood of those who are disfavored. He endeavors to specify what this attitude consists in, and to demonstrate how attending to its character can help us to better understand the moral dimensions of different forms of wrongful discrimination. The book concludes with an extended discussion of racial profiling in law enforcement. (shrink)

This book presents a contextual study of the life and work of the Cambridge Platonist Ralph Cudworth (1617-1688). Focusing on the theological basis of Cudworth's ethical philosophy, this book unlocks the hitherto ignored political aspect to Cudworth's ethical philosophy. Through a detailed examination of Cudworth's published works - particularly his voluminous "True intellectual system of the Universe" -, his posthumously published writings, and his 'freewill' manuscripts Benjamin Carter argues that the ethical and political arguments in Cudworth's philosophy develop out (...) of Cudworth's Trinitarian theology. Carter traces the link between Cudworth's trinitarianism and his ethical and political ideas by placing Cudworth's work in the turbulent religious and intellectual context of seventeenth-century England, and the University of Cambridge in particular. (shrink)

How is modern psychotherapy impacted when it is approached from the presence and understanding of the unconditioned mind? What happens when therapists are able to function as a sacred mirror for their clients' essential nature, reflecting back not only the contents of awarenessùthoughts, feelings and sensationsùbut awareness itself? Informed by their direct experience as well as by nondual teachings from both eastern and western wisdom traditions, the authors take a fresh look at what psychotherapy can be. These seminal essays will (...) challenge and inspire readers to approach psychotherapy in a new wayùas a potential portal for experiencing their deepest nature as free and joyful beings.Seasoned clinicians, Dan Berkow, Stephan Bodian, Dorothy Hunt, Sheila Krystal, Lynn Marie Lumiere, Richard Miller, John Prendergast, John Welwood, Jennifer Welwood and Bryan Wittine, and innovative western spiritual teachers, Adyashanti and Peter Fenner, explore critical issues at the interface of psychology and spirituality from a nondual perspective. (shrink)

An English language translation accompanies the original Greek text of Aristotle's book about the nature of the state, constitutions, revolutions, democracy, and oligarchy.

This Element looks at the contemporary debate on the nature of mathematical rigour and informal proofs as found in mathematical practice. The central argument is for rigour pluralism: that multiple different models of informal proof are good at accounting for different features and functions of the concept of rigour. To illustrate this pluralism, the Element surveys some of the main options in the literature: the 'standard view' that rigour is just formal, logical rigour; the models of proofs as arguments and (...) dialogues; the recipe model of proofs as guiding actions and activities; and the idea of mathematical rigour as an intellectual virtue. The strengths and weaknesses of each are assessed, thereby providing an accessible and empirically-informed introduction to the key issues and ideas found in the current discussion. (shrink)

While psychopathy research has been growing for decades, a relatively new area of research is corporate psychopathy. Corporate psychopaths are simply psychopaths working in organizational settings. They may be attracted to the financial, power, and status gains available in senior positions and can cause considerable damage within these roles from a manipulative interpersonal style to large-scale fraud. Based upon prior studies, we analyze psychopathy research pertaining to 23 moral emotions classified according to functional quality and target. Based upon our review, (...) we suggest that psychopaths are high in moral emotions associated with other-directed negative signals, low in self-directed negative signals, and low in other-directed positive signals. We found no empirical articles related to self-directed positive signals. This understanding of the specific moral emotion deficits of corporate psychopaths provides greater theoretical understanding and practical implications of knowing which individuals not to promote, though more research is needed on moral emotions that are faked for manipulative reasons. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps, and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may (...) freely copy and distribute this work, as no entity has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The problem of deviant causation has been a serious obstacle for causal theories of action. We suggest that attending to the problem of deviant causation reveals two related problems for causal theories. First, it threatens the reductive ambitions of causal theories of intentional action. Second, it suggests that such a theory fails to account for how the agent herself is guided by her reasons. Focusing on the second of these, we argue that the problem of guidance turns out to be (...) related to a number of other issues in the literature on action explanation, and that it is much more general: it threatens not only causal theories but any theory of action. Finally, we suggest that a certain version of the view that acting has a constitutive or formal aim can overcome this problem. (shrink)

This introduction argues for the importance of Suárez’s philosophy for historians of medieval philosophy as well as historians of early modern philosophy. It also provides synopses of each of the essays in the volume and a brief biography of Suárez, placing his life and works into some historical context.

In Testimony, Trust, and Authority, Benjamin McMyler argues that philosophers have failed to appreciate the nature and significance of our epistemic dependence ...

La Conscience malheureuse est un ouvrage majeur de la philosophie existentielle des années trente. Jeune poète et critique roumain expatrié en France en 1923, Benjamin Fondane (1898-1944) fait partie de ces auteurs hantés par l'absence de Dieu dans la culture rationaliste moderne marquée par le positivisme. D'abord proche de l'esprit subversif du dadaïsme, il identifie rapidement sa révolte par l'absurde à la démarche ironique et irrationaliste du philosophe russe émigré en France Léon Chestov. C'est l'adhésion sans conditions à sa (...) philosophie existentielle à partir de 1929 qui lui permet de déconstruire la tradition du logos issue d'Athènes. Il ne cessera dès lors de dénoncer un conflit profond entre le " réel " construit par la culture rationaliste et l'existant singulier, entre le savoir et le " non-voir " des poètes et de certains mystiques, entre Athènes et Jérusalem: ce divorce intime, c'est celui de la " conscience malheureuse ". (shrink)

Provides an insight into the ever changing boundaries between science and philosophy.

The paper deals with the notions of grounding and of existential dependence. It is shown that cases of existential dependence seem to be systematically correlated to cases of grounding and hence the question is raised what sort of tie might hold the two notions together so as to account for the observed correlation. The paper focusses on three possible ties between grounding and existential dependence: identity, definition, and grounding. A case for the definitional tie is made.

Mind &Language, Volume 35, Issue 1, Page 90-114, February 2020.

If whatever counts as merit for some purpose is unevenly distributed, a decision procedure that accurately sorts people on that basis will “pick up” and reproduce the pre-existing pattern in ways that more random, less merit-tracking procedures would not. This dynamic is an important cause for concern about the use of predictive models to allocate goods and opportunities. In this article, I distinguish two different objections that give voice to that concern in different ways. First, decision procedures may contribute to (...) future social injustice and other social ills by sustaining or aggravating patterns that undermine equality of status and opportunity. Second, the same decision procedures may wrong particular individuals by compounding prior injustices that explain those persons’ predicted or actual characteristics. I argue for the importance of the first idea and raise doubts about the second. In normative assessments and legal regulation of algorithmic decisionmaking, as in our thinking about anti-discrimination norms more broadly, a central concern ought to be the prospect of entrenching harmful and unjust patterns—quite apart from any personal wrong done to the individuals about whom predictions are made. (shrink)

It seems to be the case that when we look at a flower in the way that the scientist does, we see the flower in one way, but when we look at the flower in a way as to view it as a thing of beauty, charm, elegance, we see it in a different way; we see it as an aesthetic object. Viewing the flower in such a way as to see it, or any object, as an aesthetic object, is (...) to be in the aesthetic attitude. What this work means to do is to formulate necessary and sufficient conditions for adoption of the aesthetic attitude. ;Analytically and traditionally, the aesthetic attitude is an attitude or state-of-perceiving that is entered into by an agent which serves to make the agent receptive to the having of an aesthetic experience, and transform the object of the agent's attention from an object-in-the-world into an aesthetic object. ;The aesthetic attitude has figured prominently in aesthetics from the Enlightenment until the present. Its most important formulations are disinterestedness , Psychical Distance , Aldrich's Impressionistic Viewing, Scruton's Empiricistic Account, and the naturalistic work of John Dewey and Monroe Beardsley. I conclude that a naturalistic formulation of the aesthetic attitude is correct. (shrink)

Until recently, discussion of virtues in the philosophy of mathematics has been fleeting and fragmentary at best. But in the last few years this has begun to change. As virtue theory has grown ever more influential, not just in ethics where virtues may seem most at home, but particularly in epistemology and the philosophy of science, some philosophers have sought to push virtues out into unexpected areas, including mathematics and its philosophy. But there are some mathematicians already there, ready to (...) meet them, who have explicitly invoked virtues in discussing what is necessary for a mathematician to succeed. In both ethics and epistemology, virtue theory tends to emphasize character virtues, the acquired excellences of people. But people are not the only sort of thing whose excellences may be identified as virtues. Theoretical virtues have attracted attention in the philosophy of science as components of an account of theory choice. Within the philosophy of mathematics, and mathematics itself, attention to virtues has emerged from a variety of disparate sources. Theoretical virtues have been put forward both to analyse the practice of proof and to justify axioms; intellectual virtues have found multiple applications in the epistemology of mathematics; and ethical virtues have been offered as a basis for understanding the social utility of mathematical practice. Indeed, some authors have advocated virtue epistemology as the correct epistemology for mathematics (and perhaps even as the basis for progress in the metaphysics of mathematics). This topical collection brings together several of the researchers who have begun to study mathematical practices from a virtue perspective with the intention of consolidating and encouraging this trend. (shrink)