Anyone who has pondered the limitlessness of space and time, or the endlessness of numbers, or the perfection of God will recognize the special fascination of this question. Adrian Moore's historical study of the infinite covers all its aspects, from the mathematical to the mystical.

Philosophy of science in the twentieth century tends to emphasize either the logic of science (e.g., Popper and Hempel on explanation, confirmation, etc.) or its history/sociology (e.g., Kuhn on revolutions, holism, etc.). This dichotomy, however, is neither exhaustive nor exclusive. Questions regarding scientific understanding and mathematical explanation do not fit neatly inside either category, and addressing them has drawn from both logic and history. Additionally, interest in scientific and mathematical practice has led to work that falls between the two sides (...) of the dichotomy. We might call these less narrow approaches ‘holistic’. Prior to 1918, work in the philosophy of science was also somewhat more holistic and interdisciplinary in nature. An exemplar of this type of approach is found in the work of Henri Poincaré. In this paper I will consider one particularly flexible tool Poincaré uses throughout his philosophical writings about science and mathematics: the tool of the unifying concept. More specifically, I will focus on one unifying concept: that of structure. I aim to show first, that structure is a unifying scientific concept for Poincaré; second, a focus on structure helps explain his scientific and mathematical success; lastly, this case study may provide a model for how unifying concepts can facilitate progress in mathematics and science. (shrink)

The mathematical developments of the 19th century seemed to undermine Kant’s philosophy. Non-Euclidean geometries challenged Kant’s view that there is a spatial intuition rich enough to yield the truth of Euclidean geometry. Similarly, advancements in algebra challenged the view that temporal intuition provides a foundation for both it and arithmetic. Mathematics seemed increasingly detached from experience as well as its form; moreover, with advances in symbolic logic, mathematical inference also seemed independent of intuition. This paper considers various philosophical responses to (...) these changes, focusing on the idea of modifying Kant’s conception of intuition in order to accommodate the increasing abstractness of mathematics. It is argued that far from clinging to an outdated paradigm, programs based on new conceptions of intuition should be seen as motivated by important philosophical desiderata, such as the truth, apriority, distinctiveness and autonomy of mathematics. (shrink)

Though logical positivism is part of Kant's complex legacy, positivists rejected both Kant's theory of intuition and his classification of mathematical knowledge as synthetic a priori. This paper considers some lingering defenses of intuition in mathematics during the early part of the twentieth century, as logical positivism was born. In particular, it focuses on the difficult and changing views of Hermann Weyl about the proper role of intuition in mathematics. I argue that it was not intuition in general, but his (...) commitment to twodifferent types of intuition, which explains his rather unusual and tormented philosophy of the mathematical continuum. I would like to thank Geoff Gorham, David McCarty, and Rosamond Rodman for reading an earlier draft of this work. I should also thank those who provided helpful comments on several distant ancestors of this paper: Emily Carson, Ulrich Majer, Erhard Scholz, John Schuerman, Stewart Shapiro, and Richard Tieszen. I am indebted to two anonymous referees for pointing out some problems and for pointing me to work on Weyl I did not previously know about. In particular, the recent articles in [Feist, 2004a] turned out to be (somewhat uncomfortably) relevant to the focus of this paper. In this last revision I have tried to show where I agree and disagree with the authors of those papers; I apologize for whatever repetition still exists, but it was tere before I read those papers. This paper has a long history, and comes out of several talks I gave some years ago. Audiences at the Center for Philosophy of Science, University of Pittsburgh (colloquium 1995), St Andrews University Philosophy of Mathematics Workshop (1996), the British Society for the History of Mathematics meeting (1996), the University of Mainz Mathematics Department (colloquium 1996), the Canadian Philosophical Association (1997 and 1999), and the University of British Columbia (colloquium 1998) should be thanked for their helpful comments. I also thank Neil Tennant for encouraging me to resurrect this work. CiteULike Connotea Del.icio.us What's this? (shrink)

Although it is clear that Sir William Rowan Hamilton supported a Kantian account of algebra, I argue that there is an important sense in which Hamilton's philosophy of mathematics can be situated in the Newtonian tradition. Drawing from both Niccolo Guicciardini's (2009) and Stephen Gaukroger's (2010) readings of the Newton–Leibniz controversy over the calculus, I aim to show that the very epistemic ideals that underpin Newton's argument for the superiority of geometry over algebra also motivate Hamilton's philosophy of algebra. Namely, (...) Hamilton's defense of algebra, like Newton's defense of geometry, is driven by the claim that a mathematical science must have a proper object and thus a basis in truth. In particular, Hamilton aims to show that algebra is not a mere language, or tool, or a mere “art”; instead, he argues, algebra is a bona fide mathematical science, like geometry, because its methods also provide true and accurate insight into a genuine subject matter, namely, the pure form of temporal intuition. (shrink)

There is a basic division in the philosophy of mathematics between realist, ‘platonist’ theories and anti-realist ‘constructivist’ theories. Platonism explains how mathematical truth is strongly objective, but it does this at the cost of invoking mind-independent mathematical objects. In contrast, constructivism avoids mind-independent mathematical objects, but the cost tends to be a weakened conception of mathematical truth. Neither alternative seems ideal. The purpose of this paper is to show that in the philosophical writings of Henri Poincaré there is a coherent (...) argument for an interesting position between the two traditional poles in the philosophy of mathematics. Relying on a semi-Kantian framework, Poincaré combines an epistemological and metaphysical constructivism with a more realist account of the nature of mathematical truth. (shrink)

In his first philosophy book, Science and Hypothesis, Poincare provides a picture in which the different sciences are arranged in a hierarchy. Arithmetic is the most general of all the sciences because it is presupposed by all the others. Next comes mathematical magnitude, or the analysis of the continuum, which presupposes arithmetic; and so on. Poincare's basic view was that experiment in science depends on fixing other concepts first. More generally, certain concepts must be fixed before others: hence the hierarchy. (...) This paper attempts to dissolve some potential problems regarding Poincare's hierarchy. One is an apparent epistemological circularity in the hierarchy. A more serious problem regarding the epistemology of analysis is also addressed. (shrink)

The primary concern of this thesis is to investigate the explicit philosophy of mathematics in the work of Henri Poincare. In particular, I argue that there is a well-founded doctrine which grounds both Poincare's negative thesis, which is based on constructivist sentiments, and his positive thesis, via which he retains a classical conception of the mathematical continuum. The doctrine which does so is one which is founded on the Kantian theory of synthetic a priori intuition. I begin, therefore, by outlining (...) Kant's theory of the synthetic a priori, especially as it applies to mathematics. Then, in the main body of the thesis, I explain how the various central aspects of Poincare's philosophy of mathematics - e.g. his theory of induction; his theory of the continuum; his views on impredicativiti his theory of meaning - must, in general, be seen as an adaptation of Kant's position. My conclusion is that not only is there a well-founded philosophical core to Poincare's philosophy, but also that such a core provides a viable alternative in contemporary debates in the philosophy of mathematics. That is, Poincare's theory, which is secured by his doctrine of a priori intuitions, and which describes a position in between the two extremes of an "anti-realist" strict constructivism and a "realist" axiomatic set theory, may indeed be true. (shrink)

There are several distinct components of the realist anti-realist debate. Since each side in the debate has its disadvantages, it is tempting to try to combine realist theses with anti-realist theses in order to obtain a better, more moderate position. Putnam attempts to hold a realist concept of truth, yet he rejects realist metaphysics and realist semantics. He calls this view internal realism. Truth is realist on this picture for it is objective, rather than merely intersubjective, and eternal. Putnam introduces (...) a concept of epistemic idealization — epistemically ideal conditions, or idealized justification — to try to ground the strong objectivity of truth without sliding into metaphysical realism. I argue that the concept of ideal conditions to which Putnam appeals does not cohere with his (anti-realist) commitment to an assertability conditions account of meaning. (shrink)

Fundamentals -- Beginning-of-life issues -- Reproductive technologies -- Contraception, sterilization, and natural family planning -- End-of-life issues -- Cooperation with evil -- Respect for the body -- The ten commandments for health care professionals and patients.

An introduction to the new area of ignorance studies that examines how science produces ignorance—both actively and passively, intentionally and unintentionally. We may think of science as our foremost producer of knowledge, but for the past decade, science has also been studied as an important source of ignorance. The historian of science Robert Proctor has coined the term agnotology to refer to the study of ignorance, and much of the ignorance studied in this new area is produced by science. Whether (...) an active or passive construct, intended or unintended, this ignorance is, in Proctor's words, “made, maintained, and manipulated” by science. This volume examines forms of scientific ignorance and their consequences. A dialogue between Proctor and Peter Galison offers historical context, presenting the concerns and motivations of pioneers in the field. Essays by leading historians and philosophers of science examine the active construction of ignorance by biased design and interpretation of experiments and empirical studies, as seen in the “false advertising” by climate change deniers; the “virtuous” construction of ignorance—for example, by curtailing research on race- and gender-related cognitive differences; and ignorance as the unintended by-product of choices made in the research process, when rules, incentives, and methods encourage an emphasis on the beneficial and commercial effects of industrial chemicals, and when certain concepts and even certain groups' interests are inaccessible in a given conceptual framework. Contributors Martin Carrier, Carl F. Cranor, Peter Galison, Paul Hoyningen-Huene, Philip Kitcher, Janet Kourany, Hugh Lacey, Robert Proctor, Londa Schiebinger, Miriam Solomon, Torsten Wilholt. (shrink)

This book challenges the World Medical Associationâ (TM)s (WMA) International Code of Ethics statement in 2004, which declared that â ~medical ethics in armed conflict is identical to medical ethics in times of peaceâ (TM). This is achieved by examining the professional, ethical, and legal conflicts in British Military healthcare practice that occur in three distinct military environments. These are (i) the battlefield, (ii) the operational environment and (iii) the non-operational environment. As this conflict is exacerbated by the need to (...) achieve Operational Effectiveness, this book also explores the dual loyalty conflict that Military Health Care Professionals (MHCPs) encounter between following military orders and professional codes of practice. The method used to challenge the WMAâ (TM)s statement and explore these conflicts is the use of real-life problem-solving vignettes, which mirror actual ethical and professional conflicts and dilemmas that may occur in the three environments. The areas of law analysed similarly reflect the difficulties that MHCPs face when caring for the sick and wounded in violent locations when under attack. In particular, the book questions whether it is right for a MHCP to owe their patients a duty of care in hostile environments. This leads on to questioning if any MHCP could be protected by combat immunity where no duty of care is owed to fellow soldiers in the battlefield. The book also questions whether the standard of care should be variable in hostile environments. It also explores the dual loyalty conflict of a wounded senior officer refusing treatment from a junior officer. In addition, it examines the difficulties of a doctor maintaining patient confidentiality when a soldier refuses treatment for a psychological injury but wishes to redeploy to the battlefield. The book successfully challenges the WMAâ (TM)s statement. It also concludes by suggesting that neither a military-focused approach nor a professional healthcare-focused approach towards military healthcare is the best way to solve the dual loyalty conflict. (shrink)

Critical Practice: Artists, Museums, Ethics is an ambitious work that blurs the boundaries among art history, museum studies, political science and applied ethics. It takes an interdisciplinary approach to represent key developments in institutional critique as they impact museums. The book elucidates the museological and ethical implications of institutional critique, providing a much needed resource for museum studies scholars, artists, museum professionals, art historians and graduate students worldwide who are interested in mapping and unpacking the intricate relationships among artists, museums (...) and communities. It argues that institutional critique is, at heart, a museological enterprise committed to creating reconciliations between museums and their publics. The volume will show how artists are uniquely positioned as both museum insiders and outsiders to encourage reconciliation. Critical Practice demonstrates how and why museums are drawn to institutional critique as reconciliation at pivotal moments in institutional and social history. By analyzing an international group of case studies, charting their attempts at reconciling museums and communities, it identifies key issues that institutional critique interrogates. In so doing, the book illuminates both the collaborative and contentious possibilities of these projects. Critical Practice is the first book on institutional critique informed by current debates in museum ethics and brings together a diverse range of literature to make it an invaluable resource for students of Museum Studies and Art and Gallery Studies. (shrink)

Foreword by Robert H. Bork -- Culture wars -- A distorted understanding of rights -- The right to privacy -- Griswold and contraception -- Roe and abortion -- Assisted suicide and homosexuality -- Political connections and natural consequences.

A great quantity of American plants traveled with the precious metals that arrived in Europe from New Spain after ‘1492. Some were brought over intentionally, perhaps in the hands of some Spanish Indian (Spaniards who had travelled to the New World to make their fortunes and had returned were called “Indians”) who had become accustomed to new tastes in America. Others arrived by neither will nor invitation, hidden in the nooks and crannies of the ships or mixed in with the (...) ballast that the galleons carried on their return trip to the Old World. (shrink)

With this paper, from the perspective of ethics at the workplace, we problematize the taken-for-granted assumptions embedded in the use of artistic freedom in creative processes. Drawing on the notion of inequality regimes (e.g. Acker, 2006) and using empirical material from a performing arts organization in Sweden, we explore how the assumptions of artistic freedom facilitate and legitimize the emergence of inequality regimes in invisible and subtle manners. Our findings indicate that non-reflexive interpretations of the concept of artistic freedom result (...) in ethical dilemmas that impact the organization's pursuits of equality work. The aesthetic ethics oriented around the notion of ‘art for the sake of art’ tends to camouflage the centralization of aesthetic authority in processes where formal hierarchical structures are missing. Consequently, asymmetrical power relations between the Directors, actors, and producers are legitimized. Ethics of quality of art and that of the social ideal of equality have been constructed as dichotomic notions indicating that aesthetic ethics of art can only be preserved at the expense of social objectives of equality. We argue that the current interpretative practices of ‘artistic freedom’ in some cultural organizations add little value of ethics to the freedom of expressing artistic opinions and in achieving the social ideal of equality but lead to the emergence of inequality regimes in the artistic work processes. (shrink)

In his target article, Neil Levy (2011) challenges the standard philosophical practice of taking a person's judgments about whether someone acts morally in particular (actual or imaginary) situatio...

A feminist primer for philosophers of science -- The legacy of twentieth century philosophy of science -- What feminist science studies can offer -- Challenges from every direction -- The prospects of twenty-first century philosophy of science.

This collection of contributions from both linguists and lawyers brings a pragmatic perspective to the linguistic basis for legal meaning and for finding a norm by which to decide a case. That is, it turns from notions of linguistic meaning as residing in the text, as literal meaning waiting to be dug out, to focus instead on how readers infer pragmatic meaning, and on the kinds of inferencing that characterise legal discourse.

This core adoptable text provides a comprehensive overview of the challenges facing organisations as they pursue global business activities. Ethics in business has grown to be of increasing importance in the world of today, as companies have been placed in the moral spotlight by shareholders, consumers, employees and governments. The growing complexities of the global economy demand a broader and a deeper view of business ethics than that offered by current management approaches that focus on reforming corporate behaviour. Business Ethics (...) places business ethics in a richer contextual setting, focusing on the challenges that businesses must now confront, and exploring how these issues can be met by a rethinking of business models, goals and strategies. Business Ethics is the ideal textbook for students taking business ethics modules at undergraduate, postgraduate and MBA levels. (shrink)

What do we know of the wife and child the Buddha abandoned when he went off to seek his enlightenment? For the first time, The Buddha's Wife brings this rarely told story to the forefront, offering a nuanced portrait of this compelling and compassionate figure while also examining the practical applications her teachings have on our modern lives. Princess Yasodhara's journey is one full of loss, grief, and suffering. But through it, she discovered her own enlightenment within the deep bonds (...) of community and "ordinary" relationships. While traditional Buddhism emphasizes solitary mediation, Yasodhara's experience speaks of the Path of Right Relation, of achieving awareness not alone but together with others. The Buddha's Wife is comprised of two parts: the first part is a historical narrative of Yasodhara's fascinating story, and then the second part is a reader's companion filled with life lessons, practices, and reflections for the modern reader. Her story gives readers a relational path, one which speaks directly to our everyday lives and offers a doorway to profound spiritual maturation, awakening, and wisdom beyond the solitary, heroic journey. (shrink)

The Quicksands of Belief: The Need for Skepticism draws on history, anthropology, sociology, philosophy, and the cognitive sciences in an accessible, non-academic style in order to argue that humans don't question enough. The claim of this book is that humans need to question everything they think they know.