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 It is argued that far from clinging to an outdated paradigm, programs based on new conceptions of intuition should be seen as motivated by important philosophical desiderata, such as the truth, apriority,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)

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 (as most of these works have been housed in our most important libraries around the world), 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 (individual or corporate) 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)

Crisis demands -- Crisis narratives -- Crisis: refrain!

This collection is about how law makes meaning and how meaning makes law. Through clear methodology and substantial findings, chapters expose the deficits of 'literal' meaning and the difficulties in 'ordinary' meaning, in international legal contexts and in more immediate social ones, as well as in courtrooms. Further, chapters in this volume see the challenges to national and international commitments to all speakers sharing a common meaning.

This chapter contains section titled: Introduction Hume's Naturalism Hume's Skepticism The Relation between Hume's Naturalism and His Skepticism Skepticism and Naturalism after the Treatise References Further Reading.

Self-injury is a perilous and increasingly common behavior that is particularly prevalent among youth. Nonetheless, there is a deep-rooted public stigma towards people who self-injure. Consequently, people who engage in self-injury are reluctant to seek professional help or disclose their experiences to others. This article aims to combat stigma and promote help-seeking behavior by debunking the common myths surrounding self-injury in the Malaysian context. Specifically, this article aims to serve as an eye-opener for Malaysian counselors and other mental health professionals (...) to improve their multicultural knowledge, skills, and attitudes when working with those who self-injure. (shrink)

This article examines three films made during the 1950s by Elwyn James Anthony at the psychotic clinic for children at the Maudsley Hospital that marked an important transition in the purpose and practice of visual documentation in a clinical setting: film as a research tool was transitioning from the recording of external signs as indicators of internal subjective states, to the capture of the visual flow of communication between subjects. It is a shift that had a particular impact on the (...) emergent classification of autism, a modality not yet properly separated from the broader term of psychosis, as a non-relational condition whose visual capture demonstrated a void of inter-human communicational exchange. Film was significant not only as a recording apparatus, but as a method of cutting and crafting sequences of movements into brief repetitive motifs. The filmed behaviour of children remained opaque to interpretation, a ‘finding’ that facilitated the modelling of an emergent autism as subjects who were isolated, alienated and automaton-like, inhabiting a separate temporality. The article situates this ‘second’, affectless autism, within a broader context of post-war research into gestures as a language of the body, developed largely through an intellectual network of German émigré psychoanalysts who had fled to the US and UK in the 1930s. (shrink)

Introduction -- Girls and other incomplete things: on archaeological method -- Gesture: cinema muto mutato -- Dim stockings and pornography: community, spectacle and the example -- Cinema as laboratory: on insects and the anthropological machine -- When the assistants profane cinema -- Ex-centric cinema.

This enlightening text analyses the origins of Western complaints, prevalent in the late nineteenth century, that Japan was characterised at the time by exceptionally low standards of ‘commercial morality’, despite a major political and economic transformation. As Britain industrialised during the nineteenth century the issue of ‘commercial morality’ was increasingly debated. Concerns about standards of business ethics extended to other industrialising economies, such as the United States. Hunter examines the Japanese response to the charges levelled against Japan in this context, (...) arguing that this was shaped by a pragmatic recognition that Japan had little choice but to adapt itself to Western expectations if it was to establish its position in the global economy. The controversy and criticisms, which were at least in part stimulated by fear of Japanese competition, are important in the history of thinking on business ethics, and are of relevance for today’s industrialising economies as they attempt to establish themselves in international markets. (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)

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.

This study investigated effects of codes of ethics on perceptions of ethical behavior. Respondents from companies with codes of ethics (n = 465) rated role set members (top management, supervisors, peers, subordinates, self) as more ethical and felt more encouraged and supported for ethical behavior than respondents from companies without codes (n = 301). Key aspects of the organizational climate, such as supportiveness for ethical behavior, freedom to act ethically, and satisfaction with the outcome of ethical problems were impacted by (...) the presence of an ethics code. The mere presence of a code of ethics appears to have a positive impact on perceptions of ethical behavior in organizations, even when respondents cannot recall specific content of the code. (shrink)

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 study investigated effects of codes of ethics on perceptions of ethical behavior. Respondents from companies with codes of ethics (n = 465) rated role set members (top management, supervisors, peers, subordinates, self) as more ethical and felt more encouraged and supported for ethical behavior than respondents from companies without codes (n = 301). Key aspects of the organizational climate, such as supportiveness for ethical behavior, freedom to act ethically, and satisfaction with the outcome of ethical problems were impacted by (...) the presence of an ethics code. The mere presence of a code of ethics appears to have a positive impact on perceptions of ethical behavior in organizations, even when respondents cannot recall specific content of the code. (shrink)