Extending Gödel's Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite recursion on well-founded trees.

According to the Furstenberg-Zimmer structure theorem, every measure-preserving system has a maximal distal factor, and is weak mixing relative to that factor. Furstenberg and Katznelson used this structural analysis of measure-preserving systems to provide a perspicuous proof of Szemer\'edi's theorem. Beleznay and Foreman showed that, in general, the transfinite construction of the maximal distal factor of a separable measure-preserving system can extend arbitrarily far into the countable ordinals. Here we show that the Furstenberg-Katznelson proof does not require the full strength (...) of the maximal distal factor, in the sense that the proof only depends on a combinatorial weakening of its properties. We show that this combinatorially weaker property obtains fairly low in the transfinite construction, namely, by the $\omega^{\omega^\omega}$th level. (shrink)

Cardiovascular disease (CVD) and sustained high blood glucose as prediabetes are an established comorbidity. People's experience in reconciling these long‐term conditions requires deeper appreciation if nurses are to more effectively support person‐centred care for people who have them. Our analysis explores the initial experience of people admitted to hospital with CVD who then find they also have sustained high blood glucose. Our methodology is informed by the philosophy of Gadamer and applies interpretive description to develop an interpretation of participant experiences. (...) The major theme emerging from participant interviews was the ‘invisible disequilibrium’ characterised by three subthemes: ‘losing equilibrium’, ‘becoming embattled’ and ‘evolving illness’. This study examines CVD and prediabetes in conjunction with the Gadamerian notion of the ‘whole’, as being in a social and emotional world in which illness is also a component part. We explore how participants lived within an ‘invisible disequilibrium’, with prediabetes frequently remaining unnoticed, while CVD was manifest. To identify multiple conditions and support effective intervention to manage them as part of person‐centric care, nursing practice should explore the ‘whole’ of the person's experience, value people’s knowledge as potential indicators of complex illness, thereby reducing the risk of accelerating complex illness. (shrink)

One of the most influential of the Victorian philosophers, Henry Sidgwick also made important contributions to fields such as economics, political theory and classics. A proponent of the utilitarianism of Jeremy Bentham and John Stuart Mill, which he analysed in his classic work The Methods of Ethics, he later turned to the practical side of politics in this work, published in 1891. His aim was to have a 'rational discussion of political questions in modern states', and he offers (...) a thorough examination of Victorian politics, beginning with a discussion of political theory before moving on to more concrete matters such as property and law. The later chapters discuss the function of government through themes such as procedural matters, international affairs, war, political parties, and public participation, giving a comprehensive account of both ideas about and the functioning of late-nineteenth-century government. (shrink)

Henri Poincaré was not just one of the most inventive, versatile, and productive mathematicians of all time--he was also a leading physicist who almost won a Nobel Prize for physics and a prominent philosopher of science whose fresh and surprising essays are still in print a century later. The first in-depth and comprehensive look at his many accomplishments, Henri Poincaré explores all the fields that Poincaré touched, the debates sparked by his original investigations, and how his discoveries still contribute to (...) society today. Math historian Jeremy Gray shows that Poincaré's influence was wide-ranging and permanent. His novel interpretation of non-Euclidean geometry challenged contemporary ideas about space, stirred heated discussion, and led to flourishing research. His work in topology began the modern study of the subject, recently highlighted by the successful resolution of the famous Poincaré conjecture. And Poincaré's reformulation of celestial mechanics and discovery of chaotic motion started the modern theory of dynamical systems. In physics, his insights on the Lorentz group preceded Einstein's, and he was the first to indicate that space and time might be fundamentally atomic. Poincaré the public intellectual did not shy away from scientific controversy, and he defended mathematics against the attacks of logicians such as Bertrand Russell, opposed the views of Catholic apologists, and served as an expert witness in probability for the notorious Dreyfus case that polarized France. Richly informed by letters and documents, Henri Poincaré demonstrates how one man's work revolutionized math, science, and the greater world. (shrink)

is it possible to have a first-person experience of our own agency? In nineteenth-century France, this question was subject to intense philosophical debate. The two figures primarily associated with each side of the debate were Maine de Biran and Charles Renouvier. Biran developed powerful objections to Hume's arguments that purported to prove the impossibility of the experience of one's inner causal force. These objections were the match that lit this philosophical fire, and formed the foundation of the philosophy of the (...) French spiritualist school; a school that included Félix Ravaisson, Jules Lachelier, Émile Boutroux, and Henri Bergson.1... (shrink)

author. University Professor in the School of Law, Columbia University. (From July 2006, Professor of Law, New York University.) Earlier versions of this Essay were presented at the Colloquium in Legal and Social Philosophy at University College London, at a law faculty workshop at the Hebrew University of Jerusalem, and at a constitutional law conference at Harvard Law School. I am particularly grateful to Ronald Dworkin, Ruth Gavison, and Seana Shiffrin for their formal comments on those occasions and also to (...) James Allan, Aharon Barak, Richard Bellamy, Aileen Cavanagh, Arthur Chaskalson, Michael Dorf, Richard Fallon, Charles Fried, Andrew Geddis, Stephen Guest, Ian Haney-Lopez, Alon Harel, David Heyd, Sam Issacharoff, Elena Kagan, Kenneth Keith, Michael Klarman, John Manning, Andrei Marmor, Frank Michelman, Henry Monaghan, Véronique Munoz-Dardé, John Morley, Matthew Palmer, Richard Pildes, Joseph Raz, Carol Sanger, David Wiggins, and Jo Wolff for their suggestions and criticisms. Hundreds of others have argued with me about this issue over the years: This Essay is dedicated to all of them, collegially and with thanks. (shrink)

ABSTRACT The midday demon, who attacked the solitary monk with vicious temptations – above all, that of acedia – is a conventional motif in late antique and medieval ascetic literature. At the noon hour, the demonic assault was vigorous and ranging. But medieval spiritual writers like Bernard of Clairvaux (d. 1153) and Richard of Saint Victor (d. 1173) also described noontime as the high point of mystical experience. Both notions hark back to biblical statements made in the Psalms and Song (...) of Songs and were elaborated by medieval thinkers through exegetical rumination. This paper studies the propinquity of these two notions in the symbolism and vocabulary of medieval spiritual writers, and in so doing documents the biblical and monastic contribution to unfolding ideas about melancholy. As examined in Saturn and Melancholy pathological melancholy would traditionally refer to the complex of symptoms associated with sloth and sadness that beleaguered the uprooted and antisocial ascetic. But after the introduction of the Aristotelian problem to Latin writers, a contrasting view appeared in the early thirteenth century, which held melancholy for a benediction of mystical or theophanic frenzy. This paper unmoors melancholy from its classical sources and, beginning from the ambivalence of the noonday motif, argues that the traditional literature of mystics and ascetics prepared for this remarkable shift. (shrink)

In Voir l'invisible Michel Henry applies his philosophy of autoaffection (which is both inspired by, and critical of, Husserl) to the realm of aesthetics. Henry claims that autoaffection, as non-objective experience, is essential not only to self-experience, but also to the experience of objects and their qualities. Intentionality tempts us to experience objects merely from the 'outside', but aesthetic experience returns us to the inner life of objects as a lived experience. On the basis of an examination of (...) Henry's aesthetic theory in the light of Husserl's analysis of our experience of visible objects, I conclude that revisions are required in both Husserl's and Henry's approaches: Husserl's noema must be considered to be a lived-through experience, and non-objective lived-through experience must be recognized as primordial evidence; Henry's claim that intentionality makes unreal all that it objectifies must be replaced by a recognition of the interdependence between autoaffection and heteroaffection. (shrink)

The similarities between William James’ Stream of Consciousness and Henri Bergson’s La durée réelle have often been noted. Both emphasize the fundamentally temporal nature of our conscious experience and its constant flow. However, in this article, I argue that despite surface similarities between the OP theories, they are fundamentally different. The ultimate reason for the differences between the theories is that James believed that we should reject psychological explanations that depend on synthesis within the mental sphere. This is because such (...) explanations are incompatible with empiricism. Instead, we should look to the physiological mechanisms underpinning mental states. In contrast, Bergson was an adamant defender of a form of mental processing which he called qualitative synthesis. Duration itself, for Bergson, is a form of qualitative synthesis. However, in 1906, less than five years before James died, Bergson convinced him to change his mind. This results in a huge shift in James’ thought. Unless we understand how far apart James and Bergson were prior to this shift, we will not have a proper picture of the full influence of Bergson on James’ thought, nor of the major changes to James’ philosophy that occurred near the end of his life. (shrink)

The early twentieth century was a lively time for the foundations of mathematics. This ensuing debates were, in large part, a reaction to the settheoretic and nonconstructive methods that had begun making their way into mathematical practice around the turn of the twentieth century. The controversy was exacerbated by the discovery that overly na¨ıve formulations of the fundamental principles governing the use of sets could result in contradictions. Many of the leading mathematicians of the day, including Hilbert, Henri Poincar´e, ´.

One of the most influential of the Victorian philosophers, Henry Sidgwick also made important contributions to fields such as economics, political theory and classics. A proponent of the utilitarianism of Jeremy Bentham and John Stuart Mill, which he analysed in his classic work The Methods of Ethics , he later turned to the practical side of politics in this work, published in 1891. His aim was to have a 'rational discussion of political questions in modern states', and he (...) offers a thorough examination of Victorian politics, beginning with a discussion of political theory before moving on to more concrete matters such as property and law. The later chapters discuss the function of government through themes such as procedural matters, international affairs, war, political parties, and public participation, giving a comprehensive account of both ideas about and the functioning of late-nineteenth-century government. (shrink)

Why is a college or university called an alma mater? This essay looks to Newman for an answer, first by pointing out his love for Trinity College, Oxford, his undergraduate alma mater. The author, sharing his experience of Louvain as his alma mater, emphasizes that an alma mater is not a theoretical concept, but a matter of real apprehension. This essay then examines two sources where Newman discussed the Catholic University of Ireland as an alma mater: his inaugural university sermon, (...) where he insisted that the university must be a mother to its students; and his first annual report to the Irish bishops, where he emphasized that the students’ resident life must provide a sense of community and a love for their alma mater. In sum, if a university is truly to be a “nourishing mother,” she must provide her students not only with an intellectual education, but also with moral discipline. (shrink)

Why is a college or university called an alma mater? This essay looks to Newman for an answer, first by pointing out his love for Trinity College, Oxford, his undergraduate alma mater. The author, sharing his experience of Louvain as his alma mater, emphasizes that an alma mater is not a theoretical concept, but a matter of real apprehension. This essay then examines two sources where Newman discussed the Catholic University of Ireland as an alma mater: his inaugural university sermon, (...) where he insisted that the university must be a mother to its students; and his first annual report to the Irish bishops, where he emphasized that the students’ resident life must provide a sense of community and a love for their alma mater. In sum, if a university is truly to be a “nourishing mother,” she must provide her students not only with an intellectual education, but also with moral discipline. (shrink)

Updated digital transcription of Spanish translation of the paper by Henry Reeve “The Autobiography of John Stuart Mill”, Edinburgh Review, 134, pp. 91-129, originally published at Revista Europea in 1874.

This essay, which was originally the opening presentation for the 2005 conference of the Venerable John Henry Newman Association on “Newman and the Laity” at Villanova University, discusses four areas where Newman’s ideas about the voice of the laity have lessons for American Catholic life today: his non-clericalized view of the Church, the lack of appreciation for the laity, his vision of an educated laity, and the need for consulting the laity about doctrinal matters.

This is the first Italian translation of Bentham’s “Deontology”. The translation goes with a rather extended apparatus meant to provide the reader with some information on Bentham’s ethical theory's own context. Some room is made for so-called forerunners of Utilitarianism, from the consequentialist-voluntarist theology of Leibniz, Malebranche, John Gay, Thomas Brown and William Paley to Locke and Hartley's incompatible associationist theories. After the theoretical context, also the real-world context is documented, from Bentham’s campaigns against the oppression of women and cruelty (...) to animals to his projects of political reform. Another section illustrates the ideas of Bentham's followers as well as the objections raised by nineteenth- and twentieth-century critics of utilitarianism. -/- Table of contents I. BEFORE THE TEXT 1. Bentham’s legacy 2. Bentham the Reformer 3. Bentham and the enlightenment project of a reformed morality 4. The principle of utility 5. Deontology or private morality 6. Utilitarianism as «eudemonologism» -/- II. TEXT Deontology I. Deontology: theoretical II. Deontology: practical III. -/- III. CO-TEXT 1. Biography 2. The reform of legislation 3. The Philosophic Radicals between the French revolution and the Industrial revolution -/- IV. CONTEXT 1. Forerunners of Utilitarianism 2. Psychological associationism 3. The oppression of women 4. Cruelty against animals 5. Parsimony and industry in Hogarth’s prints 6. Followers 6.1. John Stuart Mill 6.2. Henry Sidgwick 7. Critics 7.1. Romantic, conservative, and Christian critics 7.2. Socialist critics 8. Consequences: neo-utilitarianism 9. Consequences: critics of utilitarianism 9.1. Deontological critics 9.2. Perfectionists critics 9.3. Sceptical critics 10. Bentham’s legacy for contemporary ethics, by Bikhu Parekh Bibliography Lexicon Index of names and concepts -/- READER'S GUIDE . (shrink)

Sous l'Ancien Regime, les champs semantiques de la preuve sont aussi complexes et plastiques que ses usages. La notion circule et innerve des pratiques tres diverses, parfois de maniere inattendue. La plaidoirie ou le requisitoire reorganisent les faits, creant des fables qui s'eloignent quelquefois de la realite et qui tendent a transformer la verite en mensonge et le mensonge en verite. Ces ressorts sont aussi ceux de la fiction qui exploite toutes les ressources de la probation ou preuve et signe (...) viennent a se confondre. Dans d'autres domaines, pour assurer le passage de liaisons necessaires entre des elements divers qui conduisent a la certitude, a l'analyse morale qui s'appuie sur des relations probables pour etablir l'innocence ou la culpabilite, il faut s'etre approprie un art de la demonstration qui, ayant traverse la metaphysique et les mathematiques, parvient au droit. Ce passage-la marque le role historiquement grandissant de la probabilite dans la prise de decision et dans la conception de la verite. Le present volume interroge les lineaments semantiques et les usages de la notion de preuve, du XVIe au XVIIIe siecle, essentiellement en France et en Grande-Bretagne. Les etudes qui le composent suggerent que ces divers usages constituent l'un des aspects du long processus de division des savoirs. Jean-Pierre Schandeler est charge de recherche CNRS a l'IRCL. Ses travaux portent sur les rapports entre l'histoire et les sciences morales et politiques au XVIIIe siecle. Nathalie Vienne-Guerrin est professeur a l'universite Paul-Valery Montpellier 3, specialiste de Shakespeare. Elle dirige l'Institut de Recherche sur la Renaissance, l'age Classique et les Lumieres (UMR 5186 du CNRS). (shrink)

Jeremy Bentham, the philosopher and reformer, was at the height of his fame and influence in the 1820s. The 301 letters in this volume, many of which are previously unpublished, contain correspondence with international leaders such as Simn Bolvar, the 'Liberator', and Bernardino Rivadavia of Buenos Aires, British statesmen such as Robert Peel and Henry Brougham, and leading intellectuals such as John Stuart Mill and Sarah Austin.

Jeremy Bentham, the philosopher and reformer, was at the height of his fame and influence in the 1820s. The 301 letters in this volume, many of which are previously unpublished, contain correspondence with international leaders such as Simón Bolívar, the 'Liberator', and Bernardino Rivadavia of Buenos Aires, British statesmen such as Robert Peel and Henry Brougham, and leading intellectuals such as John Stuart Mill and Sarah Austin.

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 117 Undoubtedly Heidegger's detractors will find in this essay the hallmarks of what they abhor: forced interpretations, dubious etymologies, and overblown claims. Heidegger's followers, on the other hand, will maintain that this essay further enhances his already sure reputation as the most profound and original metaphysician of our time. Those less committed one way or the other will at least find Heidegger's latest dialogue with his philosophical (...) forebears provocative and stimulating. PETER Fuss University o/California,Riverside Jeremy Bentham: An Odyssey of Ideas. By Mary P. Mack. (New York: Columbia University Press, 1963. Pp. xiii + 482. $7.50.) Since this is only the first of two projected volumes about Bentham, only an interim report will be possible. The study extends from its subject's birth in 1748 to the death of his father in 1792, when the 44-year-old thinker, on the way to becoming a radical democrat at the height of the French Revolution, found himself endowed with half of the fortune which had supported his father's crusty Toryism. Consequently, it is a story of rebellion and partial escape from the ancestral world of law in the direction of the promises of the new science, culminating in a career devoted to an almost incredible variety of reforms. That Bentham deserves this "first full-scale study of his thought and times in over sixty years" can hardly be doubted in view of the many part-views and caricatures which he brought upon himself by his many elderly eccentricities. This biographer sees him frankly as "one of the most subtle and powerful analytic minds in the history of Western civilization... a great man who has often been misunderstood and therefore undervalued" (pp. xi, 5). She proposes to remedy the situation by the adoption of a fresh perspective that will enable the reader to "see him whole." That admirable resolution faces formidable obstacles, as every student of Bentham knows. It is about like attempting to map a vast, swampy wilderness from an airplane. For Bentham's "odyssey of ideas" was a true wandering among a profusion of them, beginning and abandoning one project after another in a troubled period of change. The dilemma faced by the author is a cruel one: to give an authentic account of Bentham historically she must reproduce the chaotic carelessness of much of his philosophizing ; while to seek to rear a consistent philosophical system from the sketches to be found in the great masses of his wordage, often mingled and mangled by the glosses of disciples, is to lose touch with the man. In Bentham we are dealing with a writer who was always communicating and frequently talking about communication without ever having mastered the art of cumulative philosophical argument. He was more intent upon being fertile than upon being consistent. His mind kept on growing for decades, which meant that he was constantly outgrowing his earlier interests and insights. His eager and all-devouring curiosity became a veritable seed-bed of suggestions from which sprouted an unmatched array of proposals of specific reforms. Yet the story of his many projects resembles that of another seminal contemporary, Henri de Saint-Simon. The perpetual mobility of intellect which marked them both is summed up in Mary Mack's reiterated comment: "Once again Bentham ran from a good thing to a better, and left only fragments behind him" (p. 417). The philosophical underpinning of his doctrines was never quite complete. As Benjamin Franklin once said of himself in the 118 HISTORY OF PHILOSOPHY role of scientist, Bentham was a good "starter of game" for the guns of others to bring down. As portrayed with accuracy in this study, Bentham became in time an intensely pragmatic thinker, passionately desirous not only of showing the directions which reforms ought to take but also of bringing them to pass. He searched incessantly for the right audience, that is, the one with the power to improve the world according to his enlightened ideas. He began by appealing to the elite, and then turned in disgust to the people. His score as a practical reformer amounted to one long series of rebuffs, transformed after his death into... (shrink)

This twelfth volume of Correspondence contains authoritative and fully annotated texts of all known letters sent both to and from Bentham between July 1824 and June 1828. The 301 letters, most of which have never before been published, have been collected from archives, public and private, in Britain, the United States of America, Switzerland, France, Japan, and elsewhere, as well as from the major collections of Bentham Papers at University College London Library and the British Library.In mid-1824 Bentham was still (...) preoccupied with the Greek struggle for independence against Turkey, though his active involvement waned as he became disenchanted with the behaviour of the deputies sent to London by the Greek National Assembly. His international reputation was reflected in his continuing contact with Simón Bolívar and Bernardino Rivadavia in South America, and with John Quincy Adams, John Neal, Henry Wheaton, and others in the United States, and his forging of new contacts in Guatemala, India, and Egypt. In the autumn of 1825 he visited France, where he stayed with Jean Baptiste Say and La Fayette, and was fêted by the French liberals.Bentham made considerable progress drafting material for his pannomion, or complete code of laws, and in particular for his Constitutional and Procedure Codes, while John Stuart Mill edited the massive Rationale of Judicial Evidence. Bentham became increasingly active in the cause of law reform, and exchanged a series of letters on the subject with Robert Peel, the Home Secretary, and Henry Brougham. He maintained his friendships with John and Sarah Austin, George and Harriet Grote, James and John Stuart Mill, John Bowring, Joseph Hume, Francis Burdett, Francis Place, and Joseph Parkes, re-established contact with the third Marquis of Lansdowne, son of his old friend the first Marquis, and made new acquaintances in James Humphreys, Sutton Sharpe, and Albany Fonblanque. (shrink)

Principles of legislation.--Principles of the civil code.--Principles of the penal code.

Jeremy Sherman distills Terrence Deacon's breakthrough natural science hypothesis for the emergence of agents and agency, selves and aims in an otherwise aimless universe. The theory cuts a new path through the dualistic spirit vs. mechanism debate, unifying the hard and soft sciences and suggesting new solutions to philosophical mysteries.

We characterize a type of functional explanation that addresses why a homologous trait originating deep in the evolutionary history of a group remains widespread and largely unchanged across the group’s lineages. We argue that biologists regularly provide this type of explanation when they attribute conserved functions to phenotypic and genetic traits. The concept of conserved function applies broadly to many biological domains, and we illustrate its importance using examples of molecular sequence alignments at the intersection of evolution and cell biology. (...) We use these examples to show how the study of conserved functions can integrate knowledge of a trait’s causal effects on fitness and its history of natural selection without invoking adaptation. We also show how conserved function provides a novel basis for addressing objections against evolutionary functions raised by Robert Cummins. (shrink)

Although the pedagogy literature indicates significant relationships between cheating intentions and both personal and situational factors, no published research has examined the joint effect of personal moral philosophy and perceived moral intensity components on students’ cheating intentions. Hence, a structural equation model that relates magnitude of consequences, relativism, and idealism to willingness to cheat, is developed and tested. Using data from undergraduate business students, the empirical results provide insight into these relationships and evidence of mediation for magnitude of consequences on (...) idealism and students’ cheating intentions. Implications for educators are offered. (shrink)

In considering the debate about the meaning of ‘disease’, the positions are generally presented as falling into two categories: naturalist, e.g., Boorse, and normativist, e.g., Engelhardt and many others. This division is too coarse, and obscures much of what is going on in this debate. I therefore propose that accounts of the meaning of ‘disease’ be assessed according to Hare’s (1997) taxonomy of evaluative terms. Such an analysis will allow us to better understand both individual positions and their inter-relationships. Most (...) importantly, it will show that it is unlikely that there is a single unique disease-concept at issue. Rather, different authors are, for the most part, considering different concepts. (shrink)

Many philosophers think that free will requires alternative possibilities. Other philosophers deny this. There are plenty of philosophical arguments on both sides of this debate, but here I want to highlight various theological pressures that might push Christians into rejecting the principle of alternative possibilities. In this paper, I explore six cases that might push Christians in that direction: the case of divine foreknowledge, the case of prophecy, the case of the blessed in heaven, the case of Christ's human freedom, (...) the case of Mary's fiat in light of her immaculate conception, and the case of prayers for the past. As I will argue, in each of these cases, given certain other standard theological commitments, it seems that Christians are pushed to admit that the agent in question does indeed act freely but also that he or she did not possess alternative possibilities at the moment of decision. (shrink)

A rigorous, authoritative new anthology which brings together some of the most significant contemporary scholarship on the theory of knowledge Carefully-calibrated and judiciously-curated, this strong and contemporary new anthology builds upon Epistemology: An Anthology, Second Edition (Wiley Blackwell, 2008) by drawing a concise and well-balanced selection of higher-level readings from a large, diverse, and evolving body of research. Includes 17 readings that represent a broad and vital part of contemporary epistemology, including articles by female philosophers and emerging thought leaders Organized (...) into seven thoughtful and distinct sections, including virtue epistemology, practical reasons for belief, and epistemic dysfunctions among others Designed to sit alongside the highly-successful anthology of canonical essays, Epistemology: An Anthology, Second Edition (Wiley Blackwell, 2008) Edited by a distinguished editorial team, including Ernie Sosa, one of the most influential active epistemologists Highlights cutting edge methodologies and contemporary topics for advanced students, instructors, and researchers. (shrink)

"Arguing that debates over legitimacy, political violence, freedom, and justice would benefit greatly from cross-tradition theorizing, this book shows how putting analytic and continental political theory in conversation would help us to overcome these intractable problems"--.

The epsilon calculus is a logical formalism developed by David Hilbert in the service of his program in the foundations of mathematics. The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. Specifically, in the calculus, a term εx A denotes some x satisfying A(x), if there is one. In Hilbert's Program, the epsilon terms play the role of ideal elements; the aim of Hilbert's finitistic consistency proofs is to give a procedure which removes such terms (...) from a formal proof. The procedures by which this is to be carried out are based on Hilbert's epsilon substitution method. The epsilon calculus, however, has applications in other contexts as well. The first general application of the epsilon calculus was in Hilbert's epsilon theorems, which in turn provide the basis for the first correct proof of Herbrand's theorem. More recently, variants of the epsilon operator have been applied in linguistics and linguistic philosophy to deal with anaphoric pronouns. (shrink)

We have two aims. The main one is to expound the idea of renormalization in quantum field theory, with no technical prerequisites. Our motivation is that renormalization is undoubtedly one of the great ideas—and great successes--of twentieth-century physics. Also it has strongly influenced in diverse ways, how physicists conceive of physical theories. So it is of considerable philosophical interest. Second, we will briefly relate renormalization to Ernest Nagel's account of inter-theoretic relations, especially reduction. One theme will be a contrast between (...) two approaches to renormalization. The old approach, which prevailed from ca. 1945 to 1970, treated renormalizability as a necessary condition for being an acceptable quantum field theory. On this approach, it is a piece of great good fortune that high energy physicists can formulate renormalizable quantum field theories that are so empirically successful. But the new approach to renormalization explains why the phenomena we see, at the energies we can access in our particle accelerators, are described by a renormalizable quantum field theory. For whatever non-renormalizable interactions may occur at yet higher energies, they are insignificant at accessible energies. Thus the new approach explains why our best fundamental theories have a feature, viz. renormalizability, which the old approach treated as a selection principle for theories. That is worth saying since philosophers tend to think of scientific explanation as only explaining an individual event, or perhaps a single law, or at most deducing one theory as a special case of another. Here we see a framework in which there is a space of theories. And this framework is powerful enough to deduce that what seemed “manna from heaven” is to be expected: the good fortune is generic. We also maintain that universality, a concept stressed in renormalization theory, is essentially the familiar philosophical idea of multiple realizability; and that it causes no problems for reductions of a Nagelian kind. (shrink)

This essay develops a framework for understanding what I call the ethics of reflexivity, that is, the norms that govern attitudes and actions with respect to one’s own worth. I distinguish five central aspects of the reflexive commitment to living in accordance with one’s personal ideals: the extent to which and manner in which one regards oneself from an evaluative point of view, the extent to which one cares about receiving the respect of others, the degree to which one interprets (...) one’s personal ideals in an individualistic or collective manner, the degree to which one’s commitment to living in accordance with one’s personal ideals is rigid or flexible, and the worthiness of one’s personal ideals. This framework, I argue, illuminates the nature and moral significance of virtuous and vicious forms of the character trait of pride. (shrink)

One of the most important philosophical topics in the early twentieth century and a topic that was seminal in the emergence of analytic philosophy was the relationship between Kantian philosophy and modern geometry. This paper discusses how this question was tackled by the Neo-Kantian trained philosopher Ernst Cassirer. Surprisingly, Cassirer does not affirm the theses that contemporary philosophers often associate with Kantian philosophy of mathematics. He does not defend the necessary truth of Euclidean geometry but instead develops a kind of (...) logicism modeled on Richard Dedekind's foundations of arithmetic. Further, because he shared with other Neo-Kantians an appreciation of the developmental and historical nature of mathematics, Cassirer developed a philosophical account of the unity and methodology of mathematics over time. With its impressive attention to the detail of contemporary mathematics and its exploration of philosophical questions to which other philosophers paid scant attention, Cassirer's philosophy of mathematics surely deserves a place among the classic works of twentieth century philosophy of mathematics. Though focused on Cassirer's philosophy of geometry, this paper also addresses both Cassirer's general philosophical orientation and his reading of Kant. (shrink)