When moral or religious teachings have public and political effects, analysis usually focuses on the message, but attention to the manner in which the teachings are communicated is equally important in understanding their power to influence the course of events. Oscar Romero's particular style of moral discourse was remarkably effective for three reasons: First, his moral reasoning resonated with Salvadoran identity. It was intelligible within those reigning assumptions about national history and territory that could actually move a public to action. (...) Second, his moral judgments were timely. Romero sought to discern what was possible for the Salvadoran public at a given moment. Third, Romero had integrity as a public figure. He lived in such a way that his life, and especially his death, became an exemplary embodiment of the larger religious narrative that both grounded his ethics and gave meaning to the nation. (shrink)

Reproductive proteins maintain species‐specific barriers to fertilization, affect the outcome of sperm competition, mediate reproductive conflicts between the sexes, and potentially contribute to the formation of new species. However, the specific proteins and molecular mechanisms that underlie these processes are understood in only a handful of cases. Advances in genomic and proteomic technologies enable the identification of large suites of reproductive proteins, making it possible to dissect reproductive phenotypes at the molecular level. We first review these technological advances and describe (...) how reproductive proteins are identified in diverse animal taxa. We then discuss the dynamic evolution of reproductive proteins and the potential selective forces that act on them. Finally, we describe molecular and genomic tools for functional analysis and detail how evolutionary data may be used to make predictions about interactions among reproductive proteins. (shrink)

Prospective follow-up studies have shown that even though some children outgrow the disorder, a childhood diagnosis of attention deficit hyperactivity disorder is clearly a risk factor for a broad range of adverse outcomes, with extremes including drug abuse and juvenile delinquency. This article considers the use of several spectrum concepts and some neuroethical issues. It provides a list of criterion symptoms with a threshold set for the number of symptoms required for categorical diagnoses of disorders. It gives a brief review (...) of some brain imaging and pharmacological treatment studies of ADHD to set the stage for a consideration of brain-specific issues related to neuroethics. Studies using reaction time tasks of cognitive control, response inhibition, and conflict have identified interindividual variance in task performance as one of the most prominent aspects of cognitive deficits related to ADHD. (shrink)

Gliomas are diffuse and invasive brain tumors with the nefarious ability to evade even seemingly draconian treatment measures. Here we introduce a simple mathematical model for drug delivery of chemotherapeutic agents to treat such a tumor. The model predicts that heterogeneity in drug delivery related to variability in vascular density throughout the brain results in an apparent tumor reduction based on imaging studies despite continual spread beyond the resolution of the imaging modality. We discuss a clinical example for which the (...) model-predicted scenario is relevant. The analysis and results suggest an explanation for the clinical problem of the long-standing confounding observation of shrinkage of the lesion in certain areas of the brain with continued growth in other areas. (shrink)

Information is a force multiplier. Knowledge of the enemy's capability and intentions may be of far more value to a military force than additional troops or firepower. Situation assessment is the ongoing process of inferring relevant information about the forces of concern in a military situation. Relevant information can include force types, firepower, location, and past, present and future course of action. Situation assessment involves the incorporation of uncertain evidence from diverse sources. These include photographs, radar scans, and other forms (...) of image intelligence, or IMINT; electronics intelligence, or ELINT, derived from characteristics (e.g., wavelength) of emissions generated by enemy equipment; communications intelligence, or COMINT, derived from the characteristics of messages sent by the enemy; and reports from human informants (HUMINT). These sources must be combined to form a model of the situation. The sheer volume of data, the ubiquity of uncertainty, the number and complexity of hypotheses to consider, the high-stakes environment, the compressed time frame, and deception and damage from hostile forces, combine to present a staggeringly complex problem. Even if one could formulate a decision problem in reasonable time, explicit determination of an optimal decision policy exceeds any reasonable computational resources. While it is tempting to drop any attempt at rational analysis and rely purely on simple heuristics, we argue that this can lead to catastrophic outcomes. We present an architecture for a ``complex decision machine'' that performs rational deliberation to make decisions in real time. We argue that resource limits require such an architecture to be grounded in simple heuristic reactive processes. We thus argue that both simple heuristics and complex decision machines are required for effective decision making in real time for complex problems. We describe an implementation of our architecture applied to the problem of military situation assessment. (shrink)

Coastal ecosystems are increasingly dominated by humans. Consequently, the human dimensions of sustainability science have become an integral part of emerging coastal governance and management practices. But if we are to avoid the harsh lessons of land management, coastal decision makers must recognize that humans are one of the more coastally dependent species in the biosphere. Management responses must therefore confront both the temporal urgency and the very real compromises and sacrifices that will be necessary to achieve a sustainable coastal (...) ecosystem, one that is economically feasible, socially just, and ecologically sound. (shrink)

Information is a force multiplier. Knowledge of the enemy's capability and intentions may be of far more value to a military force than additional troops or firepower. Situation assessment is the ongoing process of inferring relevant information about the forces of concern in a military situation. Relevant information can include force types, firepower, location, and past, present and future course of action. Situation assessment involves the incorporation of uncertain evidence from diverse sources. These include photographs, radar scans, and other forms (...) of image intelligence, or IMINT; electronics intelligence, or ELINT, derived from characteristics (e.g., wavelength) of emissions generated by enemy equipment; communications intelligence, or COMINT, derived from the characteristics of messages sent by the enemy; and reports from human informants (HUMINT). These sources must be combined to form a model of the situation. The sheer volume of data, the ubiquity of uncertainty, the number and complexity of hypotheses to consider, the high-stakes environment, the compressed time frame, and deception and damage from hostile forces, combine to present a staggeringly complex problem. Even if one could formulate a decision problem in reasonable time, explicit determination of an optimal decision policy exceeds any reasonable computational resources. While it is tempting to drop any attempt at rational analysis and rely purely on simple heuristics, we argue that this can lead to catastrophic outcomes. We present an architecture for a ``complex decision machine'' that performs rational deliberation to make decisions in real time. We argue that resource limits require such an architecture to be grounded in simple heuristic reactive processes. We thus argue that both simple heuristics and complex decision machines are required for effective decision making in real time for complex problems. We describe an implementation of our architecture applied to the problem of military situation assessment. (shrink)

Reanimated for the contemporary literature in the writings of Quine, [16]) and Kuhn [7], the conventionalism of Duhem [2] and Poincaré [12] has emerged in the last few years as one of the genuinely interesting topics in the philosophy of science. The theory in question—let us follow Grünbaum [3] in calling it the D-thesis, after its founder, Pierre Duhem—claims three things: a single scientific hypothesis H is never disconfirmable in isolation from its fellow; every single hypothesis H of science presupposes, (...) explicitly or implicitly, the support of a conjunction A = A, • A2 • … • Am of auxiliary assumptions or hypotheses; the failure of an observational consequence of H in face of contradictory evidence disconfirms only the conjunction of H and A, not H alone—i.e. establishes only ∼. The logical picture is as follows. (shrink)

We present a one per cent measurement of the cosmic distance scale from the detections of the baryon acoustic oscillations in the clustering of galaxies from the Baryon Oscillation Spectroscopic Survey, which is part of the Sloan Digital Sky Survey III. Our results come from the Data Release 11 sample, containing nearly one million galaxies and covering approximately 8500 square degrees and the redshift range 0.2 < z < 0.7. We also compare these results with those from the publicly released (...) DR9 and DR10 samples. Assuming a concordance Λ cold dark matter cosmological model, the DR11 sample covers a volume of 13 Gpc3 and is the largest region of the Universe ever surveyed at this density. We measure the correlation function and power spectrum, including density-field reconstruction of the BAO feature. The acoustic features are detected at a significance of over 7σ in both the correlation function and power spectrum. Fitting for the position of the acoustic features measures the distance relative to the sound horizon at the drag epoch, rd, which has a value of rd,fid = 149.28 Mpc in our fiducial cosmology. We find DV = at z = 0.32 and DV = at z = 0.57. At 1.0 per cent, this latter measure is the most precise distance constraint ever obtained from a galaxy survey. Separating the clustering along and transverse to the line of sight yields measurements at z = 0.57 of DA = and H =. Our measurements of the distance scale are in good agreement with previous BAO measurements and with the predictions from cosmic microwave background data for a spatially flat CDM model with a cosmological constant. © 2014 The Author Published by Oxford University Press on behalf of the Royal Astronomical Society. (shrink)

Arnold Metzger is one of Germany’s leading philosophers. He served as an assistant to Husserl at Freiburg from 1919 to 1924 and published his first major book—Der Gegendstand der Erkenntnis —in Husserl’s Jarhbuch. [[sic]] The present title is a second unchanged edition of the work which appeared in 1955, and which received a warm reception in Germany. Metzger’s philosophy is concerned with working out the implications which lie in the concept of Being. There are two "mythologies" about Being which Metzger (...) hopes to dispel. The one hypostasizes Being as something transcendent and permanent, while the other is a reductionism which hypostasizes the factual. The problem of freedom and death must be understood within the context of the question of Being so formulated. Metzger’s approach is in the broad sense "existential," but it is developed out of a constant dialogue with Socrates, Plato and Kant. His German is highly readable and unencumbered. His book which is a cross section of the major themes of twentieth century German philosophy, is a thoughtful meditative study of one of the major themes in contemporary thought.—J. D. C. (shrink)

iinstein oered the prin™iple of gener—l ™ov—ri—n™e —s the fund—ment—l physi™—l prin™iple of his gener—l theory of rel—tivityD —nd —s responsi˜le for extending the prin™iple of rel—tivity to —™™eler—ted motionF „his view w—s disputed —lmost immedi—tely with the ™ounterE™l—im th—t the prin™iple w—s no rel—tivity prin™iple —nd w—s physi™—lly v—™uousF „he dis—greeE ment persists tod—yF „his —rti™le reviews the development of iinstein9s thought on gener—l ™ov—ri—n™eD its rel—tion to the found—tions of gener—l rel—tivity —nd the evolution of the ™ontinuing de˜—te (...) over his viewpointF.. (shrink)

Fr. James Demske first published this book in 1963 in Germany under the title: Sein, Mensch und Tod: Das Todesproblem bei Martin Heidegger. Except for minor revisions--such as changing the numeration and headings of the chapters and the occasional expansion of paragraphs--this is substantially the same book. The author follows the development of the problem of death in Heidegger through the famous discussion in Being and Time and into the later works. The fact of the continuing importance of "death" in (...) Heidegger's work is easily overlooked. But while the phrase "Being-unto-death" disappears after Being and Time the same phenomenon of Dasein's mortality reappears in the later accounts of the "Quadrate" : the heavens and earth, gods, and mortals. Chapter six of Demske's book is one of the few and clearest accounts of this central theme in Heidegger's thought. The book as a whole, apart from its thematization of the problem of death, presents a sound appraisal and a clear overview of the development of Heidegger's "path of thought" and is, on that account too, a welcome addition to the literature.--J. D. C. (shrink)

In my first study of the borrowings from Athenian sacred treasure to finance the Archidamian War I assumed, in common with others, certain irregularities in the stoichedon order of IG. i. 324. The text has subsequently been amplified and improved by Tod, notably with the addition of one amount of interest due to Athena and of the total amounts of principal credited to the Other Gods and to all the gods . This further expansion, however, has introduced additional irregularities, the (...) restoration [τάδε τος λλοις θεος έλοσι τόκο ]ν νδεκα τεα[ιν:…] being too long by one letter in line 120 and the restoration [τάδε πασι τος θεος έλοσι τόκο ν] νδεκα τεσ[ιν:…] being likewise too long in line 123. (shrink)

This narrative symposium examines the relationship of bioethics practice to personal experiences of illness. A call for stories was developed by Tod Chambers, the symposium editor, and editorial staff and was sent to several commonly used bioethics listservs and posted on the Narrative Inquiry in Bioethics website. The call asked authors to relate a personal story of being ill or caring for a person who is ill, and to describe how this affected how they think about bioethical questions and the (...) practice of medicine. Eighteen individuals were invited to submit full stories based on review of their proposals. Twelve stories are published in this symposium, and six supplemental stories are published online only through Project MUSE. Authors explore themes of vulnerability, suffering, communication, voluntariness, cultural barriers, and flaws in local healthcare systems through stories about their own illnesses or about caring for children, partners, parents and grandparents. Commentary articles by Arthur Frank, Bradley Lewis, and Carol Taylor follow the collection of personal narratives. (shrink)

This well organized and interesting anthology concerns the image of the self-directed individual as replaced by a deterministic model of his behavior. Since legal, personal-social, and religious institutions still see man as self-controlled and therefore responsible, Mr. Klausner views this replacement as particularly troublesome. The first third of the book is predominantly historical and draws from an extremely tolerant range of sources including yoga, philosophy, psychology, hypnosis and self-help publications. The remainder of the volume is psychological and sociological, with emphasis (...) on the individual acting under stress, and with the traditional philosophical problems completely ignored. While the thematic problem is not obviously tackled there is fruitful examination of significant concepts with detailed and well-researched relationships of these concepts with a manifold of phenomena. There are several extensive bibliographies accompanying the readings. Not including introductory contributions the book includes: "Self-Control in the Perspective of History": Klausner, B. Nelson, Moses Hadas; "Self-Control in a Sociological Perspective": S. M. Dornbusch, M. K. Opler, Guy E. Swanson; "Self-Control in Psychological Perspective": I. L. Janis, S. J. Korchin, H. Liddel; "Self-Control in Psychiatric Perspective": M. T. Orne, O. McK, Rioch, K. Goldstein; and "Scientific Hermeneutics": Klausner.—D. A. G. (shrink)

Sterben und Tod werden aus unterschiedlichster Sicht (medizinisch, psychologisch, mystisch) beleuchtet und reflektiert. Die Sicht von Betroffenen, die Nahtod-Erlebnisse hatten, und die daraus resultierenden Konsequenzen für die betreuenden Personen werden ebenso wie der Umgang mit Sterben und Tod in unserer Gesellschaft kritisch dargestellt.

Martin Walser's reflections on German self-identity have made him a controversial author: whereas critics have raised charges of,,literary anti-Semitism", his defenders consider him – as a writer who since the early 1960s has shown a preoccupation with his country's Nazi past – immune to such criticism. Taking both arguments seriously, Matthias N. Lorenz has reviewed Walser's allegedly untenable positions on the Holocaust in his book,,Auschwitz drängt uns auf einen Fleck": Judendarstellung und Auschwitzdiskurs bei Martin Walser. In this essay the author (...) concisely presents the main theses and thoughts of Lorenz's widely discussed Ph.D. dissertation. (shrink)

The happy death of the Stoic. Wisdom and finitude in Stoic philosophy. This paper attempts to furnish a Stoic reply to an accusation addressing the Stoics' ideal of the wise man according to which it is impossible to realize their ideal and therefore their whole system has to face a paradox: How is wisdom possible when all people are fools and it is impossible for them to become good? In addition to this question there is another important problem connected with (...) the ideal of wisdom. The Stoic philosophers deny transcendental ideas. Instead they are well known for their thorough-going materialism. Therefore, even their idea of the wise man must be based on experience. How would it otherwise be possible to form the idea of wisdom by a method of analogy if experience did not provide any example of truthful virtue to us? A possible answer to this problem can be found in the writings of Seneca, a Stoic of the first century A.D. Seneca emphasizes the close relation between wisdom and human mortality owing to which it is at least possible for the philosopher who has made sufficiently progress in his efforts to gain wisdom to find lasting happiness in death. (shrink)

Die Phänomene des kommenden Nichts haben Prozesse zum Gegenstand, die darauf hinauslaufen, menschliches Leben oder seine herkömmlichen Grundlagen zu vernichten. An ihrem Ende wird das Nichts zu einer beherrschenden Realität. Diese auf die Zukunft bezogene Dynamik soll, sofern sie sich schon voraussagen lässt, zudem den Charakter der Unvermeidlichkeit haben, d.h. die ins Nichts führenden Prozesse sollen sich durch keine heute schon als realistisch angenommene Verfahren verhindern lassen. Die von mir diskutierten Phänomene des kommenden Nichts lassen sich den zwei Wirklichkeitsbereichen der (...) Lebenswelt und der Wissenschaft zuordnen. Lebenswelt und Wissenschaft bilden fundamentale Dimensionen der menschlichen Wirklichkeit. Die Lebenswelt stellt eine elementare Form des Erlebens von Wirklichkeit dar, die sich weit in die Vergangenheit zurückverfolgen lässt. Wissenschaft bildet die führende Form der Erkenntnis und Veränderung von Wirklichkeit in der Moderne. Bei den Phänomenen des kommenden Nichts der Wissenschaft handelt es sich um die Leere des Universums und die Sinnleere in einer entzauberten wissenschaftlichen Welt. Zu diesen Phänomenen weisen die lebensweltlichen Phänomene des kommenden Nichts einige Analogien auf. Als Erscheinungen des kommenden Nichts in der Lebenswelt fasse ich den Tod und die innere Leere der Langeweile auf. Die von der Kosmologie beschriebene kommende Leere ist auch als Sterbeprozess des Universums bezeichnet worden, so dass die Analogie zum menschlichen Tod offensichtlich ist. Mit dem Entzauberungsprozess verliert die wissenschaftliche Erkenntnis weniger für Ihre Akteur*innen als vielmehr für das Publikum zunehmend die Faszination und den Reiz des Wunderbaren, womit auch die Wissenschaft in die Gegenstände der lebensweltlichen Langeweile einrücken kann. (shrink)

Fichte hat nur eine, die allererste und nicht einmal förmlich zum Abschluß gebrachte, Darstellung der Wissenschaftslehre publiziert, doch in den nächsten knapp zwei Jahrzehnten bis zu seinem Tod im Januar 1814 die Wissenschaftslehre noch insgesamt fünfzehn Mal öffentlich vorgetragen und dabei dreizehn Mal neu oder verändert dargestellt. Hinzukommen noch drei umfangreiche Ausarbeitungen, die den öffentlichen Vortrag der Wissenschaftslehre vorbereiten bzw. begleiten: »Eigne Meditationen über ElementarPhilosophie« aus den Jahren 1793-94, die Aufzeichnungen betitelt »Seit d. 1.April 1808. nach den Reden an die (...) deutsche Nation« aus dem Jahre 1808 und wesentliche Teile der als Diarium geführten Notate aus den Jahren 1813 und 1814. Nur wenige von Fichtes Zeitgenossen - praktisch nur die Zuhörer seiner fortgesetzten Vorlesungen über die Wissenschaftslehre in Berlin, Erlangen und Königsberg - haben diese öffentlichen, aber unveröffentlichten Arbeiten zur Kenntnis nehmen können. (shrink)

Fichte hat nur eine, die allererste und nicht einmal förmlich zum Abschluß gebrachte, Darstellung der Wissenschaftslehre publiziert, doch in den nächsten knapp zwei Jahrzehnten bis zu seinem Tod im Januar 1814 die Wissenschaftslehre noch insgesamt fünfzehn Mal öffentlich vorgetragen und dabei dreizehn Mal neu oder verändert dargestellt. Hinzukommen noch drei umfangreiche Ausarbeitungen, die den öffentlichen Vortrag der Wissenschaftslehre vorbereiten bzw. begleiten: »Eigne Meditationen über ElementarPhilosophie« aus den Jahren 1793-94, die Aufzeichnungen betitelt »Seit d. 1.April 1808. nach den Reden an die (...) deutsche Nation« aus dem Jahre 1808 und wesentliche Teile der als Diarium geführten Notate aus den Jahren 1813 und 1814. Nur wenige von Fichtes Zeitgenossen - praktisch nur die Zuhörer seiner fortgesetzten Vorlesungen über die Wissenschaftslehre in Berlin, Erlangen und Königsberg - haben diese öffentlichen, aber unveröffentlichten Arbeiten zur Kenntnis nehmen können. (shrink)

Fichte hat nur eine, die allererste und nicht einmal förmlich zum Abschluß gebrachte, Darstellung der Wissenschaftslehre publiziert, doch in den nächsten knapp zwei Jahrzehnten bis zu seinem Tod im Januar 1814 die Wissenschaftslehre noch insgesamt fünfzehn Mal öffentlich vorgetragen und dabei dreizehn Mal neu oder verändert dargestellt. Hinzukommen noch drei umfangreiche Ausarbeitungen, die den öffentlichen Vortrag der Wissenschaftslehre vorbereiten bzw. begleiten: »Eigne Meditationen über ElementarPhilosophie« aus den Jahren 1793-94, die Aufzeichnungen betitelt »Seit d. 1.April 1808. nach den Reden an die (...) deutsche Nation« aus dem Jahre 1808 und wesentliche Teile der als Diarium geführten Notate aus den Jahren 1813 und 1814. Nur wenige von Fichtes Zeitgenossen - praktisch nur die Zuhörer seiner fortgesetzten Vorlesungen über die Wissenschaftslehre in Berlin, Erlangen und Königsberg - haben diese öffentlichen, aber unveröffentlichten Arbeiten zur Kenntnis nehmen können. (shrink)

Il y a vingt-cinq ans, j’étais un étudiant de doctorat intéressé par la philosophie d’Aristote et à la recherche d’un sujet de thèse. Au cours de mes études supérieures, j’ai eu la chance d’étudier l’Éthique à Nicomaque avec Rémi Brague et Les Politiques avec Judith Swanson. Ces deux érudits m’ont, à leur façon, fait prendre conscience de l’importance d’enquêter sur le public cible des œuvres d’Aristote. Tous deux parlaient en bien du livre Le philosophe et la cité (Les Belles (...) Lettres, 1982) de Richard Bodéüs, qui venait d’être traduit en anglais sous le titre The Political Dimensions of Aristotle’s Ethics (State University of New York Press, 1993). Il se trouva qu’un jour de printemps, ayant été appelé à siéger comme juré, je pris avec moi mon tout nouvel exemplaire du volume de Bodéüs. Heureusement, le jury ne fut pas convoqué, mais on ne me laissa pas partir avant la fin de l’après-midi. Aussi passai-je toute la journée au palais de justice à lire l’ouvrage de Bodéüs et à réfléchir à la relation entre le concept de justice déployé dans l’Éthique à Nicomaque et les analyses des constitutions qu’on trouve dans Les Politiques. Je découvris alors une réflexion savante, riche et profondément historique, portant sur la façon de comprendre les divers traités d’Aristote sur «la philosophie des choses humaines» (EN 10.9.1181b15). C’est ainsi que je fus mis sur la voie du sujet de sur lequel porterait ma thèse : la nature de la justice politique chez Aristote. C’est aussi ainsi que j’en vins à penser en compagnie de l’un des plus éminents spécialistes et traducteurs d’Aristote du siècle dernier. En 2018, la Northeast Political Science Association annonça que sa réunion annuelle allait se tenir à Montréal et invita ses membres à soumettre des contributions dans les deux langues officielles canadiennes. Étant donné que Montréal abrite également l’université dans laquelle Bodéüs avait enseigné, l’Université de Montréal, il m’est immédiatement venu à l’esprit de proposer un panel bilingue pour explorer la philosophie d’Aristote à la lumière de son ouvrage novateur, Le philosophe et la cité, qui fut déterminant pour mon parcours intellectuel. Deux panels furent constitués. Le premier rassemblait les participants anglophones : Jordan Jochim (Cornell University), Kevin Cherry (Richmond University) et moi-même (Quinnipiac University), et fut présidé par Jill Frank (Cornell University). Le second panel rassemblait les participants francophones : Léa Derome (Université McGill), Timothée Gautier (Université Paris 1 — Panthéon-Sorbonne), Louise Rodrigue (Collège universitaire dominicain), et fut présidé par Elsa Bouchard (Université de Montréal). Bodéüs, qui est à présent professeur émérite, accepta généreusement de lire toutes les contributions à l’avance et, combattant un mal de gorge le jour de la conférence, accompagna chacune d’entre elles de commentaires à la fois perspicaces et magnanimes. N’ayant pas pu inclure toutes les présentations de la conférence de novembre 2018, ce numéro de Dialogue comprend les versions révisées de trois contributions : mon “ὁμόνοια: The Hinge of Aristotle’s Ethics and Politics?”, la contribution de Kevin Cherry, “Lawgivers, Virtue, and the Mixed Regime: Reflections on Richard Bodéüs’s The Political Dimensions of Aristotle’s Ethics,” et celle de Louise Rodrigue, «La conception aristotélicienne de la servilité dans l’Éthique et la Politique». Nous remercions tout particulièrement Léa Derome, qui a édité cette tribune du livre, coordonné la soumission de nos documents et des réponses de Bodéüs à Dialogue, et a aidé à la traduction en français. Les trois articles présentés composent avec des interrogations héritées du travail du professeur Bodéüs. Nous sommes donc particulièrement reconnaissants qu’il ait accepté de contribuer à ce projet de publication. Nous espérons que l’ensemble parvienne à capturer ne serait-ce qu’un simulacre de l’expérience intellectuelle passionnante que fut notre journée de conférences de novembre 2018. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The humble origins of Russell's paradox by J. Alberto Coffa ON SEVERAL OCCASIONS Russell pointed out that the discovery of his celebrated paradox concerning the class of all classes not belonging to themselves was intimately related to Cantor's proof that there is no greatest cardinal. lOne of the earliest remarks to that effect occurs in The Principles ofMathematics where, referring to the universal class, the class of all classes (...) and the class of all propositions, he notes that when we apply the reasoning of his [Cantor's] proofto the cases in question we find ourselves met by definite contradictions, of which the one discussed in Chapter x is an example. (P. 362) And in a footnote he adds: "It was in this way that I discovered this contradiction". Throughout his writings Russell left a number ofhints concerning the sort of connection he had drawn between Cantor's proof and his own discovery. In fact, his suggestions are so specific that there would seem to be little room left for speculation concerning how the discovery took place.2 The picture that emerges almost immediately from Russell's observations is the following. For reasons which are 1 See, e.g., Bertrand Russell, The Principles of Mathematics, 2nd ed. (London: Allen & Unwin, 1937), §§100, 344-9; G. Frege, Wissenschaftlicher Briefwechsel (Hamburg: Felix Meiner Verlag, 1976), pp. 215-16; B. Russell, Essays in Analysis, ed. D. Lackey (New York: George Braziller, 1973), p. 139; B. Russell, Introducrion to Mathemarical Philosophy (New York: Simon and Schuster, 1971), p. 136; B. Russell, My Philosophical Development (New York: Simon and Schuster, 1959), pp. 75-6; The Autobiography of Bertrand Russell, I (New York: Bantam Books, 1968), 195. 2 See, e.g., Ch. Thiel's "Einleitung des Herausgebers" in Frege, Wissenschaftlicher Briefwechsel, pp. 203 and 216 (footnote), and 1. Grattan-Guinness, "How Bertrand Russell Discovered his Paradox", Historia Marhematica, 5 (1978),127-37. 31 32 Russell, nos. 33-4 (Spring-Summer 1979) never made clear, Russell decided to analyze Cantor's argument applying it to "large" classes such as the universal class V, and the class of all classes. When, for example, we consider V, its power set and the correlationf(x) = {x} if x is not a class, f(x) =. x otherwise, then Cantor's diagonal class D turns out to be the class of all classes not belonging to themselves. Moreover, since the element ofV which is taken toD byfisD itself(i.e., sincef(D) = D), Cantor's reasoning invites us to raise the question whether D belongs tof(D) (i.e., toD) or not; and it establishes that it does precisely if it doesn't.3 The purpose of this note is to present recently uncovered information that complements and corrects our present understanding of Russell's discovery of his paradox. As it turns out, far from originating from his desire to apply the ideas in Cantor's theorem, a version of Russell's paradox first occurred in an argument that Russell had devised, late in 1900, in order to establish the invalidity of that theorem. An appeal to "large" classes such as V or Class was, as we shall see, essential to Russell's attempted refutation. As he displayed the details of his counterexample Russell's paradox emerged, at first unrecognized, as the by-product of a project that the paradox itself would eventually undermine. In a paper written in 1901 and largely devoted to a popular exposition and defence of Cantor's theory of the infinite, Russell expressed what appeared to be a rpinor reservation to Cantor's treatment : There is a greatest of all infinite numbers, which is the number of things altogether, of every sort and kind. It is obvious that there cannot be a greater number than this, because, if everything has been taken, there is nothing left to add. Cantor has a proof that there is no greatest number, and if this proof were valid, the contradictions of infinity would reappear in a sublimated form. But in this one point, the master has been guilty of a very subtle fallacy, which I hope to explain in some future work.4 3 See Principles, §349. Perhaps I should remind... (shrink)