We will prove in Zermelo-Fraenkel set theory without axiom of choice that the transitive hull R* of a relation R is not much “bigger” than R itself. As a measure for the size of a relation we introduce the notion of κ+-narrowness using surjective Hartogs numbers rather than the usul injective Hartogs values. The main theorem of this paper states that the transitive hull of a κ+-narrow relation is κ+-narrow. As an immediate corollary we obtain that, for every infinite cardinal (...) κ, the class HCκ of all κ-hereditary sets is a set with von Neumann rank ϱ ≤ κ+. Moreover, ϱ = κ+ if and only if κ is singular, otherwise ϱ = κ. The statements of the corollary are well known in the presence of the axiom of choice . To prove them without AC - as carried through here - is, however, much harder. A special case of the corollary has been treated independently by T. JECH. (shrink)

We will prove in Zermelo-Fraenkel set theory without axiom of choice that the transitive hull R* of a relation R is not much “bigger” than R itself. As a measure for the size of a relation we introduce the notion of κ+-narrowness using surjective Hartogs numbers rather than the usul injective Hartogs values. The main theorem of this paper states that the transitive hull of a κ+-narrow relation is κ+-narrow. As an immediate corollary we obtain that, for every infinite cardinal (...) κ, the class HCκ of all κ-hereditary sets is a set with von Neumann rank ϱ(HCκ) ≤ κ+. Moreover, ϱ(HCκ) = κ+ if and only if κ is singular, otherwise ϱ(HCκ) = κ. The statements of the corollary are well known in the presence of the axiom of choice (AC). To prove them without AC - as carried through here - is, however, much harder. A special case of the corollary (κ = ω1, i.e., the class HCω1 of all hereditarily countable sets) has been treated independently by T. JECH. (shrink)

Anhand einer Kontextualisierung der arbeitswissenschaftlichen Forschungen Karl Büchers untersucht der Aufsatz die Zusammenhänge zwischen anthropologischen Annahmen, theoretischen und methodischen Innovationen und der Reformulierung topischer Wissensbestände im Zeitraum der Jahrhundertwende. Im Zentrum der Untersuchung steht die Frage, auf welche Weise diese Zusammenhänge jeweils konstelliert werden und mit den Veränderungen historischer und kultureller Rahmenbedingungen interagieren. Als Resultat der Kontextualisierung arbeitswissenschaftlicher Problemstellungen zeigt sich, daß die Semantik des Rhythmus immer auch von dem Stellenwert abhängt, den Gesellschaften der sozialen Relevanz von Tanz und (...) Spiel zugestehen. (shrink)

Anhand einer Kontextualisierung der arbeitswissenschaftlichen Forschungen Karl Büchers untersucht der Aufsatz die Zusammenhänge zwischen anthropologischen Annahmen, theoretischen und methodischen Innovationen und der Reformulierung topischer Wissensbestände im Zeitraum der Jahrhundertwende. Im Zentrum der Untersuchung steht die Frage, auf welche Weise diese Zusammenhänge jeweils konstelliert werden und mit den Veränderungen historischer und kultureller Rahmenbedingungen interagieren. Als Resultat der Kontextualisierung arbeitswissenschaftlicher Problemstellungen zeigt sich, daß die Semantik des Rhythmus immer auch von dem Stellenwert abhängt, den Gesellschaften der sozialen Relevanz von Tanz und (...) Spiel zugestehen. (shrink)

Die von Karl Menger und seinen Mitarbeitern (darunter Kurt Gödel) herausgegebenen "Ergebnisse eines Mathematischen Kolloquiums" zählen zu den wichtigsten Quellenwerken der Wissenschafts- und Geistesgeschichte der Zwischenkriegszeit, mit bahnbrechenden Beiträgen von Menger, Gödel, Tarski, Wald, John von Neumann und vielen anderen. In diesem Band liegt der Inhalt erstmals gesammelt vor. Der Nobelpreisträger Gerard Debreu schrieb die Einleitung, die Kommentare wurden vom Logiker und Gödel-Biographen John Dawson jr., dem Topologen Ryszard Engelking und dem Wirtschaftstheoretiker Werner Hildenbrand verfasst. Außerdem enthält der (...) Band einen biographischen Aufsatz über Karl Menger sowie einen von Menger verfassten Überblick über die wichtigsten topologischen und geometrischen Arbeiten des Kolloquiums. (shrink)

There are presently two leading foreign policy decision-making paradigms in vogue. The first is based on the classical or rational model originally posited by von Neumann and Morgenstern to explain microeconomic decisions. The second is based on the cybernetic perspective whose groundwork was laid by Herbert Simon in his early research on bounded rationality. In this paper we introduce a third perspective — thepoliheuristic theory of decision-making — as an alternative to the rational actor and cybernetic paradigms in international (...) relations. This theory is drawn in large part from research on heuristics done in experimental cognitive psychology. According to the poliheuristic theory, policy makers use poly (many) heuristics while focusing on a very narrow range of options and dimensions when making decisions. Among them, the political dimension is noncompensatory. The paper also delineates the mathematical formulations of the three decision-making models. (shrink)

There are presently two leading foreign policy decision-making paradigms in vogue. The first is based on the classical or rational model originally posited by von Neumann and Morgenstern to explain microeconomic decisions. The second is based on the cybernetic perspective whose groundwork was laid by Herbert Simon in his early research on bounded rationality. In this paper we introduce a third perspective -- the poliheuristic theory of decision-making -- as an alternative to the rational actor and cybernetic paradigms in (...) international relations. This theory is drawn in large part from research on heuristics done in experimental cognitive psychology. According to the poliheuristic theory, policy makers use poly (many) heuristics while focusing on a very narrow range of options and dimensions when making decisions. Among them, the political dimension is noncompensatory. The paper also delineates the mathematical formulations of the three decision-making models. (shrink)

Reden Gotama Buddhas aus der Mittleren Sammlung. Ausgewählt und erläutert von Hellmuth Hecker. Übertragen von Karl Eugen Neumann. R. Piper Verlag, Munich-Zürich 1987. 536pp. DM 24.80.

This is the classic work upon which modern-day game theory is based. What began as a modest proposal that a mathematician and an economist write a short paper together blossomed, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific (...) inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences. (shrink)

Muss Philosophie immer eine bierernste Angelegenheit sein? Einer, der das vehement bestritten hat, war der griechische Denker Diogenes, jener berühmte Tonnen-Philosoph, der bis heute als eine der schillerndsten und originellsten Gestalten des Altertums gilt. Seine Gesellschaftskritik lebte er mit einer nachgerade schockierenden Konsequenz vor. Seine Forderung: nicht mehr und nicht weniger als der konsequente Ausstieg aus der Zivilisation. Karl-Wilhelm Weeber stellt in diesem locker geschriebenen Band den scharfzüngigen, schlagfertigen und respektlosen Philosophen und seine Ideenwelt vor.

This book represents the views of one of the greatest mathematicians of the twentieth century on the analogies between computing machines and the living human brain.

Zeigt, wie der äTonnenphilosophä in einer unsicheren Zeit eine auch heute noch gültige Überlebensphilosophie für das Individuum entwickelte und praktizierte.

Prolog -- Eros : auf dem Weg zur Erkenntnis -- Liebe als einheitsstiftende Macht -- Das tragische Chorspiel der Hellenen und ihre Imaginationen von Liebe -- Narkissos : die unstillbare Selbstliebe und das Spiegelmotiv -- Gnosis als erlösende Erkenntnis der Liebe -- Liebe in der kontemplativen Metaphysik Plotins -- Das Eine und das Viele -- Kontemplation und Liebe : das Mysterium Sacrum -- Sensorisches und Imaginatives : Weisen der Vergeistigung der Liebe -- Mystische Liebe : Gott-Leiden und Gott-Lieben in der (...) "Rheinischen Mystik" (Eckhart, Tauler, Seuse, Ruusbroec) -- Figurationen der Liebe auf den Brettern, die "die Welt bedeuten" (Wissen, Macht, Liebe, Tod) -- Amor fati : die Liebe zum Schicksal -- Die Liebe auf der Bühne des Theatrum Mundi -- Reflexionen und Mythopoetik der Liebe : philosophisch, theologisch, poetisch -- Liebe in der Theologie des Alten Bundes -- Liebe in der Theologie des Neuen Bundes. (shrink)

I. THE TASK OF DOGMATICS As a theological discipline dogmatics is the scientific self- examination of the Christian Church with respect to the content of ...

The influence of emotion on episodic and autobiographical memory in schizophrenia was investigated. Using an experiential approach, the states of awareness accompanying recollection of pictures from the IAPS and of associated autobiographical memories was recorded. Results show that schizophrenia impairs episodic and autobiographical memories in their critical feature: autonoetic awareness, i.e., the type of awareness experienced when mentally reliving events from one’s past. Schizophrenia was also associated with a reduction of specific autobiographical memories. The impact of stimulus valence on memory (...) performance was moderated by clinical status. Patients with schizophrenia recognized more positive than negative pictures, and recalled more positive than negative autobiographical memories while controls displayed the opposite pattern. A hypothesis in terms of a fundamental executive deficit underlying these impairments is proposed. (shrink)

The invitation of the Organizing Committee for me to speak about “Unsolved problems in mathematics” fills me as it should with considerable trepidation and a prevailing feeling of personal inadequacy. Hilbert gave a talk on this subject at the similar congress about 50 years ago and this is a very formidable precedent. He stated about a dozen unsolved problems in another widely separated areas of mathematics, and they proved to be prototypical for much of the development that followed in the (...) next decades. It would be absolutely foolish, if I tried to emulate this quite singular feat. In addition I do not know the future and the future at any rate can only be predicted ex post with any degree of reliability. I will, therefore, define what I am trying to do in a much more narrow way, hoping that in this manner I have a better chance of not failing. I will limit myself to a particular area of mathematics which I think I know and I will talk about it and about what its open ends appear to be, particularly in some directions which are not the ones that the evolution so far has mainly emphasized and which are, I think, quite important. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:700 jOURNAL OF THE HISTORY OF PHILOSOPHY 33:4 OCTOBER t995 131--35). As we should expect, Dummett's treatment of these and related matters is masterful. Chapters on Husserl and Frege on perception, and on something Dummett calls "Proto-Thoughts," exercise Dummett's peculiar gifts on new ground. The closing chapters bring us round to more familiar Dummettian themes: Since we must conceive of meaning as inextricably a feature of language, the fundamental (...) task will be to describe the character of a theory of meaning for a language. Davidson's work in this direction is subjected to new and interesting criticisms, but for those who see holism as central to the Quine/Davidson outlook, some (but not all) of these criticisms may seem misplaced. Dummett declares that if what someone means is determined by the theory of meaning which implicitly informs their utterances, then "we need to be told by what means I can recognize the other speaker as having the same theory of meaning as I do," and charges Davidson with a commitment to privacy (147ff.). But if"Davidson's holism be emphasized, there is no corroboration of a theory of meaning except rather vaguely in terms of how well it facilitates communication. It is this latter notion which wears the pants ontologically; hence meaning can only misleadingly be said to be a possession of individual speakers, something which a theory of meaning literally describes. A similar objection can be brought against the discussion of Wittgenstein which closes the book: Dummett asserts that Wittgenstein's admonition to chart statement-types rather than try to peer directly at the phenomenon "rests upon a quite definite conception of what meaning consists in" (t64); it is arguable that for Wittgenstein there is no univocally characterizable phenomenon called 'meaning' which that method is meant to capture-no single picture to substitute for the Frege-Russell picture. But on the whole this tightly conceived book is immensely stimulating, and it breaks new ground. As usual, Frege scholars will find much to argue with, direct reference theorists will be provoked, and no one whose ideas are said to be "celebrated" will imagine they are being complimented. Appended to the book is an interview in which Dummett describes the evolution of his philosophical interests. GARY KEMP University of Waikato Alan M. Olson, editor. Heidegger and Jaspers. Philadelphia: Temple University Press, 1994. Pp. viii + 177. Cloth, $44.95. Paper, $19.95. Richard Wisser and Leonard H. Ehrlich, editors. Karl Jaspers: Philosopher among Philosophers/Philosoph unter Philosophen. Wiirzburg: K6nigshausen & Neumann, 1993. Pp. vii + 37o. Paper, $44.oo. Though one of the most pivotal philosophers of the twentieth century, Karl Jaspers is known primarily for the influence he had on other intellectuals of that period, especially Heidegger, as well for challenging his contemporaries to develop a sense of social responsibility in the post-war world. The collection of essays which Alan Olson has assembled not only underscores the originality of Jaspers's thought, but also shows the political context within which Jaspers criticized Heidegger for refusing to recant his BOOK REVIEWS 7Ol allegiance to National Socialism. In this regard, the reader cannot help but notice that there is a political thematic if not an agenda to the organization of the essays. Papers devoted to "Heidegger's Philosophy of Being from the Perspective of His Rectorate" (Leonard Ehrlich), "Shame, Guilt, Responsibility" (Karsten Harries), "The Psychological Dimension in Jaspers's Relationship with Heidegger" (Harold Oliver), "On the Responsibility of Intellectuals" (Joseph Margolis), and "Philosophy and Politics" (Tom Rockmore) serve as much to reveal the inadequacy of Heidegger's political vision as to demonstrate the viability of Jaspers's alternative of combining a post-Enlightenment rationality with an existential philosophy of limits. But despite certain polemical overtones, the volume as a whole is tightly organized, and most of the articles (including the others which I will briefly mention) are of remarkably high quality and thoughtprovoking in their own right. The editor selects a previously unpublished 1954 lecture of Paul Tillich's, "Heidegger and Jaspers," as the inaugural essay in the volume. Tillich points to the uneasy balance between the "existentialist" thrust of Heidegger's early philosophy, and the more "mystical" posture... (shrink)

I wish to discuss some rather incomplete ideas concerning difficulties that arise in some parts of quantum mechanics. In general there have been no serious difficulties when we are dealing with a finite number of particles, but very essential difficulties arise as soon as we treat a system having an infinite number of degrees of freedom; for example, the theory of holes, which, because of the pair generation, requires an indefinite number of particles; also the Dirac non-relativistic theory of light (...) and the Pauli-Heisenberg relativistic quantum electro-dynamics, these being equivalent to systems consisting of an infinite number of particles. (shrink)

Particularly, but not exclusively, in Germany, concerns are uttered as to the consequences of modern biotechnological advances and their range of applications in the field of human genetics. Whereas the proponents of this research are mainly focussing on the possible knowledge that could be gained by understanding the causes of developmental processes and of disease on the molecular level, the critics fear the beginnings of a new eugenics movement. Without claiming a logical relationship between genetic sciences and eugenics movements, it (...) is nevertheless suggested in this article that a connection between both can become established when the distinction between scientifically validated statements on one hand and guiding hypotheses and assumptions on the other hand is blurred, as is observed particularly when scientists report their results to the public. This claim is demonstrated in comparisons between the current state of scientific knowledge on the role of genes in development and causation of diseases, and the way this is presented to the public. It is required that a debate on biotechnology should include reflections on the validity of claims made by scientists. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:700 jOURNAL OF THE HISTORY OF PHILOSOPHY 33:4 OCTOBER t995 131--35). As we should expect, Dummett's treatment of these and related matters is masterful. Chapters on Husserl and Frege on perception, and on something Dummett calls "Proto-Thoughts," exercise Dummett's peculiar gifts on new ground. The closing chapters bring us round to more familiar Dummettian themes: Since we must conceive of meaning as inextricably a feature of language, the fundamental (...) task will be to describe the character of a theory of meaning for a language. Davidson's work in this direction is subjected to new and interesting criticisms, but for those who see holism as central to the Quine/Davidson outlook, some (but not all) of these criticisms may seem misplaced. Dummett declares that if what someone means is determined by the theory of meaning which implicitly informs their utterances, then "we need to be told by what means I can recognize the other speaker as having the same theory of meaning as I do," and charges Davidson with a commitment to privacy (147ff.). But if"Davidson's holism be emphasized, there is no corroboration of a theory of meaning except rather vaguely in terms of how well it facilitates communication. It is this latter notion which wears the pants ontologically; hence meaning can only misleadingly be said to be a possession of individual speakers, something which a theory of meaning literally describes. A similar objection can be brought against the discussion of Wittgenstein which closes the book: Dummett asserts that Wittgenstein's admonition to chart statement-types rather than try to peer directly at the phenomenon "rests upon a quite definite conception of what meaning consists in" (t64); it is arguable that for Wittgenstein there is no univocally characterizable phenomenon called 'meaning' which that method is meant to capture-no single picture to substitute for the Frege-Russell picture. But on the whole this tightly conceived book is immensely stimulating, and it breaks new ground. As usual, Frege scholars will find much to argue with, direct reference theorists will be provoked, and no one whose ideas are said to be "celebrated" will imagine they are being complimented. Appended to the book is an interview in which Dummett describes the evolution of his philosophical interests. GARY KEMP University of Waikato Alan M. Olson, editor. Heidegger and Jaspers. Philadelphia: Temple University Press, 1994. Pp. viii + 177. Cloth, $44.95. Paper, $19.95. Richard Wisser and Leonard H. Ehrlich, editors. Karl Jaspers: Philosopher among Philosophers/Philosoph unter Philosophen. Wiirzburg: K6nigshausen & Neumann, 1993. Pp. vii + 37o. Paper, $44.oo. Though one of the most pivotal philosophers of the twentieth century, Karl Jaspers is known primarily for the influence he had on other intellectuals of that period, especially Heidegger, as well for challenging his contemporaries to develop a sense of social responsibility in the post-war world. The collection of essays which Alan Olson has assembled not only underscores the originality of Jaspers's thought, but also shows the political context within which Jaspers criticized Heidegger for refusing to recant his BOOK REVIEWS 7Ol allegiance to National Socialism. In this regard, the reader cannot help but notice that there is a political thematic if not an agenda to the organization of the essays. Papers devoted to "Heidegger's Philosophy of Being from the Perspective of His Rectorate" (Leonard Ehrlich), "Shame, Guilt, Responsibility" (Karsten Harries), "The Psychological Dimension in Jaspers's Relationship with Heidegger" (Harold Oliver), "On the Responsibility of Intellectuals" (Joseph Margolis), and "Philosophy and Politics" (Tom Rockmore) serve as much to reveal the inadequacy of Heidegger's political vision as to demonstrate the viability of Jaspers's alternative of combining a post-Enlightenment rationality with an existential philosophy of limits. But despite certain polemical overtones, the volume as a whole is tightly organized, and most of the articles (including the others which I will briefly mention) are of remarkably high quality and thoughtprovoking in their own right. The editor selects a previously unpublished 1954 lecture of Paul Tillich's, "Heidegger and Jaspers," as the inaugural essay in the volume. Tillich points to the uneasy balance between the "existentialist" thrust of Heidegger's early philosophy, and the more "mystical" posture... (shrink)

ABSTRACT Apathy may be a Bad Thing, but it is not always bad in the cases and ways it is alleged to be. The charge that the apathetic are irrational often stems from an oversimplification of political decision‐making techniques. The apathetic need not, for example, simply deny the possibility of getting one's goals, or simply ignore the benefits of action. They may, instead, have learned from experience that an avidly desired and pursued goal is always more valued before than after (...) its attainment, and that setting a low initial value on a goal may actually increase its final value. If the values of various alternatives are adjusted in the light of such knowledge, apathy looks much more rational. But that is not the end of the story. The adjustments may be either (i) a conventional and involuntary discounting and surcharging of existing alternatives in the light of known preference patterns, or (ii) a ‘voluntary decision’to value or devalue a goal in order to obtain a certain result. The latter sort of adjustment requires the introduction of new alternatives into the decision problem, and revisions to our notion of when inaction is irrational. (shrink)

William Burnside was one of the three most important algebraists who were involved in the transformation of group theory from its nineteenth-century origins to a deeper twentieth-century subject. Building on work of earlier mathematicians, they were able to develop sophisticated tools for solving difficult problems. His works are of enormous historical importance; they remain also a source of inspiration and information. The works of his contemporaries, such as Klein, Frobenius, Schur, have been published as also have the works of his (...) immediate successors such as Phillip Hall. All of Burnside's papers are reproduced here, organized chronologically and with a detailed bibliography. Walter Feit has contributed a foreword, and a collection of introductory essays are included to provide a commentary on Burnside's work and set it in perspective along with a modern biography that draws on archive material. This is the first reference volume of Burnside's collected papers, enhanced by a series of critical essays on his work, and is important for group theorists and historians and philosophers of mathematics and fills the gap in this area of literature. (shrink)