Bibliography of A. A. Fraenkel (p. ix-x)--Axiomatic set theory. Zur Frage der Unendlichkeitsschemata in der axiomatischen Mengenlehre, von P. Bernays.--On some problems involving inaccessible cardinals, by P. Erdös and A. Tarski.--Comparing the axioms of local and universal choice, by A. Lévy.--Frankel's addition to the axioms of Zermelo, by R. Mantague.--More on the axiom of extensionality, by D. Scott.--The problem of predicativity, by J. R. Shoenfield.--Mathematical logic. Grundgedanken einer typenfreien Logik, von W. Ackermann.--On the use of Hilbert's [epsilon]-operator in scientific theories, (...) by R. Carnap.--Basic verifiability in the combinatory theory of restricted generality, by H. B. Curry.--Uniqueness ordinals in constructive number classes, by H. Putnam.--On the construction of models, by A. Robinson.--Interpretation of mathematical theories in the first order predicate calculus, by T. Skolem.--The elementary character of two notions from general algebra, by R. Vaught.--Foundations of arithmetic and analysis. Axiomatic method and intuitionism, by A. Heyting.--On rank-decreasing functions, by G. Kurepa.--On non-standard models for number theory, by E. Mendelson.--Concerning the problem of axiomatizability of the field of real numbers in the weak second order logic, by A. Mostowski.--Non-standard models and independence of the induction axiom, by M. O. Rabin.--Sur les ensembles raréfiés de nombres naturels, par W. Sierpinski.--Philosophy of logic and mathematics. Remarks on the paradoxes of logic and set theory, by E. W. Beth.--Logique formalisée et raisonnement juridique, par R. Feys.--Im Umkreis der sogenannten Raumprobleme, von H. Freudenthal.--Process and existence in mathematics, by H. Wang. (shrink)

This is a chapter of a collective volume of Rawls's and Harsanyi's theories of distributive justice. It focuses on Harsanyi's important Social Aggregation Theorem and technically reconstructs it as a theorem in welfarist social choice.

At the beginning of his influential De Nominum Analogia, Thomas de Vio Cajetan mentions three mistaken positions on analogy. He does not attach names to these positions, but each one was held by distinguished Thomists of the fourteenth and fifteenth centuries. Furthermore, their proponents were responding to the same set of challenges from John Duns Scotus that set the agenda for the De Nominum Analogia. In this paper, I would like to do something that Cajetan did not do, and that (...) is, directly consider the merits of the first position in his list of mistaken accounts of analogy; namely, the position that analogy is constituted by disjunction. More specifically, this paper investigates the polemical use for which Hervaeus Natalis deployed analogy of disjunction; the reply of John Duns Scotus; and the implications of this back and forth for understanding the Thomist-Scotist dispute over the concept of being. (shrink)

In this paper, I offer a defence of aesthetic education in terms of aesthetic experience, claiming that aesthetic experience and art appreciation is a vital component of a flourishing life. Given schools have an important role to play in helping prepare young people for their adult lives, it is crucial they should consider how best to equip students with the means to achieve a flourishing life. It is on these grounds I defend arts education as compulsory across the curriculum. In (...) order to adopt this position, I firstly critically engage with two competing defences of including the arts on the curriculum on the basis of firstly, the role art has to play in supporting self-expression, and secondly, a defence of the arts in relation to their role in supporting moral improvement. After explaining why these arguments fail to do the work required to defend aesthetic education as thoroughly as is needed, I turn to the defence based on aesthetic experience because it allows for a defence of the arts to be made on the basis of art’s distinctive value. (shrink)

We outline a class of term-languages for epistemic grounding inspired by Prawitz’s theory of grounds. We show how denotation functions can be defined over these languages, relating terms to proof-objects built up of constructive functions. We discuss certain properties that the languages may enjoy both individually and with respect to their expansions. Finally, we provide a ground-theoretic version of Prawitz’s completeness conjecture, and adapt to our framework a refutation of this conjecture due to Piecha and Schroeder-Heister.

À partir d'une prise en compte de la réflexion actuelle sur la complexité du temps, illustrée par le déploiement des temps dans 1a pratique psychanalytique, il est possible de montrer qu'une spécificité chrétienne du temps est repérable, malgré la diversité des modèles théologiques qui ont pu ou peuvent en rendre compte. C'est la dimension eschatologique de ce temps chrétien qui est par elle-même significative pour nos contemporains, pourvu que les représentations qu'elle véhicule soient soumises à une régulation critique.From a consideration (...) of present day reflection on the complexity of time, illustrated by the unfolding of time in psychoanalytic practice, it is possible to show that a Christian specificity of time can be located in spite of the diversity of theological models that could have or can give an account of it. It is the eschatological dimension of itself significant for our contemporaries, as long as the representations which it transmits are controlled by critical rules. (shrink)

The Greeks have long been regarded as innovators across a wide range of fields in literature, culture, philosophy, politics and science. However, little attention has been paid to how they thought and felt about novelty and innovation itself, and to relating this to the forces of traditionalism and conservatism which were also present across all the various societies within ancient Greece. What inspired the Greeks to embark on their unique and enduring innovations? How did they think and feel about the (...) new? This book represents the first serious attempt to address these issues, and deals with the phenomenon across all periods and areas of classical Greek history and thought. Each chapter concentrates on a different area of culture or thought, while the book as a whole argues that much of the impulse towards innovation came from the life of the polis which provided its setting. (shrink)

It is almost universally believed that in quantum theory the two following statements hold: all transformations are achieved by a unitary interaction followed by a von-Neumann measurement; all mixed states are marginals of pure entangled states. I name this doctrine the dogma of purification ontology. The source of the dogma is the original von Neumann axiomatisation of the theory, which largely relies on the Schrődinger equation as a postulate, which holds in a nonrelativistic context, and whose operator version holds only (...) in free quantum field theory, but no longer in the interacting theory. In the present paper I prove that both ontologies of unitarity and state-purity are unfalsifiable, even in principle, and therefore axiomatically spurious. I propose instead a minimal four-postulate axiomatisation: associate a Hilbert space \ to each system \; compose two systems by the tensor product rule \; associate a transformation from system \ to \ to a quantum operation, i.e. to a completely positive trace-non-increasing map between the trace-class operators of \ and \; evaluate all joint probabilities through that of a special type of quantum operation: the state preparation. I then conclude that quantum paradoxes—such as the Schroedinger-cat’s, and, most relevantly, the information paradox—are originated only by the dogma of purification ontology, and they are no longer paradoxes of the theory in the minimal formulation. For the same reason, most interpretations of the theory interpret the same dogma, not the strict theory stripped of the spurious postulates. (shrink)

T. 1. Metodologicheskie osnovanii︠a︡ i modeli, Bogopoznanie i nauchnoe znanie -- t. 2. Chislo. Garmonii︠a︡. Metafizika Sveta -- t. 3. Svet bogoslovskie osnovanii︠a︡ kreatologi.

Chronic pain patients often miss receiving acknowledgement for the multidimensional struggles they face with their specific conditions. People suffering from chronic pain experience a type ofinvisibilitythat is also borne by other chronically ill people and their respective medical conditions. However, chronic pain patients face both passive and active exclusion from social participation in activities like family interactions or workplace inclusion. Although such aspects are discussed in the debates lead by the bio-psycho-social model of pain, there seems to be a lack (...) of a distinct interest in assessing more specifically the social aspects regarding chronic pain. As a result, the social aspects have yet to be taken into a more thorough theoretical consideration of chronic pain and to be practically implemented to help affected patients. By addressing chronic pain patients’ struggle for recognition, this paper attempts to shed light on some of these social aspects. We base this attempt on a theoretical framework that combines patients’ statements with an adaptation of Axel Honneth’s social-philosophical work onrecognition. Thus, this paper tries to make a suggestion on how the bio-psycho-social model of pain can live up to its name by helping to address more adequately some of the more neglected aspects in chronic pain patients’ suffering than has been possible to date. (shrink)

This article is a continuation of Part I, which looked at the relationship between Confucianism and Daoism by first introducing general approaches, before moving on to (1) perspectives on names and actualities; (2) cultivation, learning, the natural; and (3) conceptions of the person. Continuing with the theme‐based comparison of Confucianism and Daoism by looking specifically at the Lunyu 論語 (Analects of Confucius), Daodejing 道德經 (Classic of the Way and Virtuosity) or Laozi 老子 (Book of Master Lao), and the Zhuangzi 莊子 (...) (Book of Master Zhuang), this article looks at (1) politics, nonaction (wuwei 無為), and virtuosity (de 德); (2) morality, virtues, and human nature (xing 性); and finally (3) Dao 道, or “the way.” It references Part I, and while it can be read independently, it is best taken as a continuation of Part I. The conclusion included herein summarizes both Part II and Part I. (shrink)

Ce texte a déjà paru dans ÉTUDES/INUIT/STUDIES, 24, no 2, 2000, p. 89-113. Québec : Département d'anthropologie de l'Université Laval. Nous remercions Bernard Saladin d'Anglure de nous avoir autorisé à le reproduire ici. Résumé : Les rites inuit de la première fois, qui célèbrent les premières performances effectuées par les enfants et les adolescents inuit, ont été souvent mentionnés par les ethnographes de l'Arctique mais jamais véritablement analysés comme « séquence cérémonielle », pour - Anthropologie.

L'intention fondamentale de la métaphysique de l'Ecole peut-elle encore être reprise dans le contexte de la philosophie actuelle ? Cette intention est double. D'abord elle vise à parler de la réalité elle-même ou du réel tel qu'il est en soi. Ensuite elle prétend découvrir quelque chose concernant le fondement ultime de cette réalité. La phénoménologie semble condamner cette entreprise à un échec inévitable en prétendant que le réel ne se manifeste que dans la rencontre de l'homme avec lui. Ce que (...) nous connaissons portera donc toujours l'empreinte de notre présence et ne sera donc jamais le réel en lui-même. Heidegger ne semble pas moins nous éloigner de l'ancien problème de la métaphysique. Dans son intention de l'approfondir, il semble plutôt en écarter le problème pour le remplacer par un autre. Sa méditation porte en effet sur la lumière originelle -toujours oubliée -dans laquelle le monde se révèle à nous, mais il ne semble pas en arriver à réfléchir sur ce qui devient visible grâce à cette lumière. Il semble pourtant que, tant l'idée de rencontre que celle de lumière originelle élimine si peu l'affirmation du réel lui-même, qu'elles le supposent plutôt, aussi longtemps qu'on veut éviter l'idéalisme le plus radical. Or, c'est sur le sens de cette affirmation implicite et sur le réel visé par elle que la métaphysique de l'Ecole veut réfléchir. Mais un second obstacle risque de faire échouer cette tentative. Le réel n'est-il pas individuel, temporel, irréductible ? N'est-ce pas dès lors impossible d'en parler, puisque notre langue n'est faite que de concepts généraux et intemporels ? A cette question, on peut d'abord répondre que tout notre appareil de concepts généraux est soutenu par un moment de contact avec le réel lui-même. Seulement ceci ne semble pas encore nous avancer beaucoup. En effet, cette saisie intuitive n'est-elle pas condamnée à rester implicite et muette ? Une issue à ce problème nous semble possible en poursuivant la ligne de réflexion de l'ancienne théorie de l'illumination. C'est en réfléchissant sur les caractéristiques de la vérité telle qu'elle nous est accessible, que nous pourrions arriver à dire quelque chose du concret lui-même. En effet, il se manifeste à nous comme étant inséré dans la totalité du réel qui nous est ouverte dans une sorte d'ouverture antécédente et constitutive de notre existence. Or ces deux aspects, qu'on ne saurait nier sans totalement exclure l'homme du royaume de la vérité, semblent postuler la Présence Totale de l'Origine dans la moindre parcelle du réel. Cette présence devient consciente et éclairante dans l'existence humaine. (shrink)

We propose a kernel method for using combinations of features across example pairs in learning pairwise classifiers. Pairwise classifiers, which identify whether two examples belong to the same class or not, are important components in duplicate detection, entity matching, and other clustering applications. Existing methods for learning pairwise classifiers from labeled training data are based on string edit distance or common features between two examples. However, if two examples from the same class have few common features, these methods have difficulties (...) in finding these pairs and achieving high recall. One typical example is to check whether two abbreviated author names in different citations refer to the same person or not. Since similarities between examples from the same class become close to zero, classifiers fail to distinguish positive pairs from negative pairs. One approach to avoiding the problem of zero similarities is using conjunctions of different features across examples, but implementing this idea straightforwardly makes the computational cost prohibitive for practical problems. Using a kernel on pair instances, our method can use feature conjunctions across examples without actually doing feature mappings, which are computationally expensive. The kernel is a tensor product of two inner products on the original feature space. The corresponding feature mapping generates conjunctions of features only across the two different examples while that of the conventional polynomial kernel also generates conjunctions of features from the same example, which are irrelevant to pairwise classification and cause deterioration of accuracy. Our experiments on the author matching problem show that this method can give a precision 4 to 8 times higher than that of previous methods at medium recall levels. (shrink)

This essay offers a critique of the culture of specio-vocationalism in American higher education by first drawing on Edmund Husserl’s conception of “world” and connecting this notion to education conceived as a “world-disclosing” activity. The essay will then give an account of how the trends of vocationalization and specialization manifest themselves in contemporary university culture, and how they work together to “de-world” the lives of our students and deprive them of possibilities that are part of what it means to be (...) human. After showing how this impoverishment undermines the world-disclosing function of higher education, the essay will then suggest one way to counter this “de-worlding of world”: the teaching of the situated finitude of the human condition by reminding our students that our knowledge or sense of the world is always only partial. It is this realization that has the potential of placing our students once again before the vastness of the world in wonder and curiosity. In this realization they will gain a better sense of the world as a distant horizon still to be explored in all of its inexhaustible complexity and meaning. At the same time, coming to grips with their own ignorance will imbue them with an intellectual humility that will shield them not only from their own finitude, but the finitude of others as well. (shrink)

Routledge is proud to reissue these nine pivotal titles from the acclaimed series Studies in Ethics and the Philosophy of Religion. Including key works by Ahern, Beardsmore, Pike, and others, these books are essential for all serious collections. Available as single volumes or as a nine-volume set, the titles in this collection were originally published between 1950-1960 by Routledge and Kegan Paul: Volume 1: The Problem of Evil M.B. Ahern Hb: 0-415-31841-6 Volume 2: Moral Reasoning R.W. Beardsmore Hb:0-415-31842-4 Volume 3: (...) Theology and Intelligibility Michael Durrant Hb: 0-415-31843-2 Volume 4: Humanism and Ideology James R. Flynn Hb: 0-415-31844-0 Volume 5: The Five Ways: St.Thomas Aquinas' Proofs of God's Existence Anthony Kenny Hb: 0-415-31845-9 Volume 6: Moral Practices D.Z. Phillips Hb: 0-415-31846-7 Volume 7: God and Timelessness Nelson Pike Hb: 0-415-31847-5 Volume 8: Without Answers Rush Rhees Hb: 0-415-31848-3 Volume 9: Morality and Purpose J.L. Stocks Hb: 0-415-31849-1. (shrink)

On se souvient de la formule de Churchill : " La démocratie est le pire des régimes, à l'exception de tous les autres". A l'évidence, nous n " aimons " pas la démocratie. Et pourtant nous sommes tous démocrates... Étrange procès en désamour que celui-là, dont la virulence égale l'ancienneté : toute petite déjà, à Athènes, la démocratie ne manquait pas de détracteurs... Myriam Revault d'Allonnes s'interroge, non pas sur les critiques ou les sarcasmes dont la démocratie est l'objet, mais (...) sur la nature de l'expérience démocratique, travaillée par l'incertitude, le conflit, l'inachèvement, inextricablement liée à ce qui s'oppose à elle et la menace. Comment l'homme démocratique, confronté à cette existence toujours problématique, ne serait-il pas en proie à l'insatisfaction et à la déception permanentes? Cependant, si nous n' "aimons" pas la démocratie, pouvons-nous ne pas la vouloir? Car c'est bien l'expérience démocratique qui fait de nous des sujets éthiques et politiques, des citoyens qui ne veulent pas être ainsi gouvernés : " pas comme ça, pas pour ça, pas par eux ". (shrink)