1. The sequence of the organisation levels is regarded as originating from a sequence of symmetry breakings. Each breaking generates a more improbable structure. In addition to the Euclidian symmetries, homogeneity, isotropy, translation, rotation, helix displacement, neutrality and even indiscernibility can be broken. Here are considered the initial and the subatomic breaking molecular morphogenesis and other higher breakings.2.1 HOMOGENEITY BREAKING OF THE VACUUM SPACE. We studied this as a new model of wave-corpuscle relation. Every noticeable point breaks the space homogeneity. (...) Directed by a momentum this breaking operates as a fissure.2. Postulate of the corpuscle. The quantum mechanical corpuscle is the end of a fissure, the momentum of which characterises direction and velocity.2.2. Postulate of the wave. The associate wave comes from the end of the fissure and works to split the medium.2.3. Corollary to the trajectory. The fissure prefers continuity and a straight line. Nevertheless the fissure can stop at a point and then start from an other point. This discontinuity and any momentum possible discontinuity are limited only by uncertainty relationships; frequency of discontinuity is limited by the first one. Vacuum has no memory of the fissures. 2.4.Corollary to the localisation. The fissure diminishes the medium constraints and allows the medium to vibrate in a domain surrounding the end of the fissure.2.5. Physical analogies. – - Photo-elastic studies of the fissuration of solids show a little sphere and a wavelike perturbation at the end of the fissure. – - A fragile and resonating object can be broken by a sound wave. This crack emits a sound wave. Here we consider one associated wave, emitted and absorbed. – - Broken panes picture an emission of rays. li]2.6. Consequences of the fissure model. (shrink)

Atoms theory and symmetry theory dominated physics. Symmetry propagation and interactions verify the Curie principle. But its violation by symmetry breaking is spontaneous.Fragility is creative. An information breaks a generalized symmetry. Results on symmetry breakings are not valid for fuzzy symmetries. The breaking of a fuzzy symmetry leads only to a pour symmetry. Homogeneity breaking, and atom of time are not usual concepts. We examine in this work symmetry breakings which generate the living time.

Introduction Atoms theory and symmetry theory dominated physics. Symmetry propagation and interactions verify the Curie principle. But its violation by symmetry breaking is spontaneous.Fragility is creative. An information breaks a generalized symmetry. Results on symmetry breakings are not valid for fuzzy symmetries. The breaking of a fuzzy symmetry leads only to a pour symmetry (Fig.1).

Introduction Atoms theory and symmetry theory dominated physics. Symmetry propagation and interactions verify the Curie principle. But its violation by symmetry breaking is spontaneous.Fragility is creative. An information breaks a generalized symmetry. Results on symmetry breakings are not valid for fuzzy symmetries. The breaking of a fuzzy symmetry leads only to a pour symmetry (Fig.1).

In March 2020, the World Health Organization declared the disease caused by SARS-CoV-2 coronavirus “pandemic.” To reduce the risk of contamination, many countries have ordered a lockdown characterized by social distancing and restrictive isolation measures. While the lockdown has proven to be quite effective in terms of physical health, little is known about its impact on couple satisfaction in a dyadic perspective. The current research was a 4-waves longitudinal study with the objective to examine the trajectory of couple satisfaction during (...) the lockdown with a dyadic perspective, including the presence of children at home, the number of hours spent together, and the duration of the relationship as time-invariant predictors and the partner’s couple satisfaction trajectory as a time-varying covariate. Results showed positive intraindividual changes in couple satisfaction during the lockdown, especially an increase in partners’ effectiveness for resolving couple conflicts and a decrease in partners’ aggressiveness. Partners had also perceived the influence of the lockdown as more and more positive over time on couple and family functioning. Finally, the couple satisfaction of both partners changed in tandem during the lockdown: The perception of the couple relationship seems to similarly evolve between partners. (shrink)

In the twenty-first century, the debate about life on other worlds is quickly changing from the realm of speculation to the domain of hard science. Within a few years, as a consequence of the rapid discovery by astronomers of planets around other stars, astronomers very likely will have discovered clear evidence of life beyond the Earth. Such a discovery of extraterrestrial life will change everything. Knowing the answer as to whether humanity has company in the universe will trigger one of (...) the greatest intellectual revolutions in history, not the least of which will be a challenge for at least some terrestrial religions. Which religions will handle the discovery of extraterrestrial life with ease and which will struggle to assimilate this new knowledge about our place in the universe? Some religions as currently practiced appear to only be viable on Earth. Other religions could be practiced on distant worlds but nevertheless identify both Earth as a place and humankind as a species of singular spiritual religious importance, while some religions could be practiced equally well anywhere in the universe by any sentient beings. Weintraub guides readers on an invigorating tour of the world's most widely practiced religions. It reveals what, if anything, each religion has to say about the possibility that extraterrestrial life exists and how, or if, a particular religion would work on other planets in distant parts of the universe. (shrink)

Modern scholars have been concerned with the hostility shown to Alexander by the Hellenistic schools of philosophy. Two literary portraits have been distinguished, the Peripatetic and the Stoic, the former deriving from Theophrastus' book on Callisthenes, or starting with this work the Peripatetics worked out a theory of and applied it to Alexander, in order to belittle his achievements. It was a case of giving sophisticated expression to the kind of crude resentment expressed by Demades.

The locus classicus for Plutarch's own views on his methods is in the Alexander He has begun by asking for the indulgence of his readers if they do not find all the exploits of Alexander and Caesar recounted by the biographer or if they discover him not reporting some famous incident in detail (); and he goes on to compare his own search for evidence which will indicate the kind of soul, with the activity of the painter, who, in order (...) to create a likeness, concentrates on the eyes and pays little attention to the other parts. Commentators and critics have been right to take this as a key text for the purpose of understanding Plutarch's attitude towards his biographical work; nevertheless there are other passages in the Lives where we can at least glimpse his attitude to his subject, and we can only see the Alexander-remarks in correct perspective if we take these other passages into account. I propose therefore, starting with the Alexander, to see how far these critical remarks apply to Plutarch's theory and practice elsewhere in the Lives. (shrink)

According to the Ars Amatoria the notorious rape took place on the occasion of a primitive dramatic entertainment staged in a theatre, in which the seats and furnishings were also primitive. There is no time for a description of the arts of the performers—a tibicen and a ludius—before the Romans, impatient for action, receive their signal from Romulus. Nor is there any mention of a god in whose honour the entertainment had been provided.

This article focuses on the experiences of social care workers during the first wave of the Covid pandemic. The method involved analyzing diaries kept by 65 professionals in 8 French regions during the first lockdown in France in the spring of 2020. As a form of non-binding, narrative expression, keeping diaries breaks with traditional models of reporting common in social care structures and allowed professionals to reflect on the experience as it was lived. In the diaries, professionals explored how the (...) crisis disrupted and challenged their personal and professional values but also allowed innovation in care practices for vulnerable populations that will continue beyond the pandemic period. Five care values were put to forefront by professionals: (1) spontaneity/flexibility; (2) respect for persons; (3) team reflexivity; (4) innovation; (5) solidarity. Mobilizing philosopher Paul Ricoeur’s ideas on recognition, Payet and Laforgue’s analysis of weak actors, as well as research on moral distress, we discuss how these values were tested during the crisis and what effect they had on professionals’ and users’ vulnerabilities. We will also elaborate the interest of keeping account of social care work through narrative methods. (shrink)

The bookplate which Bruno Schulz designed in 1919 for his friend, Stanisław Weingarten, anticipates the motifs of his later literary work: a book, the Book, a collection of books reflecting the collector’s preferences but dependent on the laws undermining the notions of authorship and ownership. Standing on the margin of the artistic and literary scene, Pierrot/schulz acknowledges the relatedness of his and Weingarten’s “private“ vision with the recurrent, universal themes of world art and literature. The scene designed for the emblem (...) of Weingarten’s library demonstrates Schulz’s awareness that the pleasure of discovering spaces of textual cross-fertilizations belongs to the realm of discoveries made by “standard” narratives of psychoanalysis. The scene also demonstrates Schulz’s readiness to imaginatively play with that awareness. The essay traces correspondences between the elements of the 1919 Pierrot ex-libris and the books from Weingarten’s collection which, with time, included and gave privileged position to the works of Bruno Schulz. Among the authors referred to are Rainer Maria Rilke, Alfred Kubin, and Jules Laforgue. (shrink)

Trope theory is a leading metaphysical theory in analytic ontology. One of its classic statements is found in the work of Donald C. Williams who argued that tropes qua abstract particulars are the very alphabet of being. The concept of an abstract particular has been repeatedly attacked in the literature. Opponents and proponents of trope theory alike have levelled their criticisms at the abstractness of tropes and the associated act of abstraction. In this paper I defend the concept of a (...) trope qua abstract particular by rejecting arguments that purport to show that tropes should not be understood as abstract and by arguing that the abstractness of tropes plays an indispensable role in one of our more promising trope-theoretic analyses of universals and of concrete objects. (shrink)

In his 1926 lectures on metaphysical poetry, T. S. Eliot describes the work of Jules Laforgue as the “nearest verse equivalent to the philosophies of Schopenhauer and Hartmann,” a literary rendition of their philosophies of the unconscious and of annihilation.1 Yet, Eliot suggests, in Laforgue the system of Schopenhauer ultimately collapses; the poet does not find in the philosopher that metaphysical balance between thought and feeling he so desperately craves. Schopenhauer’s philosophy, Eliot asserts, is “muddled by feeling—for what (...) is more emotional than the philosophy of Schopenhauer or Hartmann?”2 Here, as elsewhere, Eliot paints Schopenhauer as a despairing, overwrought romantic. Such a presentation naturally.. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:diacritics 35.1 (2005) 3-6MuseSearchJournalsThis JournalContents[Access article in PDF]Whispers of the Flesh Essays in Memory of Pierre KlossowskiIan JamesRussell Ford Pierre Klossowski—novelist, essayist, painter, and translator—was one of the most startling, original, and influential figures in twentieth-century French intellectual culture. The older brother of the well-known painter Balthus and a close associate of Georges Bataille, Klossowski's diverse oeuvre includes novels, philosophical essays, and translations, as well as paintings and films. (...) Confined thus far to an undeserved but somehow fitting shadow existence in the margins and notes of theorists who have become mainstays of Anglo-American criticism, Klossowski's own work has increasingly become a focus of critical interest for its decisive contribution to the development of thought and aesthetics in France from the 1950s onward. Born in 1905, the eldest son of Polish émigrés, Klossowski spent his first ten years in Paris in an artistic milieu, heavily influenced by the neoimpressionism of figures such as Bonnard and Derain. His father, Erich Klossowski de Rola, was a painter and art historian, the author of an important monograph on Daumier. His mother, Baladine, was also a painter and trained under Bonnard. While still a teenager Klossowski was introduced to the German poet Rainer Maria Rilke, with whom he became close and who in turn introduced him to the novelist André Gide. At eighteen he became Gide's secretary and assisted him with the drafts of his famous novel Les faux-monnayeurs.Not until 1930, however, did Klossowski's own career properly begin, when he translated with Jean-Pierre Jouve a collection of poems by Friedrich Hölderlin. Throughout his life Klossowski was a prolific and influential translator from both German and Latin into French, translating amongst others Nietzsche, Kafka, Heidegger, and Wittgenstein from the German, and Suetonius, Virgil, Augustine, and Tertullian from the Latin. While working for the prominent Parisian psychoanalyst René Laforgue, Klossowski published his first philosophical essay on the Marquis de Sade in 1933 in the Revue française de la psychanalyse. Scandalized by Klossowski's Nietzschean-inflected psychoanalytic interpretation of Sade's writing, Laforgue dismissed Klossowski immediately. Throughout the 1930s Klossowski made a number of key friendships and acquaintances, most importantly with Georges Bataille, but also many others, including Walter Benjamin, André Masson, Jean Wahl, and Maurice Heine. During this period he published several articles and collaborated with Bataille on the review Acéphale and in the avant-garde experiment of the Collège de Sociologie (where, it is said, he would attend meetings dressed in a soutane). During the war years Klossowski trained in a number of Catholic seminaries, a vocation which ultimately failed and led to the writing of his first novel, La vocation suspendue. In the postwar period he married [End Page 3] a war widow, Denise Morin Sinclair, who had been interned in Ravensbrück for her activities in the Resistance and who became the model for Roberte, a key figure in much of Klossowski's fiction and painting. After the war Klossowski began to publish the influential works for which he will chiefly be remembered: literary-philosophical essays on Sade and Nietzsche (among others), as well as six important novels written between 1950 and 1965, La vocation suspendue (1950), the three works, originally published separately, which went on to form the Lois de l'hospitalité trilogy—Roberte ce soir (1954), La révocation de l'Édit de Nantes (1959) and Le souffleur ou le théâtre de société (1960)‚—and, finally, Le Baphomet (1965).Klossowski's seminal 1947 work, Sade mon prochain, was one of the first full-length literary and philosophical studies of Sade's work to be published in France and marked a decisive break from earlier accounts. Whereas earlier treatments of Sade had focused either on biographical detail or on the medical and psychosexual import of his life and writing, Klossowski's reading was concerned with the intertwined figures of law and transgression in Sade's work. After Sade mon prochain French intellectuals and writers... (shrink)

Pursuing Justice, Second Edition, examines the issue of justice by considering the origins of the idea, formal systems of justice, current global issues of justice, and ways in which justice might be achieved by individuals, organizations, and the global community. Part 1 demonstrates how the idea of justice has emerged over time, starting with religion and philosophy, then moving to the justice as a concern of the state, and finally to the concept of social justice. Part 2 outlines the very (...) different mechanisms used by various nations for achieving state justice, including systems based on common law, civil law, and Islamic law, with a separate discussion of the US justice system. Part 3 focuses on four contemporary issues of justice: war, genocide, slavery, and the environment. Finally, Part 4 shows how individuals and organizations can go about pursuing justice, and describes the rise of global justice. This updated timely book helps students understand the complexities and nuances of a society's pursuit of justice. It provides students with the foundations of global justice systems, integrating Greek philosophies and major religious perspectives into a justice perspective, and contributes to undergraduate understanding of international justice bodies, NGOs, and institutions. New edition is completely updated and revised to achieve relevance for today's students Covers concepts of justice as well as ideas for pursuing and achieving justice Examines how our modern laws began, and traces their evolution to today's laws Presents concepts and issues in justice studies as well as a comparison of several systems of law Teaching resources include discussion questions and real-world examples. (shrink)

This essay brings psychoanalytic theory on trauma together with film and television criticism on rape narrative in an analysis of Michael Coel’s 2020 series I May Destroy You. Beyond the limited carceral framework of the police procedural, which dislocates the act of violence from the survivor’s history and context, Coel’s polyvalent, looping narrative metabolizes rape television’s forms and genres in order to stage and restage both trauma and genre again and anew. Contesting common conceptions of vulnerability and susceptibility that prefigure (...) a violent breach of autonomy, Coel’s series and her interviews about it invite an ethics of looking that embraces a curiosity in the unknowable and untreatable kernel of subjective experience and defies and resists a policing of the survivor’s thoughts and emotions. By emphasizing and exploring what psychoanalysis calls the “afterwardness” of trauma, Coel foregrounds her main character’s subjectivity prior to her victimization, widens the sphere of consequence beyond the victim and criminal justice system to the survivor’s larger community, and entreats that community to preserve a space for her to look and look again at everything, without judgment. (shrink)

The concept of instantiation is realized differently across a variety of metaphysical theories. A certain realization of the concept in a given theory depends on what roles are specified and associated with the concept and its corresponding term as well as what entities are suited to fill those roles. In this paper, the classic realization of the concept of instantiation in a one-category ontology of abstract particulars or tropes is articulated in a novel way and defended against unaddressed objections.

It is argued that causal understanding originates in experiences of acting on objects. Such experiences have consistent features that can be used as clues to causal identification and judgment. These are singular clues, meaning that they can be detected in single instances. A catalog of 14 singular clues is proposed. The clues function as heuristics for generating causal judgments under uncertainty and are a pervasive source of bias in causal judgment. More sophisticated clues such as mechanism clues and repeated interventions (...) are derived from the 14. Research on the use of empirical information and conditional probabilities to identify causes has used scenarios in which several of the clues are present, and the use of empirical association information for causal judgment depends on the presence of singular clues. It is the singular clues and their origin that are basic to causal understanding, not multiple instance clues such as empirical association, contingency, and conditional probabilities. (shrink)

Effective public policy to mitigate climate change footprints should build on data-driven analysis of firm-level strategies. This article’s conceptual approach augments the resource-based view of the firm and identifies investments in four firm-level resource domains to develop capabilities in climate change impact mitigation. The authors denote the resulting framework as the GISTe model, which frames their analysis and public policy recommendations. This research uses the 2008 Carbon Disclosure Project database, with high-quality information on firm-level climate change strategies for 552 companies (...) from North America and Europe. In contrast to the widely accepted myth that European firms are performing better than North American ones, the authors find a different result. Many firms, whether European or North American, do not just “talk” about climate change impact mitigation, but actually do “walk the talk.” European firms appear to be better than their North American counterparts in “walk I,” denoting attention to governance, information management, and systems. But when it comes down to “walk II,” meaning actual Technology-related investments, North American firms’ performance is equal or superior to that of the European companies. The authors formulate public policy recommendations to accelerate firm-level, sector-level, and cluster-level implementation of climate change strategies. (shrink)

SECTION ONE THE STATE OF OURWORLD It may easily be said that our so called modern twentieth century was one of the most barbaric and wasteful centuries of human history. Here are the statistics: World War I (9.7 million military and 9 ...

In lieu of an abstract, here is a brief excerpt of the content:Summary Of The Spoken Responses By The Poets To Their CriticsJohn HollanderMark Strand responded to Charles Berger’s comments by mak-ing appreciative remarks about the kind of attention his work had received, adding that he did occasionally in writing perceive “glimmers, in the kind of attention I pay, to what Charles Berger has spoken of.” With regard to certain aspects of prior intention, he said that “vague formal imperatives got (...) fulfilled in the writing” and that knowing at the time “the rightness of what I’ve said,” I was nonetheless able to “know the meaning of what I’d said only weeks afterward.” He also acknowledged the kinds of allusiveness which Berger had adduced in his writing, speaking of how and when in the course of writing the resources of his particular sort of echo and allusion seemed to make themselves available.He then turned to the specific question of one of the sequences of poems that Berger had discussed, the “Great Dog Poem No. 2.” He averred that in choosing a dog as speaker he had “not just meant to be funny” [he avowed later on in his remarks that his poems frequently began with “dark humor”] but had also sought for a mode of introspection more original than the fashionably solemn ones of so much contemporary poetry: “I could look within and bark.” With respect to the final line, he observed “I like to finish with a flourish, to pretend I’m Laforgue or Rimbaud,” manifesting “a desire to be a symbolist poet.” With respect to that concluding verse, “I feel like the end of a gorgeous line,” he added that if a dog said that—particularly “a [End Page 189] platinum retriever”—it could not be self-pitying. He spoke in general of the relation of high and low in the poem (a dog named “Rex,” and so forth) and of the relation of this sequence to a much earlier poem of his called “Eating Poetry” in which the speaker is likewise a dog.With regard to formal design, he concluded by saying that in general he tended to start poems “with rough drafts in blank verse” which he then “roughened up” in various ways, preferring as he said “cadences” rather than “measure” in the framing of lines. But he added that in the De Chirico poems he had read, he felt that if one wrote a villanelle, one should keep strictly to the form, without changing words in the refrain lines, and keeping to the iambic meter, saying that “I don’t think you should cheat” under those circumstances.Strand concluded by thanking Berger for the precise nature of his critical attentiveness.John Hollander started out by acknowledging with pleasure that Eleanor Cook’s analysis of his “Owl” had certainly helped him to understand it better; he observed that he felt he had only started to write what he called “real poetry” in his third book, when he had first written a poem he could not understand at the time, and only came to understand years later. He remarked that “The relation of poet and critic as framed by this panel is this: good criticism is a poem’s best friend. We all depend on our friends to point out to us things about ourselves we may not know or acknowledge; although their cousins and other familial relations are other poems, our poems’ best friends are pieces of critical writing.”He was particularly grateful to Cook for pointing out things he hadn’t himself seen—such as the question of the terminal words in the first stanza—but which as a result of the critical insight he had to acknowledge. And this brought up the crucial question of intentionality at the practical rather than theoretical level: in the case of such observations by critics and acknowledgments by poets, it would seem that the writing of a poem could have an intention of which the writer would be unaware. Hollander adduced the analogy of dreaming to poetic composition, paralleling the question “Did you mean to write that?” with (to anyone reporting a dream) “Did you mean to dream that?”He then observed about the... (shrink)

The master narrative of Apartheid South Africa created a specific identity for white boys and men and, together with this identity, a very particular role and place within the South African context. This identity was exemplified in the men who were conscripted into the military from 1967 until 1994, and who participated in operations on the border regions of Namibia and Angola as well as within local townships in the war of liberation against apartheid and minority rule. Many veterans have (...) been left grappling not only with the traumas associated with combat but also with the loss of their identities as war heroes in a country under changed political control. As a result, many of their personal stories and experiences of combat have been silenced by society at large and also, to varying degrees, within their own families, the Church, and among the younger generation who have grown up under a different dispensation. The conflict between vacillating narratives of villains who fought on the wrong side of history and victims of a closed socialisation system has supported the identity struggle faced by many veterans today. Against this backstory, this article explores the effects of storytelling as a trauma release using a narrative approach.Contribution: This article offers a contribution to the use of storytelling in pastoral conversations as a trauma release for untold stories. This insight links to the focus and scope of the journal as a pastoral narrative approach has been used under the umbrella of Practical Theology. (shrink)

Se aborda el problema de qué es una ley científica. Se analiza la concepción tradicional hempeliana sobre la posibilidad de caracterizar una forma lógica para los enunciados de ley científica, que las distinguiría de las regularidades accidentales, concluyendo que ello no es posible. Se analiza entonces el problema de cómo es posible la predicción a partir de enunciados de ley, si no hay diferencia lógica con afirmaciones de regularidad, buscando criterios que permitan el establercimiento de afirmaciones proyectables. Correlativamente se trata (...) el problema de la normatividad de un criterio de identificación de candidatos a enunciados de ley, candidatos que ya no denominamos "lawlike statements" puesto que se ha abandonado la pretensión de que lo que determina los buenos candidatos a leyes sea su forma. A lo largo del texto se analizan de modo argumentado las posiciones filosóficas más tradicionales. Las conclusiones apuntan a la posibilidad de criterios de identificación a leyes sólo parcialmente normativos. (shrink)

In the good old days, when general philosophy of science ruled the Earth, a simple division was often invoked to talk about philosophical issues specific to particular kinds of science: that between the natural sciences and the social sciences. Over the last 20 years, philosophical studies shaped around this dichotomy have given way to those organized by more fine-grained categories, corresponding to specific disciplines, as the literatures on the philosophy of physics, biology, economics and psychology--to take the most prominent four (...) examples--have blossomed. In general terms, work in each of these areas has become increasingly enmeshed with that in the corresponding science itself, increasingly naturalistic (in at least one sense of that term), and in my view, increasingly interesting. (shrink)

In the paper, a detailed analysis of some new logical aspects of Cantor’s diagonal proof of the uncountability of continuum is presented. For the first time, strict formal, axiomatic, and algorithmic definitions of the notions of potential and actual infinities are presented. It is shown that the actualization of infinite sets and sequences used in Cantor’s proof is a necessary, but hidden, condition of the proof. The explication of the necessary condition and its factual usage within the framework of Cantor’s (...) proof makes, Cantor’s proof invalid. It’s shown that traditional Cantor’s proof has a second necessary, but hidden as well, condition which is teleological by its nature, i.e., is not mathematical. The explication of the second necessary condition makes Cantor’s statement on the uncountability of continuum unprovable from the point of view of classical logic.One of the most dramatic facts in history of science is connected just with the notion of actual infinity and consists in the following. On the one hand, Aristotle, Berkeley, Locke, Descartes, Spinoza, Gauss, Kant, Cauchy, Kronecker, Hermite, Poincaré, Bair, Borel, Brouwer, Quine, Wittgenstein, Weyl, Luzin, and a lot of other outstanding creators of classical logic and classical mathematics, during millenniums, stated categorically and insistently warned about that the actual infinity is a self-contradictory notion and its usage in mathematics is inadmissible (e.g., according to Poincare, “There is no actual infinity. - Cantorians forgot that and fell into contradictions. Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered”). On the other hand, a lot of outstanding scientists of the XX c.c., such as Hilbert, Church, Turing, Gödel, etc., and modern axiomatic set theory as a whole ignored this (intuitive though) opinion of genii and accepted Cantor’s “transfinite paradise”, based on the actual infinity. In the paper some logical, philosophical, and psychological aspects of this historical “favorable opposition” are analyzed, and the fact that the scientific intuition of genii has won the historical battle against the mytho-’logic’ of Cantor’s transfinite ‘paradise’ is explained and logically justified. (shrink)

In the paper, a detailed analysis of some new logical aspects of Cantor’s diagonal proof of the uncountability of continuum is presented. For the first time, strict formal, axiomatic, and algorithmic definitions of the notions of potential and actual infinities are presented. It is shown that the actualization of infinite sets and sequences used in Cantor’s proof is a necessary, but hidden, condition of the proof. The explication of the necessary condition and its factual usage within the framework of Cantor’s (...) proof makes, Cantor’s proof invalid. It’s shown that traditional Cantor’s proof has a second necessary, but hidden as well, condition which is teleological by its nature, i.e., is not mathematical. The explication of the second necessary condition makes Cantor’s statement on the uncountability of continuum unprovable from the point of view of classical logic.One of the most dramatic facts in history of science is connected just with the notion of actual infinity and consists in the following. On the one hand, Aristotle, Berkeley, Locke, Descartes, Spinoza, Gauss, Kant, Cauchy, Kronecker, Hermite, Poincaré, Bair, Borel, Brouwer, Quine, Wittgenstein, Weyl, Luzin, and a lot of other outstanding creators of classical logic and classical mathematics, during millenniums, stated categorically and insistently warned about that the actual infinity is a self-contradictory notion and its usage in mathematics is inadmissible (e.g., according to Poincare, “There is no actual infinity. - Cantorians forgot that and fell into contradictions. Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered”). On the other hand, a lot of outstanding scientists of the XX c.c., such as Hilbert, Church, Turing, Gödel, etc., and modern axiomatic set theory as a whole ignored this (intuitive though) opinion of genii and accepted Cantor’s “transfinite paradise”, based on the actual infinity. In the paper some logical, philosophical, and psychological aspects of this historical “favorable opposition” are analyzed, and the fact that the scientific intuition of genii has won the historical battle against the mytho-’logic’ of Cantor’s transfinite ‘paradise’ is explained and logically justified. (shrink)

Author note: Penny A. Weiss, Associate Professor of Political Science at Purdue University, is the author of Gendered Community: Rousseau, Sex, and Politics. Marilyn Friedman, Associate Professor of Philosophy at Washington University, is the author of What Are Friends For? Feminist Perspectives on Personal Relationships and Moral Theory.

Initiated by Robert Wesson, _Evolution and Human Values_ is a collection of newly written essays designed to bring interdisciplinary insight to that area of thought where human evolution intersects with human values. The disciplines brought to bear on the subject are diverse - philosophy, psychiatry, behavioral science, biology, anthropology, psychology, biochemistry, and sociology. Yet, as organized by co-editor Patricia A. Williams, the volume falls coherently into three related sections. Entitled Evolutionary Ethics, the first section brings contemporary research to an area (...) first explored by Herbert Spencer. Evolutionary ethics looks to the theory of evolution by natural selection to find values for human living. The second section, Evolved Ethics, discusses the evolution of language and religion and their impact on moral thought and feeling. Evolved ethics was partly Charles Darwin's subject in _The Descent of Man._ The last section bears the title Scientific Ethics. A nascent field, scientific ethics asks about the evolution of human nature and the implications of that nature for ethical theory and social policy. Together, the essays collected here provide important contemporary insights into what it is - and what it may be - to be human. (shrink)