One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the author's lectures, presents several new directions of mathematical research. (...) All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI). (shrink)

The third volume in the distinguished Progress in Self Psychology series brings together the most exciting issues in a rapidly expanding field. _Frontiers in Self Psychology_ is highlighted by sections dealing with self psychology and infancy and self psychology and the psychoses. Clinical contributions include several case studies along with a reconsideration of dream interpretation. Theoretical contributions span issues of gender identity, boundary formation, and the biological foundation of self psychology.

Volume 16 of Progress in Self Psychology, _How Responsive Should We Be_, illuminates the continuing tension between Kohut's emphasis on the patient's subjective experience and the post-Kohutian intersubjectivists' concern with the therapist's own subjectivity by focusing on issues of therapeutic posture and degree of therapist activity. Teicholz provides an integrative context for examining this tension by discussing affect as the common denominator underlying the analyst's empathy, subjectivity, and authenticity. Responses to the tension encompass the stance of intersubjective contextualism, advocacy of (...) "active responsiveness," and emphasis on the thorough-going bidirectionality of the analytic endeavor. Balancing these perspectives are a reprise on Kohut's concept of prolonged empathic immersion and a recasting of the issue of closeness and distance in the analytic relationship in terms of analysis of "the tie to the negative selfobject." Additional clinical contributions examine severe bulimia and suicidal rage as attempts at self-state regulation and address the self-reparative functions that inhere in the act of dreaming. Like previous volumes in the series, volume 16 demonstrates the applicability of self psychology to nonanalytic treatment modalities and clinical populations. Here, self psychology is brought to bear on psychotherapy with placed children, on work with adults with nonverbal learning disabilities, and on brief therapy. Rector's examination of twinship and religious experience, Hagman's elucidation of the creative process, and Siegel and Topel's experiment with supervision via the internet exemplify the ever-expanding explanatory range of self-psychological insights. (shrink)

Volume 17 of Progress in Self Psychology, _The Narcissistic Patient Revisited_, begins with the next installment of Strozier's "From the Kohut Archives": first publication of a fragment by Kohut on social class and self-formation and of four letters from his final decade. Taken together, Hazel Ipp's richly textured "Case of Gayle" and the commentaries that it elicits amount to a searching reexamination of narcissistic pathology and the therapeutic process. This illuminating reprise on the clinical phenomenology Kohut associated with "narcissistic personality (...) disorder" accounts for the volume title. The ability of modern self psychology to integrate central concepts from other theories gains expression in Teicholz's proposal for a two-tiered theory of intersubjectivity, in Brownlow's examination of the fear of intimacy, and in Garfield's model for the treatment of psychosis. The social relevance of self psychology comes to the fore in an examination of the experience of adopted children and an inquiry into the roots of mystical experience, both of which concern the ubiquity of the human longing for an idealized parent imago. Among contributions that bring self-psychological ideas to bear on the arts, Frank Lachmann's provocative "Words and Music," which links the history of music to the history of psychoanalytic thought in the quest for universal substrata of psychological experience, deserves special mention. Annette Lachmann's consideration of empathic failure among the characters in Shakespeare's _Othello_ and Silverstein's reflections on Schubert's self-states and selfobject needs in relation to the specific poems set to music in his Lieder round out a collection as richly broad based as the field of self psychology itself. (shrink)

A collection of thoughtul presentations on transference and countertransference highlights _The Realities of Transference_, Volume 6 in the Progress in Self Psychology series. The selfobject transferences receive special attention. Elsewhere in this volme, selfobject phenomena are examined in relation to the process of working through, the origins of ambition, the psychology of addiction, the psychodynamic consequences of AIDS, and creativity. An exploration of the selfobjects of the second half of life offers new insight into later development.

A special section of papers on the evolution, current status, and future development of self psychology highlights _The Evolution of Self Psychology_, volume 7 of the Progress in Self Psychology series. A critical review of recent books by Basch, Goldberg, and Stolorow et al. is part of this endeavor. Theoretical contributions to Volume 7 examine self psychology in relation to object relations theory and reconsider the relationship of psychotherapy to psychoanalysis. Clinical contributions deal with an intersubjective perspective on countertransference, the (...) trauma of incest, and envy in the transference. (shrink)

_New Therapeutic Visions_ begins with Lachmann and Beebe's developmental perspectives on representational and selfobject transferences, followed by commentaries. In Section II, the self-psychological approach is brought to bear on the clinical treatment of an adolescent girl, incest survivors, addictive personalities, patients exhibiting codependency, and a case of desomatization. Section III, on applied self psychology, contains chapters on the theory of creativity; subjectivism, relativism, and realism in psychoanalysis; and quantum physics and self psychology. The final section offers two critical review essays (...) on major contributions to the self psychology literature by Wolf, by Bacal and Newman, and by Lichtenberg. Stolorow's chronicle of his personal odyssey into self psychology and intersubjectivity theory rounds out volume 8 of the Progress in Self Psychology series. (shrink)

_The Widening Scope of Self Psychology_ is a watershed in the self-psychological literature, being a contemporary reprise on several major clinical themes through which self psychology, from its inception, has articulated its challenge to traditional psychoanalytic thinking. The volume opens with original papers on interpretation by eminent theorists in the self-psychological tradition, followed by a series of case studies and clinically grounded commentaries bearing on issues of sex and gender as they enter into analysis. Two thoughtful reexaminations of the meaning (...) and treatment challenges of chronic rage are followed by clinical papers that focus, respectively, on mourning, alter ego transferences, resistance to change, and pathological identification. Applied analytic contributions and a review of Goldberg's _The_ _Prisonhouse of Psychoanalysis_ round out a collection that testifies not only to the widening scope of self psychology, but to its deepening insights as well. (shrink)

The tenth volume in the Progress in Self Psychology series begins with four timely assessments of the selfobject concept, followed by a section of clinical papers that span the topics of homosexuality, alter ego countertransference, hypnosis, trauma, dream theory, and intersubjective approaches to conjoint therapy. Section III, "A Dialogue of Self Psychology," offers Merton Gill's astute appreciation of "Heinz Kohut's Self Psychology," followed by commentaries by Leider and Stolorow and Gill's reply. The concluding section offers Stolorow and Atwood's "The Myth (...) of the Isolated Mind," followed by discussions by Gehrie and the Shanes. A forum for the kind of spirited, productive exchanges that have long found a home within the self-psychological community, _A Decade of Progress_ builds on the past in responding to the theoretical and clinical challenges of the present. (shrink)

Volume 12 of the Progress in Self Psychology series begins with reassessments of frustration and responsiveness, optimal and otherwise, by MacIsaac, Bacal and Thomson, the Shanes, and Doctors. The philosophical dimension of self psychology is addressed by Riker, who looks at Kohut's bipolar theory of the self, and Kriegman, who examines the subjectivism-objectivism dialectic in self psychology from the standpoint of evolutionary biology. Clinical studies focus on self- and mutual regulation in relation to therapeutic action, countertransference and the curative process, (...) and the consequences of the negative selfobject in early character formation. A separate section of child studies includes a case study exemplifying a self-psychological approach to child therapy and an examination of pathological adaptation to childhood parent loss. With a concluding section of richly varied studies in applied self psychology, _Basic Ideas Reconsidered_ promises to be basic reading for all students of contemporary self psychology. (shrink)

Volume 13 provides valuable examples of the very type of clinically grounded theorizing that represents progress in self psychology. The opening section of clinical papers encompasses compensatory structures, facilitating responsiveness, repressed memories, mature selfobject experience, shame in the analyst, and the resolution of intersubjective impasses. Two self-psychologically informed approaches to supervision are followed by a section of contemporary explorations of sexuality. Contributions to therapy address transference and countertransference issues in drama therapy, an intersubjective approach to conjoint family therapy, and the (...) subjective worlds of profound abuse survivors. A concluding section of studies in applied self psychology round out this broad and illuminating survey of the field. (shrink)

1. Die Hymnen des Rigveda, herausgegeben Oldenberg von Hermann. Band.I. Metrische und Textgeschichtliche Prolegomena. Berlin, 1888. 14 Mk.2. Vedische Studien, Pischel von Richard und Karl F. Geldner. Stuttgart, 1888–1889. 12 Mk.

I present a formally explicit statement of Church's celebrated argument against Carnap's analysis of belief and defend it against well-known objections by W.V.O. Quine, R.M. Martin, and Michael Dummett.

W.V.O. Quine has famously objected that (1) properties are philosophically suspect because (2) there is no entity without identity and (3) the synonymy criterion for property identity won't do because there's no such concept as synonymy. (2) and (3) may or may not be right but do not prove (1). I reply that Leiniz's Law handles property identity, as it does for everything else, then respond to a variety of objections and confusions.

It is sometimes said that there are two, competing versions of W. V. O. Quine’s unrelenting empiricism, perhaps divided according to temporal periods of his career. According to one, logic is exempt from, or lies outside the scope of, the attack on the analytic-synthetic distinction. This logic-friendly Quine holds that logical truths and, presumably, logical inferences are analytic in the traditional sense. Logical truths are knowable a priori, and, importantly, they are incorrigible, and so immune from revision. The other, radical (...) reading of Quine does not exempt logic from the attack on analyticity and a priority. Logical truths and inferences are themselves part of the web of belief, and the same global methodology applies to logic as to any other part of the web, such as theoretical chemistry or ordinary beliefs about ordinary objects. Everything, including logic, is up for grabs in our struggle for holistic confirmation. The purpose of this paper is to examine the law of non-contradiction, and the concomitant principle of ex falso quodlibet, from the perspective of the principles advocated by the radical Quine. I show that he has no compelling reason to accept either of these. To put it bluntly, neither the law of non-contradiction nor the rule of ex falso quodlibet is empirically confirmed, and these principles fare poorly on the various criteria for theory acceptance on the methodology of the radical Quine. So the radical Quine is led rather quickly and rather directly into something in the neighborhood of Graham Priest’s dialetheism. (shrink)

Bd. 1. Philosophische Schriften, I (1925-1933).--Bd. 2. Philosophische Schriften, II (1933-1938).--Bd. 3. Der Mensch, Seine Natur und seine Stellung in der Welt : textkritische Edition (2 v.).--Bd. 4. Philosophische Anthropologie und Handlungslehre -- Bd. 5. Urmensch und Spätkultur, sowie weitere Schriften zu einer Theorie der Institutionen -- Bd. 6. Die Seele im technischen Zeitalter und andere socialpsychologische, soziologische und kulturanalytische Schriften --Bd. 9. Zeit-Bilder und andere kunstsoziologische Schriften.

This is a series of lectures on formal decision theory held at the University of Bayreuth during the summer terms 2008 and 2009. It largely follows the book from Michael D. Resnik: Choices. An Introduction to Decision Theory, 5th ed. Minneapolis London 2000 and covers the topics: -/- Decisions under ignorance and risk Probability calculus (Kolmogoroff Axioms, Bayes' Theorem) Philosophical interpretations of probability (R. v. Mises, Ramsey-De Finetti) Neuman-Morgenstern Utility Theory Introductory Game Theory Social Choice Theory (Sen's Paradox of Liberalism, (...) Arrow's Theorem) . (shrink)

Mont Publishing House and Valery Vino deliver the first volume of an eclectic collection in aesthetic education. Aesthetic Literacy is an experiment in philosophy of culture, and this volume features cross-genre contributions by: Theodore Gracyk (Minnesota), Babette Babich (Fordham), David Konstan (NYU), Katya Mandoki (UNAM), Arnold Berleant (Long Island), Jale Erzen (Middle East Tech), Curtis Carter (Marquette), Clive Cazeaux (Cardiff), Fabrizio Desideri (Florence), Ken-ichi Sasaki (Tokyo), and many others... -/- .

В книге очерки Владимира Брагинского в жанре ироничного эссе о любви.

The article is devoted to the memory of Vyacheslav Semenovich Stepin and Nikita Nikolaevich Moiseev, whose multifaceted work was integrally focused on philosophical, interdisciplinary and transdisciplinary research of the key ideas and principles of universal human-dimensional evolutionism. Other remarkable Russian scientists V.I. Vernadsky, S.P. Kurdyumov, S.P. Kapitsa, D.S. Chernavsky worked in the same tradition of universal evolutionism. While V.I. Vernadsky and N.N. Moiseev had been the originators of that scientific approach, V.S. Stepin provided philosophical foundations for the ideas of those (...) remarkable scientists and thinkers. The scientific legacy of V.S. Stepin and N.N. Moiseev maintained the formation of a new quality of research into the philosophy of science and technology as well as into the philosophy of culture. This new quality is multidimensional and it is difficult to define unambiguously, but we presume the formation of those areas of philosophical knowledge as constructively oriented languages of interdisciplinary and transdisciplinary co-participation of philosophy in the convergent-evolutionary development of scientific knowledge in general. In this regard, attention is paid to V.S. Stepin’s affirmations about non-classical nature of modern social and humanitarian knowledge. Quantum mechanics teaches us that the reality revealed through it is a hybrid construct, or symbiosis, of both mean and object of cognition. Therefore, the very act of cognitive observation constructs quantum reality. Thus, it is very close to the process of cognition in modern sociology and psychology. V.S. Stepin insisted that these principles are applicable to all complex selfdeveloping systems, and such are all “human-dimensional” objects of modern humanities. In all the phases of homeostasis changes, or crises, there is necessarily a share of chaos, instability, uncertainty in the selection process of future development scenarios, which is ineliminably affected by our observation. Therefore, a cognitive observer in the humanities should be considered as a concept of post-non-classical rationality, that is as an observer of complexity. (shrink)

Quantum cognition in decision making is a recent and rapidly growing field. In this paper, we develop an expected utility theory in a context of non-classical uncertainty. We replace the classical state space with a Hilbert space which allows introducing the concept of quantum lottery. Within that framework, we formulate axioms on preferences over quantum lotteries to establish a representation theorem. We show that demanding the consistency of choice behavior conditional on new information is equivalent to the von Neumann–Lüders postulate (...) applied to beliefs. A dynamically consistent quantum-like agent may violate dynamic recursive consistency, however. This feature suggests interesting applications in behavioral economics as we illustrate in an example of persuasion. (shrink)

In this article, Savage’s theory of decision-making under uncertainty is extended from a classical environment into a non-classical one. The Boolean lattice of events is replaced by an arbitrary ortho-complemented poset. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. Then, we discuss the issue of beliefs updating and investigate a transition probability model. An application to a simple game context is proposed.

Under the conditions of the revolution in science and technology, of tremendous social changes, of the tempestuous and significant growth in the prestige of scientific knowledge, and of the exacerbation of the ideological struggle, there has been an immeasurable broadening of the social tasks and spheres of operation of such social phenomena as scientific criticism and self-criticism. Study of social, theoretical, and psychological cross-sections of these phenomena is one of the necessary conditions for cultivating lofty civic qualities, a communist world-view, (...) and the moral and aesthetic improvement of the individual. Special attention is directed to the socializing function of criticism and self-criticism in the Program of the CPSU, the materials of the Twenty-fourth Congress of the CPSU, and the resolutions of the Central Committee of the CPSU "On Literary and Artistic Criticism" and "On the State of Criticism and Self-Criticism in the Tambov Regional Party Organization." Scientific criticism reveals the extent to which the results or processes of practical activity are in accord with communist ideals and to what degree the moral and aesthetic norms of individuals and collectives are an expression of proletarian and general human culture. This is a distinctive intellectual and theoretical form of solution of social contradictions. Criticism is organically interwoven into theoretical and practical human activity. It breaks down old and established social traditions and customary values and impels human thought to undertake scientific quests. It does not permit society to content itself merely with its past triumphs. Scientific criticism arouses and cultivates class consciousness and provides an evaluation of social phenomena from the standpoint of the progressive class. Under the conditions of developed socialist society, criticism and self-criticism become an active means for improving ideological, political, and educational work, the development of the toilers' creative capacities, and activation of the sociopolitical and intellectual life of society. (shrink)

Автор предлагает читателю новую психоантропологическую концепцию человеческой агрессии. Анализируя последствие 4000 лет мировой истории, он приходит к выводу, что истоки агрессии заложены в нарастающей мутации души, деформации генофонда. Для специалистов.

-- v. 2. Pami︠a︡ti Vitalii︠a︡ Ivanovicha Svint︠s︡ova.