We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...) Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace −∫ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy. (shrink)

This article seeks to clarify the concept of progress in philosophy. It treats progress as a kind of development. But not every development is a progress. When we talk about progress, what really matters is the direction of development. In some cases it is relatively easy to reach agreement about this direction. But not in the case of philosophy, if we abstract it from the obvious and the trivial, like the number of books on philosophy. As a result, the article (...) concludes that there cannot be progress in philosophy. Instead we see a continual multiplication of interpretations. (shrink)

The paper deals with the possible readings of The Reaper Argument premisses. Some conjectures related to the Stoics’ alleged proof of the argument are discussed.

Knowledge representation, which lies at the core of artificial intelligence, is concerned with encoding knowledge on computers to enable systems to reason automatically. The aims are to help readers make their computer smarter, handle qualitative and uncertain information, and improve computational tractability.

One of the 20th century's most popular non-realistic genre is absurd. The root "absurd," connotes something that does not follow the roots of logic. Existence is fragmented, pointless. There is no truth so the search for truth is abandoned in Absurdist works. Language is reduced to a bantering game where words obfuscate rather elucidate the truth. Action moves outside of the realm of causality to chaos. Absurdists minimalize the sense of place. Characters are forced to move in an incomprehensible, void-like (...) realm. Danish philosopher Sїren Kierkegaard was the first to use the term "absurd" in its modern context. His application of the term related it to, what he considered, the incomprehensibility and unjustifiability of Christianity. Existentialist philosophers such as the Frenchman, Jean-Paul Sartre and the German, Martin Heidegger propagated use of the terms in their work. In the philosophical world of the novel, Albert Camus employed absurdism to portray the difference between man's intent and the resultant chaos he encounters. In modern civilization man is posited as the subject of knowledge in science and technology, animating the utopian projects of industrial civilization, and culminating in great urban conglomerates, as in the sealed universe of commodities which constitutes the omnipresent mall. Technique, defined as the ensemble of means, is the driving force of social development, moreimportant than the ends it is supposed to serve. Unfortunately, technique became an end in itself and the society is organized around it. Of course, we are all aware that we need a certain changes to subdue technique, but I think it is now too late to change the course of technique. However, technique is frequently pictured as the only hope for a better future and the only means of making the world more humane. And that is the sort of statement that French philosopher Jacques Ellul calls the technological bluff. Technology is a discourse on techniques: therefore, the bluff lies not in the failure of techniques as such but in presenting them in a falsely optimistic light. The author formulated in 1954 two laws of technical progress: first, it is irreversible: second, it advances by a geometric progression. Thus, a computer revolution changes nothing in the nature of technical progress, although products are new. This progress is hamperednot by internal mechanisms, but by maladaptation of the social body to it, since society is rooted in the past and constantly refers to it. On the other hand, technique is future oriented and discards as valueless everything that cannot be incorporated into the web of techniques. (shrink)

Книга предназначена для специалистов и всех, кто интересуется этой проблемой.

Several key substantive, methodological, and science-practice issues that concern the field designated as empirical psycho-aesthetics were examined in part I (in the Winter 2012 issue of JAE) of this two-part article. Also presented was an outline of the discipline's origin and its relationship with elder and younger "sisters"—philosophical aesthetics, experimental philosophy, cognitive-science-and-art, (cognitive) neuroscience of art, and neuroaesthetics. The comparative goal was in part approached through the analysis of several recent significant controversies and debates.Here, in the six sections of part (...) II of the article, empirical work on various problems that are relevant to the discussion initiated in part .. (shrink)

In “Elementa Juris Naturalis” (1671) G.W. Leibniz formulated the genius intuition about the fundamental unity of juridical and Aristotelian modalities. Interpreting and explicating this intuition by virtue of the deontic logic G.W. Wright arrived to the conclusion that the unity of modalities in question is not an equivalence relation but an analogy one. However a complement for G.W. Wright’s explication of the intuition of G.W. Leibniz was submitted. This complement was a two-valued algebra of formal-natural-law philosophy of juridical and Aristotelian (...) modalities as moral-legal evaluation-functions determined by one variable. In thepresent paper I submit a binary generalization of the mentioned unary complement. By virtue of this generalization some significant shortcomings of the complement in question are eliminated. The generalization deals with the modalities as moral-legal evaluation-functions determined by two variables. (shrink)

Философия науки возникла в итоге неспособности теории познания ответить на важные вопросы, вставшие перед научным сообществом в конце XIX века. И в дальнейшем философия науки и теория познания шли каждая свом путем, оказывая друг на друга немалое влияние, но ставя и решаявесьма разные задачи. Главным различием между ними является то, что эпистемология является теоретическим видом знания, тогда как философия науки – посттеоретическая дисциплина. Эпистемология – это теория, включающая в себя объяснительную схему, это философский проект познания, это дисциплина, содержащая набор запретов (...) и предписаний. Философия науки представляет собой изучение научногопоиска как состоявшегося реального события, а также экспертную оценку результатов. Философия науки предполагает критическое и рефлексивное сравнение проекта и результата, тогда как теория познания совершенствует нормативы и регулятивы познавательной активности. Там, где теория познания создает метод и сама опирается на метод, философия науки обходится историко‐критической рефлексией, логико-грамматическим анализом, поиском культурных или социальных детерминант. (shrink)

Este livro é o resultado do II Encontro Nacional de Pesquisadores em Filosofia e Psicanálise, realizado em 2006 na Universidade de São Paulo, e reúne vários pesquisadores em torno de três temas - a filosofia após Freud, os problemas ...

Representative models are considered parts of real scientific theories.

The text focuses on reflecting on the role of modern university in a man intellectual development, starting from Nietzsche’s ideas. By drawing up some of the main methodological and philosophical concepts of the German philosopher, the text highlights a series of aspects on the Humboldian nature of current universities – a state of tension under the political, economic and social factors. Thus, the classic concepts of Bildung and Kultur specific to the XIX-century University are analyzed in relation with the crisis (...) that marked the Prussian state of Bismarck period. Higher education being available to the masses is a current problem Nietzsche didn’t avoid to call „savageness” and „decline” of the higher educational system. The purpose of the text is to point out if Nietzsche’s ideas can be still applied nowadays. (shrink)

My dear Aleksandr!I have finally found some quiet time for a slow and attentive read of your article “The Beginning of the Black Notebooks.”1 I very much liked the article, especially for your trul...

This article discusses the connection between the ideas of Fyodor M. Dostoevsky and Vladimir S. Solovyov on the need for cultural and moral transformation of those who would claim to participate in...

Philosopher Vladimir Jankélévitch has only recently begun to receive his due from the English-speaking world, thanks in part to discussions of his thought by Jacques Derrida, Emmanuel Lévinas, and Paul Ricoeur. His international readers have long valued his unique, interdisciplinary approach to philosophy’s greatest questions and his highly readable writing style. Originally published in 1967, Le Pardon, or Forgiveness, is one of Jankélévitch’s most influential works. In it, he characterizes the ultimate ethical act of forgiving as behaving toward the (...) perpetrator as if he or she had never committed the action, rather than merely forgetting or rationalizing it—a controversial notion when considering events as heinous as the Holocaust. Like so many of Jankélévitch’s works, Forgiveness transcends standard treatments of moral problems, not simply generating a treatise on one subject but incorporating discussions of topics such as free will, giving, creativity, and temporality. Translator Andrew Kelley masterfully captures Jankélévitch’s melodic prose and, in a substantive introduction, reviews his life and intellectual contributions. Forgiveness is an essential part of that legacy, and this indispensable English translation provides key tools for understanding one of the great Western philosophers of the twentieth century. (shrink)

The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on: admissible or permissible inference rules the derivability of the admissible inference rules the structural completeness of logics the bases for admissible and valid inference rules. There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered. The book is basically self-contained and special (...) attention has been made to present the material in a convenient manner for the reader. Proofs of results, many of which are not readily available elsewhere, are also included. The book is written at a level appropriate for first-year graduate students in mathematics or computer science. Although some knowledge of elementary logic and universal algebra are necessary, the first chapter includes all the results from universal algebra and logic that the reader needs. For graduate students in mathematics and computer science the book is an excellent textbook. (shrink)

"This personification of wisdom with golden hair and a radiant aura echoes both the eternal feminine and the world soul. Rooted in Christian and Jewish mysticism, Eastern Orthodox iconography, Greek philosophy, and European romanticism, the Sophiology that suffuses Solovyov's philosophical and artistic works is both intellectually sophisticated and profoundly inspiring. Judith Deutsch Kornblatt brings together key texts from Solovyov's writings about Sophia: poetry, fiction, drama, and philosophy, all extensively annotated and some available in English for the first time (with assistance (...) from the translators Boris Jakim and Laury Magnus)."--Amazon website. (shrink)