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)

This article focuses on Alexei Losev’s literary texts that embrace his mythology of music: “I was 19 years old,” “A meteor,” “A woman-thinker,” “The Tchaikovsky trio,” and “An encounter.” It is shown that Losev’s musical mythology developed from his early musical-critical works—through the artistic-mythological episodes of his philosophical works per se —to his fiction of the 1930s. Losev’s intentionally abstract philosophy of music required to be complemented by the artistic, emotional, socially and historically specific expression. The main idea of Losev’s (...) musical myth in its historical-cultural aspect is to reflect the relevant self-consciousness of an individual. The epoch of religious super-individualism and “prayerful delight” is replaced by the epoch of “musical delight” and professed idealization of an individual. This change was a reason of the extreme ambivalence of music, which, on the one hand, expresses the highest order and harmony and, on the other, is a continuous evolvement and chaos, a substantive uncertainty. The novelty of the article consists, firstly, in the analysis of correspondence between musical ambivalence and drama in the lives of the heroes, especially heroines symbolizing music itself; and secondly, in identifying the constant features of Losev’s musical myth, as well as its specific features that emerge at different stages. (shrink)

Сакральная (священное) - одна из самых общих, многозначных и глубоких категорий человеческой культуры. Для специалистов и студентов гуманитарных специальностей.

The article considers A.F. Losev''s philosophy of music in the context ofhis entire religious worldview and as the part of hisChristian-Neoplatonic philosophy. Synthesizing Pythagorean-Platonic andRomantic musical doctrines, Losev concludes: music is the expression ofthe life of numbers, a meonic-hyletic element that rages inside numericconstructions. So it is necessary to analyse the concept of number inthe system of Neoplatonic thought. In the Neoplatonic hierarchy of theuniverse both numeric sphere and music are located at the source of allthe eidei, above them and (...) between the One (the first hypostasis) and theWorld Intelligence (the second hypostasis). Then music is considered inthe context of the relation between the uncreated Absolute (Tetrade A)and the created world (Tetrade B). Losev''s doctrine on the Tetrades Aand B (connected not by essence but by energies) is the importantmodification of Neoplatonism. Finally the article considers Losev''saccount of music in relation to the absolutized individual person. (shrink)

In the 1970s, particularly in his article “The Model of the Text: Meaningful Action Considered as a Text”, Paul Ricœur proposed a hypothesis concerning the homology between the text and social action. That hypothesis is not reducible to the narrative logic prevailing in late Ricœur’s writings, and we are searching to elucidate its further implications in social sciences. A new hermeneutics of social meanings can be founded upon it, enriched by the methodological experience of structural semiotics and taking into account (...) some special processes of sense-giving as “remote-model behavior” and “sense-suppressing action”. . (shrink)

"A consistently clear, comprehensive and accessible introduction which carefully sifts Foucault's work for both its strengths and weaknesses. McHoul and Grace show an intimate familiarity with Foucault's writings and a lively, but critical engagement with the relevance of his work. A model primer." -Tony Bennett, author of Outside Literature In such seminal works as Madness and Civilization, Discipline and Punish , and The History of Sexuality , the late philosopher Michel Foucault explored what our politics, our sexuality, our societal conventions, (...) and our changing notions of truth told us about ourselves. In the process, Foucault garnered a reputation as one of the pre-eminent philosophers of the latter half of the twentieth century and has served as a primary influence on successive generations of philosophers and cultural critics. With A Foucault Primer , Alec McHoul and Wendy Grace bring Foucault's work into focus for the uninitiated. Written in crisp and concise prose, A Foucault Primer explicates three central concepts of Foucauldian theory-discourse, power, and the subject-and suggests that Foucault's work has much yet to contribute to contemporary debate. (shrink)

Talking Politics is a philosophical examination of some of the basic concepts of political discourse. Its primary focus is on the ordinary ; on what is said by politicians, in newspapers and by people in pubs, rather than on the works of political theorists. This is a work of , but not on political theory. Talking Politics is: * Invaluable as a source of reference for students, and contains a detailed index * Arranged thematically, around topics such as `Nation'. Each (...) entry has copious cross-references and suggestions for further reading A. W. Sparkes is uniquely qualified to write such a book, combining some thirty years' teaching as a philosopher with wide experience of, and a life-long fascination with, politics. His attitude is that of a critical, but uncynical, observer. (shrink)

Edited with New Translation by Richard McKirahan With a New Preface by Malcolm Schofield This book is a revised and expanded version of A.H. Coxon's full critical edition of the extant remains of Parmenides of Elea—the fifth-century B.C. philosopher by many considered "one of the greatest and most astonishing thinkers of all times." Coxon's presentation of the complete ancient evidence for Parmenides and his comprehensive examination of the fragments, unsurpassed to this day, have proven invaluable to our understanding of the (...) Eleatic since the book's first publication in 1986. This edition, edited by Richard McKirahan and with a new preface by Malcolm Schofield, is released on the 100th anniversary of Coxon's birth. This new edition for the first time includes English translations of the testimonia and of any Ancient Greek throughout the book, as well as an English/Greek glossary by Richard McKirahan, and revisions by the late author himself. The text consists of Coxon's collations of the relevant folios of manuscripts of Sextus Empiricus, Proclus and Simplicius and includes all extant fragments, a commentary, the testimonia, a complete list of sources, linguistic parallels from both earlier and later authors, and the fullest critical apparatus that has appeared since Diels’ _Poetarum Philosophorum Fragmenta _. The collection of testimonia includes the philosophical discussions of Parmenides by Plato, Aristotle and the Neoplatonists, most of which had been omitted by Diels. The introduction discusses the history of the text, the language and form of the poem, Parmenides’ use and understanding of the verb ‘to be’, his place in the history of earlier and later philosophy and the biographical tradition. In the commentary Coxon deals in detail with both the language and the subject matter of the poem and pays full attention to Parmenides’ account of the physical world. The appendix relates later Eleatic arguments to those of Parmenides. (shrink)

Aṣṭāvakragītā, Hindu philosophical work; retold.