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)

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)

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)

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

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)

The purpose of this book is to trace the main developments in Greek philosophy during the period which runs from the death of Alexander the Great in 323 B.c. to the end of the Roman Republic. These three centuries, known to us as the Hellenistic Age, witnessed a vast expansion of Greek civilization eastwards, following Alexander's conquests; and later, Greek civilization penetrated deeply into the western Mediterranean world assisted by the political conquerors of Greece, the Romans. But philosophy throughout this (...) time remained a predominantly Greek activity. The most influential thinkers in the Hellenistic world were Stoics, Epicureans and Sceptics. This book gives a concise critical analysis of their ideas and their methods of thought. The last book in English to cover this ground was written sixty years ago. In the interval the subject has moved on, quite rapidly since the last war, but most of the best work is highly specialized. There is a clear need for a general appraisal of Hellenistic philosophy which can provide those who are not specialists with an up-to-date account of the subject. Hellenistic philosophy is often regarded as a dull product of second-rate thinkers who are unable to stand comparison with Plato and Aristotle. This book will help to remove such misconceptions and arouse wider interest in a field which is fascinating both historically and conceptually. (shrink)

Background: Increasing collaboration between industrialised and developing countries in human research studies has led to concerns regarding the potential exploitation of resource deprived countries. This study, commissioned by the former National Bioethics Advisory Commission of the United States, surveyed developing country researchers about their concerns and opinions regarding ethical review processes and the performance of developing country and US international review boards .Methods: Contact lists from four international organisations were used to identify and survey 670 health researchers in developing countries. (...) A questionnaire with 169 questions explored issues of IRB review, informed consent, and recommendations.Results: The majority of the developing country researchers were middle aged males who were physicians and were employed by educational institutions, carrying out research on part time basis. Forty four percent of the respondents reported that their studies were not reviewed by a developing country IRB or Ministry of Health and one third of these studies were funded by the US. During the review process issues such as the need for local language consent forms and letters for approval, and confidentiality protection of participants were raised by US IRBs in significantly higher proportions than by host country IRBs.Conclusion: This survey indicates the need for the ethical review of collaborative research in both US and host countries. It also reflects a desire for focused capacity development in supporting ethical review of research. (shrink)

The objective of this paper is to develop neutrosophic quadruple algebraic hyperstructures. Specifically, we develop neutrosophic quadruple semihypergroups, neutrosophic quadruple canonical hypergroups and neutrosophic quadruple hyperrings and we present elementary properties which characterize them.

The philosophy of Epictetus, a freed slave in the Roman Empire, has been profoundly influential on Western thought: it offers not only stimulating ideas but practical guidance in living one's life. A. A. Long, a leading scholar of later ancient philosophy, gives the definitive presentation of the thought of Epictetus for a broad readership. Long's fresh and vivid translations of a selection of the best of Epictetus' discourses show that his ideas are as valuable and striking today as they were (...) amost two thousand years ago. This is a book for anyone interested in what we can learn from ancient philosophy about how to live our lives. (shrink)

Background: The magnitude of bullying and harassment among psychiatrists is reportedly high, yet no peer-review published studies addressing this issue could be found. Therefore, it was decided to conduct a pilot study to assess the degree of the problem, the types of bullying/harassment and to provide some insights into the situation.Methods and Principal Findings: Following multiple focus group meetings, a yes/no response type questionnaire was developed to assess the degree and type of bullying and harassment experienced by psychiatrists. Over a (...) 3-month period the questionnaire was administered to a random sample of 60 psychiatrists. 57 out of the 60 psychiatrists reported harassment and bullying. Frequencies of the following response variables are presented in descending order: rumours 40% ; defamation 20% ; passing remarks 20% ; false accusations 15% ; threats 13.3% ; verbal abuse 13.3% ; unjustified complaints 13.3% ; promotion blocked 13.3% ; humiliation 13% ; bad reference given 10% ; credentials questioned 8.3% ; physical attacks 5% ; termination 5% ; derogatory remarks 1.7% and 1.7% were subjected to personal work. As a result of being subjected to harassment, 66.7% of the psychiatrists did not take any action, whereas 33.3% confronted the person they believed responsible. Asked whether the bullying and harassment caused distress, 18.3% of the psychiatrists did not report any effect, 30% reported mild distress, 40% moderate distress and severe distress was reported by 11.7%.Conclusions: It was concluded that the magnitude of bullying and harassment among psychiatrists may be quite high, as evidenced by this pilot study. There is a need for extensive systematic studies on this subject and to establish strategies to prevent and address this issue at a national and regulatory level. (shrink)

Education as Freedom is a groundbreaking edited text that documents and reexamines African-American empirical, methodological, and theoretical contributions to knowledge-making, teaching, and learning and American education from the nineteenth through the twenty-first century, a dynamic period of African-American educational thought and activism. Education as Freedom is a long awaited text that historicizes the current racial achievement gap as well as illuminates the myriad of African American voices and actions to define the purpose of education and to push the limits of (...) the democratic experiment in the United States. (shrink)

Volume 1 presents the texts in new translations by the authors, and these are accompanied by a philosophical and historical commentary designed for use by all readers, including those with no background in the classical world. With its glossary and indexes, this volume can stand alone as an independent tool of study.

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.1 (2003) 121-122 [Access article in PDF] Harold Tarrant. Plato's First Interpreters. Ithaca, NY: Cornell University Press, 2000. Pp. viii + 263. Cloth, $55.00. This is Tarrant's third book on the ancient Platonist tradition, following his Scepticism or Platonism? (1985) and Thrasyllan Platonism (1993). In those earlier volumes his focus was on the first centuries bc and ad. Here his scope is much (...) wider. Stating that "Platonic interpretation is today at a crossroads," he has written a book that explores "ancient attempts to wrestle with this corpus," with the ultimate objective "to encourage a fresh, almost primitive reading of Plato himself" (vii).He begins engagingly by confronting the ancients with questions any modern reader of Plato must ask: What kind of text is this? Are there doctrines here? Where do I look for Plato's doctrines? The second part of his book is a historical survey, taking us from Plato, the early Academy and Aristotle, through the Hellenistic and early Roman Imperial period, and concluding with the principal Neoplatonist interpreters. In the third and longest part, he focuses on the interpretation of specific dialogues, giving most space to the Gorgias and Theaetetus, but also dealing in particular detail with the Meno, Parmenides, and Philebus. Something is said about every dialogue, but Tarrant writes only briefly about such major works as the Republic and Timaeus. He explains his selectivity (not very convincingly) as due to his wish to "discuss issues of meta-interpretation, with emphasis on the period before Plotinus" (198).Taking his book as a whole, one realizes that few strands of modern interpretation were not prefigured to quite a large extent in antiquity. The two most obvious exceptions are the chronological and developmental approach (Early, Middle, and Late), at present under strong attack from some quarters, and the theological, numerological, and allegorical readings practiced by Neoplatonists. Plato's ancient interpreters were doctrinal unitarians, but they implicitly anticipated our tendency to distinguish "Socratic dialogues," which some of them called "gymnastic" and "inquisitive," from such "canonical" works as the Phaedo,Republic, Symposium, and Timaeus, to which they applied the labels "dogmatic" and "expository." And they recognized that both types of characteristics could be found in the same dialogue, as in the Meno and Theaetetus. Plato himself, they proposed, spoke primarily through the voices of Socrates, Timaeus, and the Eleatic and Athenian strangers; but other characters, such as Pausanias in the Symposium, or Protagoras in the dialogue of that name, utter thoughts with some philosophical value. In explaining difficult passages of one dialogue, they would typically refer to passages from other parts of the corpus. An especially intriguing instance is the strategy of the Anonymous Commentator on the Theaetetus, who reads the Meno into the dialogue on which he is officially commenting.Ancient scholars, just like ourselves, asked questions about the unifying themes of complex dialogues. Hence the sub-titles given to certain works: "On the soul" for the Phaedo, and "On justice" for the Republic, etc. For Olympiodorus (whose commentary on the Gorgias Tarrant has recently co-edited [Leiden, 1998]), earlier interpreters have seriously erred by giving too limited an account of that dialogue's scope. It is not, he says, simply about rhetoric, nor about justice and injustice; nor is its theme the divine demiurge (as some Neoplatonists had strangely proposed, on the basis of the concluding myth). Rather, the subject of the Gorgias is "the ethical principles that lead to constitutional well-being" (125). [End Page 121] However, Olympiodorus's eminently "sensible" reading (as Tarrant calls it) is deeply embedded in the Neoplatonic contrast between the "purificatory virtues" of the Phaedo and the "constitutional virtues" of Republic4.Strong or weak scepticism, esotericism, unwritten doctrines, spurious versus genuine, a canon of central dialogues, dramatic considerations, and the philosophical importance or non-importance of the dialogues' prologues—all of these are interpretive approaches that Tarrant surveys in this immensely learned book, and all of them continue to resonate for us. Modern scholars, who emphasize the literary and philosophical unity of each dialogue, are walking... (shrink)

During recent years we have seen and assisted at a significantly increased number of twin births. The main reason for this increase in the frequency of twin births is the increasing number of so called “induced pregnancies”, whether through hormonal stimulation or artificial insemination techniques.It is well known1 that twins have high mortality and morbidity rates during the perinatal and the following period. The characteristics of conception and pregnancy can determine the development of several pathologies, including prematurity and intrauterine growth (...) retardation, …. (shrink)

In this book the authors introduce and study the following notions: Neutrosophic Crisp Points, Neutrosophic Crisp Relations, Neutrosophic Crisp Sets, Neutrosophic Set Generated by (Characteristic Function), alpha-cut Level for Neutrosophic Sets, Neutrosophic Crisp Continuous Function, Neutrosophic Crisp Compact Spaces, Neutrosophic Crisp Nearly Open Sets, Neutrosophic Crisp Ideals, Neutrosophic Crisp Filter, Neutrosophic Crisp Local Functions, Neutrosophic Crisp Sets via Neutrosophic Crisp Ideals, Neutrosophic Crisp L-Openness and Neutrosophic Crisp L-Continuity, Neutrosophic Topological Region, Neutrosophic Closed Set and Neutrosophic Continuous Function, etc. They compute (...) the distances between neutrosophic sets and extend it to Neutrosophic Hesitancy Degree. The authors also generalize the Crisp Topological Space and Intuitionistic Topological Space to the notion of Neutrosophic Crisp Topological Space. At the end, they present applications to Neutrosophic Database, and show a security scheme based on Public Key Infrastructure (PKI) using Neutrosophic Logic Manipulation. The authors utilize neutrosophic sets in order to analyze social networks data conducted through learning activities, and for the Geographical Information Systems (GIS) they employ fundamental concepts and properties of a Neutrosophic Spatial Region. Keywords: Neutrosophic Crisp Points; Neutrosophic Crisp Relations; Neutrosophic Crisp Sets; Neutrosophic Crisp Continuous Function; Neutrosophic Crisp Compact Spaces; Neutrosophic Crisp Nearly Open Sets; Neutrosophic Crisp Ideals; Neutrosophic Crisp Filter; Neutrosophic Crisp Local Functions; Neutrosophic Crisp Sets via Neutrosophic Crisp Ideals; Neutrosophic Crisp L-Openness and Neutrosophic Crisp L-Continuity; Neutrosophic Topological Region; Neutrosophic Closed Set and Neutrosophic Continuous Function; Neutrosophic Hesitancy Degree; Neutrosophic Crisp Topological Space; Neutrosophic Database; Neutrosophic Logic Manipulation; Neutrosophic Spatial Region. (shrink)

Since the world is full of indeterminacy, the Neutrosophics found their place into contemporary research. We now introduce for the first time the notions of Neutrosophic Crisp Sets and Neutrosophic Topology on Crisp Sets. We develop the 2012 notion of Neutrosophic Topological Spaces and give many practical examples. Neutrosophic Science means development and applications of Neutrosophic Logic, Set, Measure, Integral, Probability etc., and their applications in any field. It is possible to define the neutrosophic measure and consequently the neutrosophic integral (...) and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need to solve. Indeterminacy is different from randomness. Indeterminacy can be caused by physical space, materials and type of construction, by items involved in the space, or by other factors. In 1965 [51], Zadeh generalized the concept of crisp set by introducing the concept of fuzzy set, corresponding to the situation in which there is no precisely defined set;there are increasing applications in various fields, including probability, artificial intelligence, control systems, biology and economics. Thus, developments in abstract mathematics using the idea of fuzzy sets possess sound footing. In accordance, fuzzy topological spaces were introduced by Chang [12] and Lowen [33]. After the development of fuzzy sets, much attention has been paid to the generalization of basic concepts of classical topology to fuzzy sets and accordingly developing a theory of fuzzy topology [1-58]. In 1983, the intuitionistic fuzzy set was introduced by K. Atanassov [55, 56, 57] as a generalization of the fuzzy set, beyond the degree of membership and the degree of non-membership of each element. In 1999 and 2002, Smarandache [71, 72, 73, 74] defined the notion of Neutrosophic Sets, which is a generalization of Zadeh’s fuzzy set and Atanassov's intuitionistic fuzzy set. Some neutrosophic concepts have been investigated by Salama et al. [61-70]. Forwarding the study of neutrosophic sets, this book consists of seven chapters, targeting to:  generalize the previous studies in [1-59], and[91-94] so to define the neutrosopic crisp set and neutrosophic set concepts;  discuss their main properties; A. A. Salama & Florentin Smarandache  introduce and study some concepts of neutrosophic crisp and neutrosophic topological spaces and deduce their properties;  deduce many types of functions and give the relationships between different neutrosophic topological spaces, which helps to build new properties of neutrosophic topological spaces;  stress once more the importance of Neutrosophic Ideal as a nontrivial extension of neutrosophic set and neutrosophic logic [71, 72, 73, 74];  propose applications on computer sciences by using neutrosophic sets. (shrink)

This paper studies, by way of an example, the intuitionistic propositional connective * defined in the language of second order propositional logic by * ≡ ∃Q. In full topological models * is not generally definable but over Cantor-space and the reals it can be classically shown that *↔ ⅂⅂P; on the other hand, this is false constructively, i.e. a contradiction with Church's thesis is obtained. This is comparable with some well-known results on the completeness of intuitionistic first-order predicate logic. Over (...) [0, 1], the operator * is undefinable. We show how to recast this argument in terms of intuitive intuitionistic validity in some parameter. The undefinability argument essentially uses the connectedness of [0, 1]; most of the work of recasting consists in the choice of a suitable intuitionistically meaningful parameter, so as to imitate the effect of connectedness. Parameters of the required kind can be obtained as so-called projections of lawless sequences. (shrink)

In his thesis 'Para uma Teoria Geral dos Homomorfismos' (1944) the Portuguese mathematician José Sebastião e Silva constructed an abstract or generalized Galois theory, that is intimately linked to F. Klein’s Erlangen Program and that foreshadows some notions and results of today’s model theory; an analogous theory was independently worked out by M. Krasner in 1938. In this paper, we present a version of the theory making use of tools which were not at Silva’s disposal. At the same time, we (...) tried to keep in mind, so much as possible, the gist of his standpoint. (shrink)

In this paper we introduce the notion of filter on the neutrosophic crisp set, then we consider a generalization of the filter’s studies. Afterwards, we present the important neutrosophic crisp filters. We also study several relations between different neutrosophic crisp filters and neutrosophic topologies. Possible applications to database systems are touched upon.