Tom 1. Logicheskie ischisleni͡a, algebry i funkt͡sionalnye svoĭstva.

The term 'Machiavellianism', used to designate a tough politics knowing no ethical barriers, entered firmly into circulation as far back as the sixteenth century. It was the negative reaction to the maxims in The Prince that defined the initial attitude toward Machiavelli's doctrine, and the internal polemic with this initial assessment has spawned an endless stream of literature endeavoring to justify in one way or other the ill-starred secretary of the Florentine Republic. In sheer number of publications, pro-Machiavelli views exceed (...) anti-Machiavelli views by many times. And yet questions remain; the original negative reaction is not eradicated, just as the striving for apologetics is not eradicated. (shrink)

As is well known, Plotinus's philosophy served as the starting point for the development of all Neoplatonism. It created the basic schema that set the framework for the thought of all later representatives of this tendency from Porphyry to Damascius. The doctrine of the transcendence of the One, of the three original hypostases, the application of the categories of Plato's Parmenides in the construction of ontology—all this and much else besides became the property of the Neoplatonic schools, which were scattered (...) throughout the Roman empire, and was incorporated partly into the Christian theology, which was then in the process of formation. Naturally, as a result of its wide dissemination and the change in its cultural and social environment, Plotinus's legacy appeared in a different light and took on new forms; through these changes in form we can try to understand the difference in content. For this purpose Plotinus's treatise on the virtues is of special interest. The point is that Porphyry relies precisely on this treatise and at times even literally borrows large fragments from it in setting out the doctrine concerning the virtues in the thirty-second maxim . The same treatise serves as a basis for Marinus in his biography of Proclus. The aim of my lecture is to analyze the content of the treatise and its interpretations. (shrink)

In the present article the author studies and reviews the essential scientific opinions and discourse on the understanding of the term and phenomena of Cybernetics. The article is the author's vision of the concept of cybernetic epistemology based on its progressive methodological features. The main idea of the understanding of the information warfare category as a complex social system in the context of cybernetic epistemology is also developed in the present research. The concept of complexity theory has not yet been (...) applied in the study of ontological characteristics of the "information warfare" phenomenon so far. This kind of analyzing method allows us to highlight the true essential characteristics of "information warfare". There are recursiveness and spontaneous nature among them. This kind of epistemology methods and their possible and proper application in Cybernetics were analyzed and reviewed in the present paper. Such an analyzing confirmed the relevance of this research for the formalization of the world’s complex phenomena. It also determined the possibility of constructive generalization of knowledge and research data. However, this knowledge should be gained in the process of complex formalization of the studied phenomena characteristics and the maximum permissible changes and transformation in their conditions and forms. (shrink)

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)

Tijdens zijn bewogen leven schreef Dirck Volckertsz Coornhert (1522-1590) vele teksten en voerde hij talloze gesprekken. Zijn doel: zijn medemensen overtuigen van het belang om niet slaafs achter anderen aan te lopen maar zélf na te denken. Want elk mens heeft voldoende redelijke vermogens om het leven zelfstandig vorm te geven en het goede te doen. De Kruidhofjes bevat twee bundels met dialogen – gesprekken die Coornhert zelf voerde of onderweg heeft gehoord. De dialogen zijn te zien als medicijnen tegen (...) wat Coornhert zag als de ziekte van zijn tijd: onnadenkendheid en religieuze scherpslijperij. Enerzijds probeert Coornhert obstakels voor een goed en gelukkig persoonlijk leven weg te halen. Hier gaat het vooral om het bestrijden van onbegrip en onwetendheid. Anderzijds probeert Coornhert obstakels voor vreedzaam samenleven op te ruimen. Dat is de reden waarom nogal wat dialogen ingaan op religieuze kwesties als kerkbezoek, de mis en kerkelijke ceremonies; onenigheid over deze onderwerpen vormde immers de belangrijkste oorzaak van de heftige onderdrukking, vervolging en oorlog in de zestiende eeuw. Dit verklaart ook de felheid van veel van de dialogen. Discussies over religieuze denkbeelden en gebruiken waren niet zomaar interessant tijdverdrijf voor bij de borrel. Het ging ergens om: om de waarheid, je zielenheil en de inrichting van de maatschappij. In 45 dialogen probeert Coornhert zo zijn medemens te motiveren tot eerlijkheid naar zichzelf en verdraagzaamheid naar de ander. (shrink)

Propositions are the result of hypostatization in accordance with the principle of the identification of indiscernibles wherever differences among inscribed or uttered statemental units are systematically ignored. Criteria for identity of propositions are, thus, to be found in each context of discourse about statemental units where qualitatively different units are treated as interchangeable. Ayer's notion of proposition as opposed to statement, Goodman's notion of replication, and the notion of constructional definition or reduction are discussed in the light of this thesis. (...) The so-called "problem of identifying propositions" is shown to be a bogus problem because the propositions simpliciter to be identified are incoherently conceived, though in the course of discussion the prospect appears that many different and limitedly applicable sets of criteria for identification of propositions relative to different discourses can be given. (shrink)

The article discusses a key issue for Russian and international Max Weber Studies: the epistemological possibilities and place of Weberian sociology in modern social theory. Discussion articles by well-known Russian scientists — who sharply criticized the actualizing direction of Weberian studies in general, and the religious, cultural, and sociological orientation in particular — are contrasted with the re-actualization and rethinking of key Weberian themes in the “New Critical Theory” of the influential German sociologist Hartmut Rosa. Such a projection will make (...) it possible, on the one hand, to thematize the axiomatic assertion about the heuristic rather than concrete-content relevance of the classics; on the other hand, it will provide an opportunity to read Weber as a macrosociologist. In the original, criticized, and often rejected sociology of Rosa, Weber appears not only as a predecessor whose mention enhances the relevance of the new theoretical framework, but, above all, as an analyst and diagnostician of early modernity. Weber’s main ideas and theoretical constructions are organically built into Rosa’s methodological framework: analysis-diagnosis-praxis. The analysis of rationalization as a universal historical process of modernity in Weber’s sociology is rethought by Rosa as expansion and acceleration; disenchantment becomes a diagnosis of modernity and is recoded into alienation, while the concept of charisma is transformed into the key concept of resonance. (shrink)

A collection of articles about P.A. Sorokin's work are preceded by a Russian translation of selected chapters of his 1947 work "Society, culture and personality" and a collection of correspondence (also translated into Russian) between him and Robert Merton.