Монография представляет собой исследование философских взглядов одного из представителей второй половины XIX века, мыслителя, публициста, литературного критика, переводчика, издателя, Н. Н. Страхова.

Монография представляет собой исследование философских взглядов одного из представителей второй половины XIX века, мыслителя, публициста, литературного критика, переводчика, издателя, Н. Н. Страхова.

Для юристов-практиков и разработчиков законов, студентов, аспирантов и преподавателей юридических вузов и факультетов.

Increased abstraction of modern mathematical theories has revived interest in traditional philosophical and methodological problem of internally consistent system of axioms where the contradicting each other statements can’t be deduced. If we are talking about axioms describing a well-known area of mathematical objects from the standpoint of local consistency this problem does not appear to be as relevant. But these problems are associated with the various attempts of formalists to explain the mathematical existence through consistency. But, for example, with regard (...) to the problem of establishing of consistency of mathematical analysis the solution of which would clarify the fate of Hilbert’s proof theory it has not solved yet so as the problem of the consistency of axiomatic set theory. Therefore it can be assumed that the criterion of consistency despite its essential role in axiomatic systems both formal and substantive nature is the same auxiliary logical criterion as well as mathematical provability. An adequate solution of the problem of consistency of mathematics can be achieved in the area of methodological and substantive arguments revealing the mechanism of appearance of contradictions in the mathematical theory. The paper shows that from a systemic point of view in the context of philosophical and methodological synthesis of various directions of justification of modern mathematics it can’t insist on only the rationale for consistency of mathematical theories. (shrink)

In the article, philosophical and methodological analysis of the program of Hilbert’s formalism as a really working direction for consideration of the bases of modern mathematics is presented. For the professional mathematicians methodological advantages of the program of formalism advanced by David Hilbert, consist primarily in the fact that the highest possible level of theoretical rigor of modern mathematical theories was practically represented there. To resolve the fundamental difficulties of the problem of bases of mathematics, according to Hilbert, the theory (...) of mathematical proof is needed, but contrary to popular belief rigorous formalization of the proof is not a synonym of reliability and rigor of mathematical reasoning from the point of view of the philosophy of the foundations of mathematics. In fact, the consistency of the theories is "more important" than their logical consistency because not every statement, which does not contradict to the reasonable ones, can be attributed to a true statement. However, for working mathematicians, Hilbert is logical and consistent and the axiomatic method and formalism are an essential part of their rules of thinking. (shrink)

It is well known that the largest philosophers differently explain the origin of mathematics. This question was investigated in antiquity, a substantial and decisive role in this respect was played by the Platonic doctrine. Therefore, discussing this issue the problem of interaction of philosophy and mathematics in the teachings of Plato should be taken into consideration. Many mathematicians believe that abstract mathematical objects belong in a certain sense to the world of ideas and that consistency of objects and theories really (...) describes mathematical reality, as Plato quite clearly expressed his views on math, according to which mathematical concepts objectively exist as distinct entities between the world of ideas and the world of material things. In the context of foundations of mathematics, so called ‘Gödel’s Platonism‘ is of particular interest. It is shown in the article how Platonic objectification of mathematical concepts contributes to the development of modern mathematics by revealing philosophical understanding of the nature of abstraction. To substantiate his point of view, the author draws the works of contemporary experts in the field of philosophy of mathematics. (shrink)

The paper is devoted to the analysis and identification of new philosophical aspects of the problem of justification of modern mathematics according to which to the end of the 20th century the most exact of sciences had experienced new shocks associated with the crisis of excessive complexity of the mathematical theories. In the context of justification of mathematics philosophical conclusion consists in the fact that from a methodological point of view for general assessment of whether mathematics is developed or not (...) just the lack of crises is more negative phenomenon than its too long trouble-free state. Accomplished fact is that a computer can be regarded as one of the serious revolutionary technological inventions of the last century, which has had a huge influence on mathematics. In this development of progress of contemporary mathematics, more precisely, in its instrumental technologies the new philosophical problems are revealed - this is the role of computers and the new standards of mathematical thinking. In addition, with the development of contemporary mathematics and the emergence of increasingly complicated and long proofs, they lose their methodological advantage - the property of visibility and convincingness. Within the philosophy of mathematics this problem has not been discussed yet, possibly because the leading mathematicians haven’t expressed their opinions on the subject. After that, we can wait for a methodologically important period clarifying details, which can make the process itself foundations of mathematics philosophical consummation as the crisis complexity; in mathematics it is not a ‘systemic crisis‘ carrying the potential danger of the destruction of all mathematical knowledge. (shrink)

The concept of truth of the mathematical theory plays an important methodological role in philosophy of mathematics in the context of a link between ontological and gnoseological aspects of a problem of mathematics substantiation. In the article, the author analyzes how the features of mathematical knowledge are reflected in the understanding of concept of truth in the contemporary mathematics. The author claims that the concept of truth of mathematical offers and theorems is metamathematical concept; therefore, underestimation of distinction between mathematics (...) and metamathematics can lead to philosophical misunderstanding. They consist primarily in the fact that theoretically possible level of rigor of contemporary mathematical theories has been virtually represented in the science. In order to resolve the fundamental philosophical and methodological difficulties of the problem of mathematics substantiation, the formal provability in logically consistent theory is necessary. However, contrary to the widespread belief, a rigid formalization of the proof is still not the synonymous with reliability and rigor of mathematical reasoning from the standpoint of the philosophy of contemporary mathematics substantiation. (shrink)

The author of the work proposes a philosophical and methodological interpretation of the mathematical objects, using the system triad of the main directions of substantiation of mathematics: the formalism of Hilbert, Brouwer’s intuitionism and Godel’s Platonism. The need for these directions in the concept of substantiation of mathematics from the point of view of the current state of the philosophy of mathematics is shown on the mathematical examples. The philosophical and methodological analysis of objects of mathematics has never been unambiguous, (...) therefore in this paper the results of studies of philosophers, logicians and mathematicians, in which the problem of substantiation is explicated in the context of trends in the development of mathematics, are used. Their professional view on philosophical characteristics of the objects of mathematics contributes to the identification of the unity of all mathematical knowledge maintaining the initial mathematical base of knowledge and revealing new ways of integrating the directions of substantiation in the philosophy of mathematics. The practical problem of substantiation of mathematics is realized through the elaboration of metatheoretical knowledge under the paradigm shift in the philosophy of mathematics to the productive direction from analysis to synthesis. (shrink)

The extensive introduction of statistical methods of empirical analysis into modern science to describe social phenomena and their mechanisms calls for more attentive study of the philosophical foundations of notions of statistical probability and of the dialectics of necessity and chance in the area of societal cognition.

In the years since World War II, the social critic has become a rather popular figure in the West. The demand for critical theories of society is readily explainable where the contradictions of social development take the form of sharp paradoxes recognized by the broad public. It may be assumed that interest in critical concepts of society will increase. People who recognize themselves as cogs without rights in the system of bureaucratic organization of state-supported monopoly capitalism, who react acutely to (...) the threat of social catastrophes , endow such concepts with the halo of humanism if only because they often find in them their own moods, given shape and seemingly elevated to the level of general social protest. These feelings represent a concrete dissatisfaction with the present situation, and the sense that the society in which they live is in crisis. (shrink)

Two years ago, a professor at the University of California, Herbert Marcuse, an American social philosopher with traditional German training, came to be regarded as the recognized theoretician of the "New Left" movement. Marcuse's popularity compelled many writers, including ourselves , to make a careful examination specifically of the theoretical content of that teaching, which laid claim to performing the role of a critical and revolutionary theory of society. The development of a critique of the philosophical and theoretical foundations and (...) the internal contradictions of Marcuse's teachings was thus dictated by a real situation, by the actual struggle of ideas, and has perhaps still not lost its significance. Another problem, which aroused the interest of researchers even then but which had not found an answer in our article because of its specific purpose, had to do with the relationship between Marcuse's philosophical concept and the spontaneous consciousness of the "mass" participants in the real protest movement that came to be known as the "New Left" movement. (shrink)

Dissatisfied with purely negative clichés about the development of Russian philosophy in the Soviet period, the author advocates for a scrupulous and objective reevaluation of the textual materials and the historical circumstances of that time, considering this work an important task for historians of philosophy. Despite strong ideological pressure and control that Soviet officials put on philosophy in general, in many cases the history of philosophy provided a kind of niche in which creativity and freedom were still allowed. For this (...) reason, even in the Soviet period the research output in the history of philosophy was very significant and the quality of the work very high. Many outstanding and well-known Soviet philosophers were historians of philosophy. (shrink)

In his book A History of the Culture of the Modern Period, the eminent scholar Egon Friedell wrote concerning Descartes's influence in seven-teenth-century France that all the efforts of the great philosopher's critics notwithstanding, "his school inexorably extended its influence not only through the ‘occasionalists,’ as his closest disciples and followers in philosophy were called, and through the remarkable logic of the Port-Royal school The Art of Thinking and Boileau's tone-setting work The Poetic Art: rather, all of France, headed by (...) the "Sun King," who at one time had banned Descartes's works, became his school. The state, economy, theater, architecture, religious affairs, strategy, and the art of gardening all became Cartesian. Descartes reigned unrestricted, as a sovereign, in all things: in tragedy, where the passions struggled with one another; in comedy, where algebraic formulas were devised for human characters; in the area around Versailles, dominated by the abstract symmetry of gardens; in the analytic methods for waging war and running the economy; and in the so to speak deductive ritual of hairstyles and manners, dances and genteel conversation. One can even say that to this day every Frenchman is a born Cartesian.". (shrink)

An objective, honest, impartial history of our country's philosophy in the Soviet period—in a word, a history meeting the requirements of the times—is yet to be written. But it is much needed. Its creation is one of the most important, but perhaps also one of the most difficult of our tasks. There are still many superimposed layers that must be peeled away: for example, the bitter truth must be told about those who inscribed in this history—of course honorifically—their own names (...) and those of dogmatists who shared their ideas. But fortunately, it is not only naked emperors and their stooges, not only their subjects with their mutilated destinies, who will figure in a historical narration oriented toward the truth and facts. This grim context makes even brighter the noble role played by those figures—personalities in the highest sense of the word—whose names, works, and very lives were simply "expunged" from history. And by those who remained alive and in philosophy in the direst times, those who despite all the persecution, all the tribulations they endured, abandoned neither their honor nor philosophical truth. The unofficial authority of talented, creatively thinking scholars has always been extremely high. One of those highly authoritative philosophers of our country, one who today has an international name, was Valentin Ferdinandovich Asmus. (shrink)

The author traces the evolution of Mamardashvili's critique of Sartre's existentialism, undertaken from the perspective of his creative and unorthodox Marxism.