The paper explicates the stages of the author’s philosophical evolution in the light of Kopnin’s ideas and heritage. Starting from Kopnin’s understanding of dialectical materialism, the author has stated that category transformations of physics has opened from conceptualization of immutability to mutability and then to interaction, evolvement and emergence. He has connected the problem of physical cognition universals with an elaboration of the specific system of tools and methods of identifying, individuating and distinguishing objects from a scientific theory domain. The (...) role of vacuum conception and the idea of existence (actual and potential, observable and nonobservable, virtual and hidden) types were analyzed. In collaboration with S.Crymski heuristic and regulative functions of categories of substance, world as a whole as well as postulates of relativity and absoluteness, and anthropic and self-development principles were singled out. Elaborating Kopnin’s view of scientific theories as a practically effective and relatively true mapping of their domains, the author in collaboration with M. Burgin have originated the unified structure-nominative reconstruction (model) of scientific theory as a knowledge system. According to it, every scientific knowledge system includes hierarchically organized and complex subsystems that partially and separately have been studied by standard, structuralist, operationalist, problem-solving, axiological and other directions of the current philosophy of science. 1) The logico-linguistic subsystem represents and normalizes by means of different, including mathematical, languages and normalizes and logical calculi the knowledge available on objects under study. 2) The model-representing subsystem comprises peculiar to the knowledge system ways of their modeling and understanding. 3) The pragmatic-procedural subsystem contains general and unique to the knowledge system operations, methods, procedures, algorithms and programs. 4) From the viewpoint of the problem-heuristic subsystem, the knowledge system is a unique way of setting and resolving questions, problems, puzzles and tasks of cognition of objects into question. It also includes various heuristics and estimations (truth, consistency, beauty, efficacy, adequacy, heuristicity etc) of components and structures of the knowledge system. 5) The subsystem of links fixes interrelations between above-mentioned components, structures and subsystems of the knowledge system. The structure-nominative reconstruction has been used in the philosophical and comparative case-studies of mathematical, physical, economic, legal, political, pedagogical, social, and sociological theories. It has enlarged the collection of knowledge structures, connected, for instance, with a multitude of theoreticity levels and with an application of numerous mathematical languages. It has deepened the comprehension of relations between the main directions of current philosophy of science. They are interpreted as dealing mainly with isolated subsystems of scientific theory. This reconstruction has disclosed a variety of undetected knowledge structures, associated also, for instance, with principles of symmetry and supersymmetry and with laws of various levels and degrees. In cooperation with the physicist Olexander Gabovich the modified structure-nominative reconstruction is in the processes of development and justification. Ideas and concepts were also in the center of Kopnin’s cognitive activity. The author has suggested and elaborated the triplet model of concepts. According to it, any scientific concept is a dependent on cognitive situation, dynamical, multifunctional state of scientist’s thinking, and available knowledge system. A concept is modeled as being consisted from three interrelated structures. 1) The concept base characterizes objects falling under a concept as well as their properties and relations. In terms of volume and content the logical modeling reveals partially only the concept base. 2) The concept representing part includes structures and means (names, statements, abstract properties, quantitative values of object properties and relations, mathematical equations and their systems, theoretical models etc.) of object representation in the appropriate knowledge system. 3) The linkage unites a structures and procedures that connect components from the abovementioned structures. The partial cases of the triplet model are logical, information, two-tired, standard, exemplar, prototype, knowledge-dependent and other concept models. It has introduced the triplet classification that comprises several hundreds of concept types. Different kinds of fuzziness are distinguished. Even the most precise and exact concepts are fuzzy in some triplet aspect. The notions of relations between real scientific concepts are essentially extended. For example, the definition and strict analysis of such relations between concepts as formalization, quantification, mathematization, generalization, fuzzification, and various kinds of identity are proposed. The concepts «PLANET» and «ELEMENTARY PARTICLE» and some of their metamorphoses were analyzed in triplet terms. The Kopnin’s methodology and epistemology of cognition was being used for creating conception of the philosophy of law as elaborating of understanding, justification, estimating and criticizing legal system. The basic information on the major directions in current Western philosophy of law (legal realism, feminism, criticism, postmodernism, economical analysis of law etc.) is firstly introduced to the Ukrainian audience. The classification of more than fifty directions in modern legal philosophy is suggested. Some results of historical, linguistic, scientometric and philosophic-legal studies of the present state of Ukrainian academic science are given. (shrink)

Coming fromI andCl, i.e. from intuitionistic and classical propositional calculi with the substitution rule postulated, and using the sign to add a new connective there have been considered here: Grzegorozyk's logicGrz, the proof logicG and the proof-intuitionistic logicI set up correspondingly by the calculiFor any calculus we denote by the set of all formulae of the calculus and by the lattice of all logics that are the extensions of the logic of the calculus, i.e. sets of formulae containing the axioms (...) of and closed with respect to its rules of inference. In the logiclG the sign is decoded as follows: A = (A & A). The result of placing in the formulaA before each of its subformula is denoted byTrA. The maps are defined (in the definitions of x and the decoding of is meant), by virtue of which the diagram is constructed. (shrink)

The short exposition of the triplet model of concepts and some definitions connected with it are given. In this model any concept may be depicted as having three characteristics: a base, a representing part and the linkage between them. The paper introduces the fuzzification of concepts in terms of the triplet model.

The article examines the problem of alienation as a result of the conflict between consciousness and instincts, which includes aspects of 1) temporal conflict and 2) attempts to self-destruct the individual. Through this conflict, the imperfection of the individual makes it possible for him to develop. The authors also correlate the concepts of alienation and consciousness, which opens up space for criticism of Nietzsche's concepts of herd mentality and the possibility of human cognition of the external world.

Born and Pauli, in talking of the style of science, meant its relatively stable features, which characterized a long period of scientific progress. “I do not mean,” wrote Born in 1953, “that there exist (outside mathematics) any unchanging principles, a priori principles in the strict sense of the term. But I think that certain general tendencies of thought exist, which change very slowly and which form definite philosophical periods with their own characteristic ideas in all fields of human activity, including (...) science. In a recent letter to me, Pauli used the expression ‘styles’; styles of thought, not only in art but in science too. In adopting this term, I would assert that style is also a characteristic of physical theory, and it is precisely this fact that gives its principles a certain constancy. They are, as it were, relatively a priori principles in relation to the particular period. If one is familiar with the style of one's time, one can make certain cautious predictions. One can at least reject ideas that are foreign to the style of one's time”. (shrink)

Although robots are largely designed with industrial, scientific or military aims in mind, many designers seek to endow them with anthropomorphic forms, even at the risk of compromising their functionality. Why do they not content themselves with constructing useful machines, rather than also incorporating human-like features? What drives them to cover their machines with a latex coating to simulate human skin? The utopia of the creation of a double appears also in the world of art, the history of which shows, (...) above all, an outcome that coincides with the abandonment of the naturalistic imperative, and the inauguration of various periods of exploration and innovation. That is why a possible roboaesthetics—i.e. robotics and aesthetics combined could give rise to a new scenario. This view would acknowledges the radical novelty of these ‘species’ and induce the adoption of a new observation level, constructed on the basis of a common project. (shrink)

This article opens a cycle of articles devoted to the ontological aspects of the phenomenon of Enlightenment. The Enlightenment is treated as an internal mechanism of civilization designed to manipulate being (establishment in being – deprivation or attenuation of being). Comparing autochthonous and borrowed Enlightenments, the author tries to trace some patterns of interactions of ontologizing mechanisms of the enlightenmental type and to compare them with the similar mechanisms of different types. In the first article the author analyses the ideas (...) of autochthonous European Enlightenment from Antiquity to Post-Modern. (shrink)

This paper is dedicated to V. V. Rosanov views on the issue of sexual love. Analyzing the system of Rosanov’s notions of the God, nature and sex, authors show how the philosopher is trying to create pansexualistic quasireligious doctrine versus Christianity. The thinker is referred to as a radical ideologist of mystical-erotic revolution and a mouthpiece of peculiar to Russian culture trend towards the construction of a national religion.

The article is an attempt at the reverse engineering of conceptual architecture and logic of David Bloor's Strong Programme (SP) in the sociology of scientific knowledge via explicating key resources and interpretative techniques for constructing it. To do this I show how problematic is a conventional interpretation of the SP as a radicalization of Kuhn's theory of science and as a sociologization of epistemology. This problematization allows me to put anew three questions concerning the SP. In what sense it is (...) post-positivist? In what sense it is sociological? Does it belong to social epistemology? To answer these questions I set myself four tasks. First, Bloor’s theoretical position concerning the Kuhn-Popper debate is located. Second, I point to and present Mary Hesse’s network model of science (NM) as a crucial theoretical source for the early SP. Third, I analyze in detail how Bloor interpreted and appropriated NM. Finally, I show what theoretical and methodological effects this interpretation had for the SP as presented in 1976. The general layout of the conceptual architecture of SP is modeled on the Hesse’s NM. It combines the principle of correspondence and that of coherence and sees the language of science as a network of predicates and laws segmented by contingent and empirical boundaries and not a priori logical divisions between theory and observation. But Bloor creatively interprets and appropriates NM by the double move of generalization and specification. Whereas Hesse’s NM refers to the functioning of scientific language, in Bloor’s hands, it comes to describe human learning in general inscribed in psychological processes (perception and thinking). As a result, SP is based on a form of psychological empiricism that sees science as a two-storied building. The first floor (perception) ensures correspondence and the second one (thinking) provide conditions of coherence. SP of 1976 is a specific model for the sociological segmentation of the second floor. (shrink)

The author of this article tries to make clear whether there are any elements of Russian enlightenmental paradigm. They are: 1) specific educationizm that needs processing of human nature; 2) anthropological utopia that is constructing the human ideal, identical with the world and the Absolute as final result of Universal process of educationizm; 3) the attempt to adapt Christianity to enlightenmental ideology; 4) the desire to highlight erotic and gender problem. All this items can be found in the texts of (...) Solovyov. But instability discovered in the course of the foresaid problem Solovyov’s points of view doesn’t allow to give definite answer to the question, whether one should call Solovyov’s art Enlightenment itself or its environment. (shrink)

Knowledge is systemic by its nature. The highest expression of the systematic character of knowledge is to be found in scientific theories. Any scientific theory is a rigorously organized conceptual system, quite complex in structure. What defines the manner in which knowledge is organized in a theory? Is it independent of the nature and structural features of that sphere of the material world for cognition of which the theory was created, or is it conditioned by these features and does it (...) derive from them? Is there a correspondence between the structure of knowledge concentrated in a theory and the structure of that fragment of material reality that is modeled by that theory? Is it possible at all for a theory to be a form of reflection of objective reality, if there is no definite correspondence between its structure and the structure of the region of reality to which it pertains? These questions are of primary importance to the treatment of the theory of scientific knowledge. (shrink)

A vast literature has been devoted to the Dialectics of Nature and dialectics in Capital. There is a considerable number of works in which the connection between the philosophical generalization of natural science in the Dialectics of Nature and the philosophical aspects of the economic categories in Capital are analyzed. I should like to touch upon only one aspect of the problem — that aspect which pertains to certain new problems in philosophical and economic thought. Reference is, first, to the (...) new, unprecedented role of philosophy and natural science in the period of the scientific and technological revolution under the conditions of the unification and planning of science and, second, to the unprecedented dynamism of the economy today. This dynamism requires a radical rethinking of categories, and that rethinking, in turn, requires a return to the fundamental categories of Capital. (shrink)

El artículo presenta una reconstrucción del método del psicoanálisis existencial sartriano especificando su finalidad, campo de aplicación, y provee un análisis interpretativo de su necesidad dentro del desarrollo de la ontología sartriana. Se defenderá que la meta del psicoanálisis existencial es el acaecimiento de la reflexión pura, la cual abre la posibilidad del reconocimiento del proyecto fundamental y la conversión existencial. El análisis se basa en una lectura de El ser y la nada que toma como concepto central a la (...) noción de “deseo”. (shrink)

Physical theories are complex and necessary tools for gaining new knowledge about their areas of application. A distinction is made between abstract and practical theories. The last are constantly being improved in the cognitive activity of professional physicists and studied by future physicists. A variant of the philosophy of physics based on a modified structural-nominative reconstruction of practical theories is proposed. Readers should decide whether this option is useful for their understanding of the philosophy of physics, as well as other (...) philosophies of particular sciences. (shrink)

En el presente trabajo nos proponemos trazar la distinción entre la subjetividad preteórica y el sujeto cognoscente en las lecciones tempranas de Friburgo de Martin Heidegger desde el punto de vista de la función metodológica y el carácter ontológico de la reflexión, en vistas a pensar si se puede hablar de una noción de subjetividad no egológica en el planteo heideggeriano. Entendemos por «subjetividad no egológica», el dominio subjetivo originario de la existencia humana, previo a la constitución del ego. Para (...) nuestro propósito abordamos, en una primera instancia, las nociones de discurso originario y discurso derivado para, en un segundo momento, distinguir la subjetividad preteórica de la subjetividad originaria y analizar, finalmente, si se puede hablar de la presencia de una subjetividad no egológica en Heidegger a partir del análisis del estatus metodológico y ontológico de la reflexión. (shrink)

El artículo ofrece un análisis, desde la epistemología feminista, del Juicio a la Justicia Patriarcal, proceso feminista y latinoamericano llevado adelante por la organización Feministas de Abya Yala. La hipótesis es que esta experiencia constituyó un foco de resistencia epistémica al conjunto de injusticias epistémicas que padecen las mujeres, lesbianas, travestis y trans de América Latina, y que actúan como barreras de acceso a la justicia.

Ofrecemos un análisis de los aspectos ontoepistemológicos de los debates actuales sobre el cuerpo sexogenerizado en Argentina. Con herramientas teóricas de la fenomenología feminista, la epistemología feminista y los nuevos materialismos feministas analizamos, por un lado, la manera en que el Estado argentino comprende el cuerpo sexogenerizado y, por el otro, una serie de afirmaciones en los discursos transexcluyentes que conflictúan estas discusiones. Buscamos despejar el terreno conceptual del debate feminista para determinar qué posturas nos permiten avanzar y cuáles nos (...) hacen retroceder. Concluimos que, mientras que las nociones en la ley de identidad de género están amparadas por el conocimiento feminista actual, los discursos transexcluyentes que cuestionan su contenido representan un marco de comprensión ontoepistemológico patriarcal. (shrink)

Infinitary action logic can be naturally expanded by adding exponential and subexponential modalities from linear logic. In this article we shall develop infinitary action logic with a subexponential that allows multiplexing (instead of contraction). Both non-commutative and commutative versions of this logic will be considered, presented as infinitary sequent calculi. We shall prove cut admissibility for these calculi, and estimate the complexity of the corresponding derivability problems: in both cases it will turn out to be between complete first-order arithmetic and (...) the \(\omega ^\omega \) level of the hyperarithmetical hierarchy. Here the complexity upper bound is much lower than that for the system with a subexponential that allows contraction. The complexity lower bound in turn is much higher than that for infinitary action logic. (shrink)

El propósito del presente trabajo consiste en analizar la conexión existente entre feminismo, fenomenología y marxismo, por medio de la exploración de las prácticas de autoconciencia y la teoría del punto de vista feminista. Sostenemos que las prácticas de autoconciencia feminista y su sucedánea teoría del punto de vista feminista se apartaron de sus raíces fenomenológicas y marxistas. Esto contribuyó a la reapropiación de cierta retórica perteneciente a estas prácticas por parte de la ideología capitalista dominante, con un contenido y (...) un propósito sustantivamente diferentes. Afirmamos que para producir teoría situada desde Latinoamérica es necesario partir de la materialidad de la propia experiencia. Para esto, reivindicamos las raíces fenomenológicas y marxistas de las prácticas de autoconciencia y las teorías del punto de vista feminista. Finalmente, argumentamos que es posible recuperar la impronta revolucionaria de estas prácticas, en el marco del paradigma del feminismo post-identitario e interseccional actual, en especial, en su expresión latinoamericana. (shrink)

Non-classical science gives a very specific answer to the question of scientific errors and their epistemological value. But for all the specificity of this answer, it casts light on a problem that remains with us century after century, the historically constant problem of truth and error—one of the most fundamental problems of knowledge. At first sight, these two poles have always stood opposite each other, like good and evil, beauty and ugliness. But moral and aesthetic theories have long since left (...) behind this initial conception, and shown that the two polar concepts are in fact inseparable. As regards truth and error, their indivisibility has only become apparent in the context of non-classical science. Truth has ceased to be the absolute contradiction of error. Contemporary science finds it to be something relative, inseparable from its opposite pole. But the non-classical, retrospective approach, a re-evaluation of the past of science in the light of its present, and indeed even more in the light of its prognosis, its future, allows one to see that scientific truths that are adequate for the object of knowledge always reflect only one side of the objective world, a world which has an infinite number of sides. The irreversible process that leads from relative error to relative truth has an absolute character: an irreversible process of generalization, concretization and complication of a Weltanschauung that more accurately reflects the infinite complexity of life. (shrink)

In a cultural setting in which the imitation of nature continues to be regulated by the ambitious project to cancel the dividing line between the natural and the artificial, man continues to find space for his replicative fantasies, even at the cost of breaking cultural boundaries and taboos. On the other hand, as shown in the historical analogy, this ambition, aimed not only at a partial reproduction but a true replication, seems to exhibit developmental contours that lead to the same (...) final results in terms of disillusionment and subsequent abandonment. (shrink)

The role of cultural models in the process of adaptation to the new technologies is very different according to different civilizations. Some basic cultural items seem to be particularly crucial, such as, for example, the levels of pragmatism or rationalism which characterize a civilization or some periods of its history. This paper presents a sketch aimed at setting up a comparison between Western and Eastern cultures facing the problem of adapting to new technologies. The concept ofcold utilitarianism is introduced. It (...) allows a way of defining adaptation which is only partial and contradictory in Western culture, while it completely describes, though perhaps provisionally, the Eastern way of making and using technology. (shrink)

In our times, when the pace of economic, scientific and technological, social and cultural change calls to mind the relativist velocities of contemporary physics, Einstein's criterion begins to be applicable to the historical process itself; movement can be recorded (and consequently the notion of velocity acquire meaning) provided an adequate reference system is available. Where science is concerned, such systems have always existed: historians have brought out the increase in adequate knowledge in the past by comparing it with present knowledge, (...) which then offered a system of absolute reference. But now, the theory of relativity, quantum mechanics, molecular biology and the radical transformation of standards of value in all cultural areas have made like absolutization of contemporary ideas impossible. Today ideas furnish no more than a point of departure for non-classical retrospection which, as Jaurès said, seeks the fire, not. the ashes, in the history of science. But: the fire of science, its dynamics, its movement, is inseparable from its value, its effect, its psychological ‘accompaniment.’ Contemporary science, with unprecedented dynamism, is distinguishable from classical science by its far more emotional coloring. It lays bare not only the logical collisions of knowledge but also the emotional collisions. Einstein called the history of science the ‘drama of ideas.’ A drama which sometimes turns into a tragedy. The tragic sense Lorentz was aware of in the crumbling of old conceptions is easily perceptible in the remark he made when he confessed he would have prefered to be dead before the structure of classical physics collapsed. For Erenfest the tormenting experience of a personal inability to understand the positive bases of non-classical physics was also tragic and, according to Einstein, was what drove him to suicide. Einstein's own dissatisfaction tor thirty years while he strove in the field theory alone to find a stable universal conception possessing more complete ‘internal perfection’ than the then existing solution, was again tragic. The real characteristic of the collisions of non-classical science, however, is their ambivalence: the tragic notes blend with the optimistic perception of irreversible general progress in knowledge. The collisions of knowledge and this optimistic perception together sound a very complex chord, major on the whole, but with minor harmonics. (shrink)

Through the prism of republican theory, the paper discusses the nature of environmental protests and the judiciary’s responses to the related cases. The text argues that climate protesters act not solely to realise their freedom of assembly but also to understand their obligations to the environment and the community of citizens. An argumentation grounded in their belief that they were obliged to protest against climate change and even commit certain unlawful acts due to the state of necessity could give their (...) defence more strength, on the one hand, and inspire the courts to be more active in forcing governments to act on the climate cause, on the other hand. The paper consists of two sections, with the first discussing theoretical approaches to environmental citizenship, the alleged duty to protest against climate change, and their relationships with republicanism. The second section scrutinises case law from selected domestic and international courts dealing with climate protests. Specifically, it analyses the justifications for the right to protest against climate change presented in the submissions of applicants or defendants before the courts and the reasoning employed by the courts. (shrink)

The articles examines the teleofunctional solution to the problem of mental causation, presented by Dmitry Volkov in his recently published book Free Will. An Illusion or an Opportunity. D.B. Volkov proposes solutions to three big metaphysical problems – mental causation, personal identity, and free will. Solving the first problem, Volkov creatively combines the advantages of Dennett’s teleofunctional model and Vasilyev’s local interactionism. Volkov’s teleofunctional model of mental causation seeks to prove the causal relevance of mental properties as non-local higher order (...) properties. In my view, its substantiation is based on three points: (a) critics of the exclusion problem and Kim’s model of mental causation, (b) “Library of first editions” argument, (c) reduction of the causal trajectories argument (CTA 1) by Vasilyev to the counterpart argument (CTA 2) by Volkov. Each of these points faces objections. Kim’s criticism is based on an implicit confusion of two types of reduction – reduction from supervenience and from multiple realizability. The latter type does not threaten Kim’s ideas, but Volkov uses this very type in his criticism. The “Library of first editions” argument does not achieve its goal due to compositional features and because non-local relational properties are a type of external properties that cannot be causally relevant. The reduction of CTA 1 to CTA 2 is unsuccessful since, in the case of this reduction, important features of CTA 1 are lost – these are local mental properties, due to which the influence of non-local physical factors occurs. My main objection is that the concept of causally relevant non-local properties is incompatible with the very concept of cause. The set of causally relevant properties of cause can only be local. (shrink)

This article is devoted to the analysis of arguments from empirical science against free will. Its main purpose is to reveal their deep anti-naturalism. This anti-naturalism lies in the use of a concept of free will that cannot be the subject of naturalistic consideration, as well as in the various explanatory and ontological paradoxes that arguments from empirical science lead in case when someone is trying to generalize the explanatory principles underlying them. At the beginning of the article, the author (...) gives a general notion of the free will problem, a working definition of naturalism and the place of arguments from empirical science in discussions about free will. To achieve the main goal of the article, the author suggests a classification of arguments from empirical science, which includes five types: from prediction, from manipulation, from the brain, from illusion, from the substitution of concepts. In accordance with this classification, the structure of the article is defined, where each of the presented types is sequentially considered. The logic of considering each type of argument is approximately the same: explication of the essence of the argument of a particular type, its analysis, identification of basic principles and their generalization, demonstration of the negative consequences that it leads to, and answers to possible objections. In the course of the consideration, the author formulates an ontologically neutral concept of free will as a set of abilities associated with the agent’s control over his actions. At the end of the article, the main points is summed up, the idea of naturalistic compatibilism is proposed, the role of arguments from empirical science in discussions about free will is clarified, as is the problem of free will itself, the question of the sources of “chimerization” of naturalism is briefly highlighted, and the problem of completeness of the proposed reasoning is touched upon. (shrink)

We consider the Lambek calculus, or noncommutative multiplicative intuitionistic linear logic, extended with iteration, or Kleene star, axiomatised by means of an$\omega $-rule, and prove that the derivability problem in this calculus is$\Pi _1^0$-hard. This solves a problem left open by Buszkowski (2007), who obtained the same complexity bound for infinitary action logic, which additionally includes additive conjunction and disjunction. As a by-product, we prove that any context-free language without the empty word can be generated by a Lambek grammar with (...) unique type assignment, without Lambek’s nonemptiness restriction imposed (cf. Safiullin, 2007). (shrink)

Modern physics is developing with extraordinary rapidity. It is passing through a tremendous revolution. The boldest and most fantastic imaginings, which only yesterday appeared virtually unrealizable, are being brought to reality in the course of this revolution.

The English Synopsis is after the text of the book. The book presents an original and generalizing substantive vision of the philosophy of science through the prism of a detailed analysis of the polysystem structure of scientific theories. Theories are considered, firstly, as complex specialized forms of developed scientific thinking about the realities studied by natural science, secondly, as constantly improving tools for producing new knowledge in interaction with experimental research, and thirdly, as carriers of ordered and verified knowledge. Emphasis (...) is placed on their nominal and ontic subsystems. The book develops personal and joint research of the authors (theoretical physicist and philosopher), the experience of teaching philosophy of physics at NaUKMA, philosophy of science at the Higher School of Philosophy at the H. Skovoroda Institute of Philosophy of the National Academy of Sciences of Ukraine and theoretical physics at the National Technical University "Ihor Sikorsky Kyiv Polytechnic Institute". The research is based on a significant source base covering works of modern Western researchers in natural science and philosophy of science. For students, teachers, and scientists who are interested in the problems of modern philosophy of science and have a certain amount of scientific knowledge. It will also be useful for high school students who are eager to become scientists. (shrink)

The genesis of classical science was accompanied by a transition from logical to mathematical analysis. This change did not mean a rejection of Aristotle's canons of logic; it was simply that these canons became inadequate. They underwent a certain generalization and, in the course of this, came closely to approximate mathematical analysis, the foundations of the calculus of the infinitesimal. Classical science no longer took as its point of departure the notion of motion from "something" into "something," as did Peripatetic (...) physics and cosmology . The initial concept is motion, considered from point to point and instant to instant. This kind of differential notion of motion was clearly expressed by Kepler when he wrote: "Where Aristotle sees direct oppositeness between two things, with no mediating links, there I, looking at geometry philosophically, find a mediated opposition; so that where Aristotle employs a single term, ‘other,’ I use two: ‘larger’ and ‘smaller.’". (shrink)