The question whether Kuhn's theory of scientific revolutions could be applied to mathematics caused many interesting problems to arise. The aim of this paper is to discuss whether there are different kinds of scientific revolution, and if so, how many. The basic idea of the paper is to discriminate between the formal and the social aspects of the development of science and to compare them. The paper has four parts. In the first introductory part we discuss some of the questions (...) which arose during the debate of the historians of mathematics. In the second part, we introduce the concept of the epistemic framework of a theory. We propose to discriminate three parts of this framework, from which the one called formal frame will be of considerable importance for our approach, as its development is conservative and gradual. In the third part of the paper we define the concept of epistemic rupture as a discontinuity in the formal frame. The conservative and gradual nature of the changes of the formal frame open the possibility to compare different epistemic ruptures. We try to show that there are four different kinds of epistemic rupture, which we call idealisation, re-presentation, objectivisation and re-formulation. In the last part of the paper we derive from the classification of the epistemic ruptures a classification of scientific revolutions. As only the first three kinds of rupture are revolutionary (the re-formulations are rather cumulative), we obtain three kinds of scientific revolution: idealisation, re-presentation, and objectivisation. We discuss the relation of our classification of scientific revolutions to the views of Kuhn, Lakatos, Crowe, and Dauben. (shrink)

There are several ontological and consequently also methodological mistakes in contemporary mainstream economics. Among them, the so-called ergodic axiom is play significant role. It is understandable that the real economy elaborated as formalized mental model looks like dynamic system on first sight. However, that is right only of dynamical systems in mathematical formalism. Economy that is in our understanding societal and/or collective economy is complex evolving organism. If we imagine such organism in the form of dynamical system that is as (...) clear mathematical formalism, we are losing their crucial authentic character. The significant irredeemable attribute of societal economy is lying in his complex evolving network process character created by large population of people with different decision-making and complex realizing among them. Going from these imaginations the two entities in a question that is dynamical system with their ergodicity and societal economic organism as complex evolving network are qualitative very different ones. That is the reason why we cannot accede with endeavours to draw on living economy straitjacket of ergodic axiom. To articulate that cause by other words ergodic dynamical systems are applicable for physical and partly for chemical entities and only scarcely are fit for living organisms. On the other hand however, as clear method the ergodic dynamical system have good applying for didactical approaches in economics where helping in better understanding some types of complexities in dynamics. The purpose of that essay is to discuss problems around usability of ergodic dynamical system theory and methods in economics in the age of advanced ICT knowledge based society. (shrink)

The presented paper substantiates the principle that values are an immanent component of science and any rational cognitive activity. This principle belongs to the European cultural tradition starting from the book of Genesis of the Old Testament, the values of certainty in the antique Greek philosophy and Francis Bacon's coincidence of knowledge and power. Values in science form complicated structures inconnection with different types of knowledge including “the knowledge that”, empirical evidence, various types of generalizations or rules, methods, directions, algorithms, (...) “the knowledge how”, “the knowledge why” or other types of knowledge. Since the assignments of different types of values are the products of a decision-making, it is useful to distinguish many types of decision-making, especially semantic decision-making, information decision-making and decision-making with distinctly pragmatic dimensions. The values assignable to scientific activities and their results also include their social recognition, respect and prestige granted to knowledge and bearers of knowledge by society and social groups or communities. Knowledge generation and the rational and justified application of the achieved and acceptable impacts are also connected with decision-making procedures, values and criteria of social acceptance. (shrink)

The aim of this article is to analyse relations between China and Russia over the Belt and Road Initiative (BRI) in the context of deepening Sino-Russian relations and the general rise of Eurasia. China and Russia are pivotal non-Western Eurasian powers in political, economic and military terms and the key motors of Eurasian multi-faceted integration. Both countries pursue their own interests and present their own projects and initiatives. Nevertheless, over the last few years, Sino-Russian cooperation has become strategic and is (...) starting to pursue a new model of globalisation and international order. In the article, I refer to this approach as the “New Eurasian Paradigm” (NEP). I follow Axel Honneth’s Hegelian-based theory of threefold-level recognition Hrubec (2011, p. 267). which I extend and employ at the interstate level to interpret the behaviour of China and Russia and their integration projects in terms of a struggle for political recognition as full, equal members of the global community determining global processes. Both countries thus aim to reform the global order and boost the integration of Eurasia in order to achieve successful development. These common interests are the main reasons behind their mutual strategic collaboration. (shrink)

The nature of changes in mathematics was discussed recently in Revolutions in Mathematics. The discussion was dominated by historical and sociological arguments. An obstacle to a philosophical analysis of this question lies in a discrepancy between our approach to formulas and to pictures. While formulas are understood as constituents of mathematical theories, pictures are viewed only as heuristic tools. Our idea is to consider the pictures contained in mathematical text, as expressions of a specific language. Thus we get formulas and (...) pictures into one linguistic framework, and so we are able to analyse their interplay in the course of history. (shrink)

For a decade, we have admired the incisive and broadly informed works of Ladislav Tondl on the foundations of science. Now it is indeed a pleasure to include this book among the Boston Studies in the Philosophy of Science. We hope that it will help to deepen the collaborative scholar ship of scientists and philosophers in Czechoslovakia with the English reading scholars of the world. Professor Ladislav Tondl was born in 1924, and completed his higher education at the (...) Charles University iIi Prague. His doctorate was granted by the Institute of Information Theory and Automation. He was a professor and scientific research worker at the Institute for the Theory and Methodology of Science, which was a component part of the Czechoslovak Academy of Sciences. Tondl's principal fields of interest are the methodology of the empirical and experimental sciences, logical semantics, and cybernetics. For many years, he collaborated with Professor Albert Perez and others at the Institute of Information Theory and Automation in Prague, and he has undertaken fruitful collaboration with logicians in the Soviet and Polish schools, and been influenced by the Finnish logicians as well, among them Jaakko Hintikka. We list below a selection of his main publications. Perhaps the most accessible in presenting his central conception of the relationship between modem information theory and the methodology of the sciences is his 1965 paper with Perez, 'On the Role of Information Theory in Certain Scientific Procedures'. (shrink)

This study critically reflects and assesses a recent debate over the nature of uniquely human cognition. The two standpoints in this debate are advocated by Michael Tomasello and Henrike Moll. Both agree that _shared intentionality_ is a key difference-maker, affording qualitatively new mental processes that support new forms of cooperative sociality and cumulative culture and thoroughly _transform_ human cognition. But Moll argues that Tomasello is infirm in his commitment to the transformative impact of shared intentionality on human cognition, flirting with (...) a conflicting, _additive_ account of shared intentionality as making a key difference only in the social domain. On her own view, human-unique social development innervated by human-unique forms of shared intentionality makes a difference across the board, and all the way down. This, we are told, is a reason not only to reject additive accounts, but to accept cognitive discontinuity across the board. Having reconstructed the two standpoints, I argue that Tomasello develops a consistently transformative approach immune to most objections leveled by Moll and in key respects more modest and plausible than her own alternative proposal. And I draw from this debate some general methodological lessons for theorizing about the nature and scope of human-unique cognition. (shrink)

This book offers new insights into the nature of human rational capacities by engaging inferentialism with empirical research in the cognitive sciences. Inferentialism advocates that humans' unique kind of intelligence is discursive and rooted in competencies to make, assess and justify claims. This approach provides a rich source of valuable insights into the nature of our rational capacities, but it is underdeveloped in important respects. For example, little attempt has been made to assess inferentialism considering relevant scientific research on human (...) communication, cognition or reasoning. By engaging philosophical and scientific approaches in a productive dialogue, this book shows how we can better understand human rational capacities by comparing their respective strengths and weaknesses. In this vein, the author critically revisits and constructively develops central themes from the work of Robert Brandom and other language rationalists: the nature of the assertoric practice and its connection to reasoned discourse, the linguistic constitution of the shared space of reasons, the social nature and function of reasoning, the intersubjective roots of social-normative practices and the nature of objective thought. Practices of Reason will be of interest to scholars and advanced students working in philosophy of mind, philosophy of language and philosophy of logic. (shrink)

Over the last decade, Hugo Mercier and Dan Sperber have elaborated an influential naturalistic account of human reasoning. Their distinctive hypothesis is that its adaptive rationale – and primary function – is to produce and assess reasons in interpersonal justification and argumentation. In this paper I argue, first, that their characterisation of reasoning as based on metarepresentations threatens to oversophisticate reasoning and faces the problem of vicious regress. Second, I argue that they owe us a coherent account of the cognitive (...) role of reasons in reasoning. (shrink)

In contemporary global knowledge based society there are scorching needs for new knowledge and unprecedented vision of future development. Author is focuses attention to new possibilities of fostering creative abilities and gaining new socio-economic knowledge by the assistance of ICT, Internet and mainly by using products and services of computational intelligence. His method used is prevailingly new knowledge creation by experimentation in virtual laboratories. In using conventional methods, he combines inductive and deductive methods as set up for developing mental models (...) from up to down and bottom to up. Because in socio-economic branches it is very difficult and even almost wholly impossible to do experiments in objective reality the experimentation by the assistance of computational intelligence is promising advance in gaining new socioeconomic knowledge in contemporary complex world. Using such new approaches, methods and tools is the main scientific aim of the author. He uses convictive demonstration of successful using these unprecedented possibilities in gaining deeper knowledge about complex evolutionary phenomena. The distinction of such knowledge is against conventional one is consisting in very deep understanding of complex socio-economic dynamics. Using meant knowledge acquisition approaches is promising in quality and in abiding knowledge and skill of single individuals but the extraordinary progress of creative knowledge based society fostered by using them in advanced webs is useful for whole society. (shrink)

In economics there are several complex learning themes and tasks connected with them difficult for deeper understanding of the learning subject. These are the reasons originating serious learning problems for students in the form of Virtual Environment because deeper understanding requires high level mathematical skills. Actually the most important feature for discerning this part of economics is the set of qualitative shapes emerging in discrete dynamic systems when they are undergoing iterations and/or experimentation with parameters and initial coordinates of variables. (...) Among such shapes there are: - trajectories in evolving time; - trajectories in R2 of two variables; - cobweb portraits; - one control parameter bifurcation with first and/or with second variables; - two control parameters bifurcation in R2 ; - cycles; - basin of attraction of two variables; - one Lyapunov’s exponent against some of control parameters; - Lyapunov’s exponents with two control parameters in R2; - absorbing area with possibility to create critical curves and/or attractors. The hope is that products of computational intelligence may help them solve such problems. Naturally, the meant complex economic problems and tasks have discrete, qualitative and nonlinear nature resulting in increased level of difficulties. So with the term used in the head of this paper one has to understand narrowly: “qualitative nonlinear computational economics”. For better understanding the very nature of the problem we are using as appropriate example actual simulation of the model of new ICT products monopolies in virtual laboratory built in the routines setting dominantly in the software iDMC. (shrink)

Mathematics is traditionally considered being an apriori discipline consisting of purely analytic propositions. The aim of the present paper is to offer arguments against this entrenched view and to draw attention to the experiential dimension of mathematical knowledge. Following Husserl’s interpretation of physical knowledge as knowledge constituted by the use of instruments, I am trying to interpret mathematical knowledge also as acknowledge based on instrumental experience. This interpretation opens a new view on the role of the logicist program, both in (...) philosophy of mathematics and in philosophy of science. (shrink)

Humankind, the biological species _Homo sapiens_, lives today in a very different world from the one for which it was evolutionarily selected in the geological epoch Pleistocene (2.6 million to twelve thousand years BC). The Anthropocene, as the epoch we live now has been called, is characterized by increasing tension between human nature and technological civilization, and humans live in an atmosphere of uncertainty, insecurity, and threat. By “naturalizing” the human condition, cognitive biology offers the only painless alternative to the (...) many scenarios that depict the extinction of _Homo sapiens_ as a consequence of violent conflicts and unimaginable suffering. (shrink)

The paper analyses the model as an artefact sui generis establishing the role of semiosis, as a homomorphic representation, as an artefact securing the function of an interface between the author and the receiver. The receiver's ability of accepting the model and its interpretation possibility and/or quality depends on the receiver's competence including the linquistic competence, his knowledge of the represented sphere and the knowledge of the applied sign system and its rules.

The aim of the present paper is to offer a new analysis of the multifarious relations between mathematics and reality. We believe that the relation of mathematics to reality is, just like in the case of the natural sciences, mediated by instruments . Therefore the kind of realism we aim to develop for mathematics can be called instrumental realism. It is a kind of realism, because it is based on the thesis, that mathematics describes certain patterns of reality. And it (...) is instrumental realism, because it pays atten-tion to the role of instruments by means of which mathematics identifies these patterns. The article concludes by offering solutions to some famous semantic paradoxes based on the diagonal construction as corroboration for this claim. (shrink)

This paper is a polemic response to the essay “The Semantics of Proper Names and Identity Theory of Predication” by L. Novák (SN 1–2/2004). In the first part of the article, the so-called descriptive theories of proper names and Kripke’s challenge to these views are briefly presented. It is pointed out that Novák’s exposition rests upon certain presuppositions in the theories of meaning and mind, which are controversial and which – without further argument – can hardly cast doubt on the (...) so-called New Theory of Reference. Furthermore, it is argued that Novák’s “minimal sense” of a proper name is too minimalistic and cannot be of service to the original idea of descripitivism. In the second part of the paper, an attempt is made to show that Novák’s extensional-intensional identity theory of predication is not based on identity, insofar as it is characterised by the axioms of the theory of identity. (shrink)

This book argues that Descartes’ physics was a milestone on the road to modern mathematical physics. After Newton introduced a completely different approach to mathematical description of motion, Descartes’ physics became obsolete and even difficult to comprehend. This text follows the language of Descartes and the means of which motion can be described. It argues that Descartes achieved almost everything that later Newton was able to do—to describe the motion of interacting bodies- by different (i.e. algebraic) means. This volume completely (...) refutes the received view according to which Descartes’ physics was merely a kind of discursive natural philosophy. To make this interpretation more plausible the book follows Descartes’ ideas from his early work in mathematics, through his invention of the analytic method towards his mature physics. It shows that Descartes followed a similar heuristic pattern. The volume appeals to students and researchers; it invites the reader equippedwith minimal understanding of college mathematics to follow Descartes on his intellectual journey through the Scientific Revolution. The reader will gain a deeper understanding of the role of mathematical language in the creation of modern physics and a glimpse into the fascinating world of Descartes’ scientific thought. Several of Descartes’ philosophical ideas can be traced back to his scientific interests and thus the book elucidates the motivation behind some of Descartes’ key positions in the area of epistemology and method. In the penultimate chapter the book presents four arguments in favor of seeing Descartes as a physicist on par with Galileo and Newton. (shrink)

There are many interpretations of the birth of modern science. Most of them are, nevertheless, confined to the analysis of certain historical episodes or technical details, while leaving the very notion of mathematization unanalyzed. In my opinion this is due to a lack of a proper philosophical framework which would show the process of mathematization as something radically new. Most historians assume that the world is just like it is depicted by science. Thus they are not aware of the radical (...) novelty of the mathematization of nature and focus their attention on the details of this process. Phenomenology by its radical questioning of the traditional interpretations of reality provides an ideal means for the reconstruction of the process of mathematization of nature and the birth of mathematical natural science. In a series of papers I tried to show the power of Husserl 's concept of mathematization by filling in the historical details into his interpretation. In the present article I want to compare Husserl 's approach with the approach of Heidegger. I believe that by comparing these two phenomenological theories of mathematization the advantages of Husserl 's approach will come to the fore. _German_ Es gibt mehrere Interpretationen der Entstehung der modernen Wissenschaft. Die meisten von ihnen beschränken sich allerdings auf die Analyse bestimmter historischer Episoden oder technischer Details, während der Begriff der Mathematisierung unanalysiert bleibt. Meiner Meinung nach ist dies auf das Fehlen eines richtigen philosophischen Rahmens zurückzuführen, der den Prozess der Mathematisierung als etwas radikal Neues zeigen würde. Die meisten Historiker gehen davon aus, dass die Welt so ist, wie sie von der Wissenschaft dargestellt wird. So verkennen sie die Radikalität der Mathematisierung der Natur und konzentrieren ihre Aufmerksamkeit auf die Details dieses Prozesses. Die Phänomenologie bietet dank ihrer radikalen Kritik der traditionellen Interpretationen der Realität ein ideales Mittel für die Rekonstruktion des Prozesses der Mathematisierung der Natur und der Geburt der mathematischen Naturwissenschaft. In einer Reihe von Arbeiten habe ich versucht, die Stärke der Husserlschen Interpretation der Mathematisierung zu zeigen, indem ich die historischen Details in seine Interpretation einfügte. Im vorliegenden Artikel möchte ich Husserls Ansatz mit dem Ansatz von Heidegger vergleichen. Durch diesen Vergleich der beiden phänomenologischen Theorien der Mathematisierung der Natur werden die Vorteile von Husserls Ansatz in den Vordergrund treten. (shrink)