Foundational Crisis Research Articles

“If the End Justifies the Means, Then This Is Permissible…”: Academic Deviations of Russian Postgraduate Students in Socio-Humanitarian Areas

This article looks at academic deviation practices from the viewpoint of graduate students, as well as whether or not they find certain types of deviant behavior in science and education acceptable. The theoretical framework consisted of two mutually exclusive approaches to the interpretation of academic deviations: the normativist R. Descartes and the epistemic anarchism of P. Feyerabend. The study purpose is to evaluate graduate students in socio-humanitarian scientific specializations regarding the prevalence and attitude toward academic deviation. Main hypothesis: postgraduate students’ views regarding academic deviations, especially plagiarism, fall on a continuum, ranging from total denial to total acceptance. Research design: quantitativequalitative. Empirical base: online survey (1276 respondents, including 185 graduate students), 5 focus groups. Methods of analysis: cluster analysis using the k-nearest neighbors method, qualitative analysis of focus group materials. Main results. It was discovered that creating crib sheets was the most prevalent form of academic deviation among graduate students. Of the respondents, 66% selected “often” and “very often” as their options. The purchase of exams, abstracts, and coursework showed the least amount of variation. Ten percent of those surveyed said that graduate students used plagiarism frequently or extremely frequently. Based on their attitudes regarding plagiarism, five distinct groups could be identified using cluster analysis, three of which would be more tolerant of it. Simultaneously, two of the five groups place the blame on students, and three see plagiarism as a result of the educational system’s failure to some extent. Directions for further research are related to the analysis of other forms of deviation, for example, practices of academic collusion within a university, as well as a description of the objective reasons for graduate students committing academic deviations, consideration of the prevalence of academic deviations of graduate students as a sign of a crisis in the normative foundations of the institution of graduate school.

Motifs of the crisis of the Russian family and national statehood in the epic trilogy of Boleslav Markevich (“A Quarter of a Century Ago”, “The Turning Point” and “The Void”)

In Soviet times, Boleslav Markevich's novel trilogy was unconditionally considered to be among the most orthodox anti-nihilistic works. However, already contemporary to the author, conservative criticism considered the nihilists to be the artistically weakest heroes of this trilogy. What is in the centre of Boleslav Markevich's narrative, is the historical fate of the Russian nobility, which suffered a crushing defeat during the “great reforms” of the 1860s, rather than nihilists. Boleslav Markevich shows that that defeat was associated with a deep spiritual crisis of the enlightened part of the nobility, which supported the national statehood, with the latter preserving the moral foundations which strengthened the Russian family. In his trilogy, Boleslav Markevich depicts the rapidly growing crisis of those spiritual foundations, which was a fertile ground for flourishing of Russian nihilism. In this case, Boleslav Markevich is close to Fyodor Dostoevsky, who in the novel “Demons” for the first time had showed the continuity between cultural nobles and nihilists who are their heirs, the spiritual children of the latter. The lack of faith in fathers gave rise to nihilism in sons. That is why Boleslav Markevich’s focus is on the nobility rather than on Russian nihilists as, due to which that writer turned out to be a thoughtful art historian.

The problem of incommensurability and the crisis of foundations of the Ancient Greek mathematics

The subject of this research is the problem of incommensurability and the crisis of foundations of the Ancient Greek mathematics. The article describes that the crisis of foundations was caused by the discovery of irrationality by the Pythagorean Hippasus of Metapontum, which resulted in the theoretical instability of mathematics of the Pythagoreans, who believed that everything could be expressed through numbers. The discovery of incommensurable line segments demonstrated that the relations between rational numbers cannot express any variable, for example the diagonal of a square with one side equal to one. Analysis is conducted on the achievements of the Pythagorean School in the field of mathematics. Special attention is given to the role of a number in the philosophy of this school. The article explores the main ways for overcoming this crisis, philosophical explanation of the unfolded situation, based on which the Pythagoreans formulate the methodological ways out of the discovered problem of incommensurability. It is noted that the Pythagoreans were actively elaborating on their philosophy and mathematical apparatus intending to find the answer to the discovery of incommensurability. The author’s special contribution lies in the statement that the discovery of irrationality was not critical for the Pythagoreans: they continued working towards the answer to the problem of incommensurability, as well as refined the mathematical theory of proportions, reconsidered the representation of infiniteness as a certain numerical characteristic of the things and processes. This article is first to advance a hypothesis on the possibility of dividing the object into an infinitely large number of infinitely small parts, which is now understood as the limit of function, which contributes to the development and application of dialectics. The problem of incommensurability led to the creation of new, complex theories in the history of science, culture, architecture, and art.

Crisis” and “re-foundation” of psychology – outmoded topics of theoretical-psychological discourse?

In the 1970-80ies critical assessments of the problematic state of psychology as science were flourishing, stressing the theoretical disintegration and practical irrelevance of psychological basic research and connecting both defects to a misplaced dependence of mainstream psychology on a scientistic notion of scientific cognition. Talks of a crisis in psychology were gaining ground again. Controverting the paradigmatic maturity vs. the pre-/non-paradigmatic state of our discipline or, alternatively, its necessarily multi-paradigmatic character, the quest for unification as against a programmatic theoretical pluralism became a top issue of scholarly dispute. The institutionalisation of ISTP in 1985 and its initial epistemological and meta-theoretical core themes clearly reflected this pervasive trend. Some 35 years later, it has become noticeably quiet about such concerns, and there is no evidence of a renewal of large-scale discussions on a foundational crisis in psychology, let alone of ambitious attempts at theoretical unification or re-foundation – despite the fact that none of the “epistemopathologial“ (Koch, 1981) diagnoses of traditional variable-psychology have been refuted or lost strategic importance. Combining historical retrospection with an exemplary analysis of topical theoretical-psychological subjects, the aim of my paper is to get a clearer idea of where Theoretical Psychology currently stands in regard to the meta-scientific study of psychological theory-problems.

Towards a new philosophical perspective on Hermann Weyl's turn to intuitionism.

The paper explores Hermann Weyl's turn to intuitionism through a philosophical prism of normative framework transitions. It focuses on three central themes that occupied Weyl's thought: the notion of the continuum, logical existence, and the necessity of intuitionism, constructivism, and formalism to adequately address the foundational crisis of mathematics. The analysis of these themes reveals Weyl's continuous endeavor to deal with such fundamental problems and suggests a view that provides a different perspective concerning Weyl's wavering foundational positions. Building on a philosophical model of scientific framework transitions and the special role that normative indecision or ambivalence plays in the process, the paper examines Weyl's motives for considering such a radical shift in the first place. It concludes by showing that Weyl's shifting stances should be regarded as symptoms of a deep, convoluted intrapersonal process of self-deliberation induced by exposure to external criticism.

Миф о трех кризисах в основаниях математики Часть 2

The story of “the three crises in foundations of mathematics” is widely popular in Russian publications on the philosophy of mathematics. This paper aims at evaluating this story against the background of the contemporary scholarship in the history of mathematics. The conclusion is that it should be considered as a specimen of modern myth-making activity brought to the fore by an unconscious tendency to model the whole history of mathematics on the pattern of the foundational crisis of the first decades of the 20th century. What is more, the consideration of the specific role and character of the foundations in both early Greek mathematics and 18th-century mathematics gives an occasion to raise a more general question regarding the true meaning of the historicity of mathematics. In the first part of this paper, it has been demonstrated that there is no evidence to recognize the so-called “first foundational crisis” in pre-Euclidean Greek mathematics caused by the discovery of incommensurable magnitudes. The second part is mainly devoted to the historical situation of the 18th century and the beginning of the 19th century, the alleged epoch of “the second foundational crisis” caused by the obscurity of the basic notions of the calculus. Despite the lack of clarity as far as the foundations of mathematical analysis are concerned, there are no signs of a foundational crisis in 18th-century mathematics. On the contrary, in the 19th century, at the time of “the second scientific revolution”, there are striking illustrations of crisis awareness. The cultural processes that engendered this awareness are shown to be identical for the 19th century and the beginning of the 20th century, hence the second and the third foundational crises are proved to be the different stages of the same unique crisis. Finally, we have only one foundational crisis instead of three.

The crisis of the metaphysical foundations of human existence as a global problem of post-modernityand the ways of managerial solutions

The relevance of the study of the crisis of the metaphysical foundations of human existence is due to the fact that humanity is in a crisis of global development of the world associated with the Fourth Industrial Revolution 4.0, the technological development of the world, the demographic and environmental crisis, the epidemic of the coronavirus COVID-19. The purpose of the study is to conceptualize the socio-philosophical reflection of the crisis of the metaphysical foundations of human existence, which is a global problem of our time, which threatens our civilization, is associated with economic and social development, with many problems, including the problem of COVID-19. The objectives of the research are to identify the problems of the metaphysical dimensions of human existence and find ways that promise to lead to great achievements - to raise living standards, create new economic opportunities, solve anthropological, existential and ontological problems of human being associated with the real de-objectification of human existence, loss of the integrity of self-determination.The scientific novelty of the research is that it presents a solution to new problems of the crisis of the metaphysical foundations of human existence and ways to solve them.

Миф о трех кризисах в основаниях математики Часть 1

The story of “the three crises in foundations of mathematics” is widely popular in Russian publications on the philosophy of mathematics. This paper aims at evaluating this story against the background of the contemporary scholarship in the history of mathematics. The conclusion is that it should be considered as a specimen of modern myth-making activity brought to the fore by an unconscious tendency to model the whole history of mathematics on the pattern of the foundational crisis of the first decades of the 20th century. What is more, the consideration of the specific role and character of the foundations in both early Greek mathematics and 18th-century mathematics gives an occasion to raise a more general question regarding the true meaning of the historicity of mathematics. The first part of this paper deals with the point whether there was a foundational crisis in pre-Euclidean Greek mathematics caused by the discovery of incommensurable magnitudes and Zeno’s paradoxes. The result is negative: we have no direct historical evidence of such a crisis; as for secondary considerations, they also mainly count against it. The idea of the first crisis in foundations of mathematics has emerged as a result of the unjustified transference of the modern grasp of foundational issues and the modern “mentalité de crise” to the ancient past.

Cassirer, der Grundlagenstreit und die „idealen Elemente“ der Mathematik

Abstract This paper shows that Cassirer’s philosophy of mathematics underwent a significant transformation by the end of the 1920s. This transformation was due to Cassirer’s reception of the ‘foundational crisis’ within mathematics itself. David Hilbert’s conception of the ‘ideal elements’ of mathematics attracted Cassirer’s particular attention. Indeed, he sought a ‘transcendental deduction’ of these elements. Reflection on this issue is therefore essential to providing an adequate interpretation of the later Cassirer’s enterprise in the philosophy of mathematics.

Понятие социализации как путь выхода из методологического кризиса педагогической науки

The paper discusses various approaches to the pedagogical science object and subject definition. It is noted that modern pedagogy is one of the few sciences that, existing for more than a century, still cannot decide on the conceptual questions. The rationale that the scientists opinions pluralism has led to a methodological crisis in the pedagogy foundations is given. The problem seems to be in the comprehensive integration wake, pedagogy may lose its independence and become an education sciences faceless field. Three approaches to the pedagogy conceptual questions understanding are considered: utilitarian, historiographical and anthropological, the simlified application of which has led to the modern “twilight” state. As the way out of the crisis, an approach is proposed. It integrates the various authors positions and leaves pedagogy with its own problem field – the social experience translation.

Моральный баланс социального государства и правда леволиберального дискурса

The article focuses on revealing the objective role of left-liberal discourse in the context of the current crisis of philosophical, moral and ideological foundations of the welfare state. The author shows that morally and ideologically the social state is a compromise combination of local statist and economic utilitarianism and universalist liberal-socialist humanism. One can see the description of optimal moral balance of the social state, achievable within the framework of this “limited universalism”. Due to the destruction of this balance, it becomes necessary to search for new philosophical, moral and ideological bases of social policy. Currently, this search is unfolding within the framework of left-liberal discourse, which involuntarily contributes to the neoliberal “fragmentation policy”. Nevertheless, it destroys the obsolete moral and ideological foundations of the former social state, while the left and right populists, who oppose the left-liberal discourse, are still capable of only putting forward utopian slogans of its revival or protection.

Masculinity, Affect, and Carlist Malestar in Zumalacárregui / [Masculinidad, afecto y malestar carlista en Zumalacárregui

In 1898, Galdós inaugurated the Third Series of the Episodios Nacionales with the publication of Zumalacárregui. Published in the midst of the escalating conflict with the United States, Galdós's novel revisits the foundational crisis of the liberal nation state: the First Carlist War. Galdós embeds the reader in the Carlist army through the point of view of José Fago, a military chaplain who abandons ecclesiastical life to become a soldier in an attempt to imitate his hero, the famed General Zumalacárregui. The tension between Fago's vocation and his frustrated desire for military glory provokes a crisis of identity and masculinity, which reveals Fago's emotionality. Dierdra Reber has proposed that the dominant episteme of the modern age is based on feelings, rather than logic; the thinking head of the Cartesian episteme has been replaced by the body that "thinks" by feeling. This essay analyzes how Galdós critiques Carlism through Fago's affective understanding of the war and the Cause. Galdós portrays Fago as a subject suffering from the "effects" of Carlism, a system that causes "malestar," both emotionally and physically, for its followers.

Ideen zu einer Kritik ‚algorithmischer‘ Rationalität

Abstract A critique of algorithmic rationalisation offers at best some initial reasons and preliminary ideas. Critique is understood as a reflection on validity. It is limited to an “epistemological investigation” of the limits of the calculable or of what appears “knowable” in the mode of the algorithmic. The argumentation aims at the mathematical foundations of computer science and goes back to the so-called “foundational crisis of mathematics” at the beginning of the 20th century with the attempt to formalise concepts such as calculability, decidability and provability. The Gödel theorems and Turing’s halting problem prove to be essential for any critical approach to “algorithmic rationalisation”. Both, however, do not provide unambiguous results, at best they run towards what later became known as “Gödel’s disjunction”. The chosen path here, however, suggests the opposite way, insofar as, on the one hand, the topos of creativity appear constitutive for what can be regarded as cognitive “algorithmic rationalisation” and which encounters systematic difficulties in the evaluation of non-trivial results. On the other hand, the investigations lead to a comparison between the “mediality” of formally generated structures, which have to distinguish between object-and metalanguages, and the “volatile” differentiality of human thought, which calls for syntactically non-simulatable sense structures.

Radical views on cognition and the dynamics of scientific change

Radical views on cognition are generally defined by a cluster of features including non-representationalism and vehicle-externalism. In this paper, I concentrate on the way radical views on cognition define themselves as revolutionary theories in cognitive science. These theories often use the Kuhnian concepts of “paradigm” and “paradigm shift” for describing their ambitions and the current situation in cognitive science. I examine whether the use of Kuhn’s theory of science is appropriate here. There might be good reasons to think that cognitive science is in a situation of foundational crisis, but that does not entail that the classical paradigm (computationalism) is currently displaced to the benefit of a new paradigm. Larry Laudan’s theory of research traditions is more enlightening than Kuhn’s theory for describing the scope and ambitions of radical views on cognition, and their relations with an anti-intellectualist tradition in philosophy.

On some aspects of Kazakhstan’s media equipment as the basis of the national spirit

This article provides an axiological analysis of the national socio-cultural and media-educational spaces of Kazakhstan. The authors of the article put forward a hypothesis about the relationship of spiritual values with other spheres of public life, about the possibility of the revival of the national spirit under their influence. The features of the functioning and development trends of the domestic media industry and media education are revealed. Education is shown as a historical phenomenon that is directly dependent on the level of development of society. In the article, the authors attempt, within the framework of social philosophy, to overcome the crisis of traditional foundations and principles of upbringing and education, to ensure the priority of universal human values in the hierarchy of educational goals. The authors come to the conclusion that the study of the modern educational landscape, the possibilities and ways of establishing media education in the sociocultural space will help understanding the education of the individual as the process of forming conscious independence, independence and human freedom in its tolerant and equal interaction with society and nature. Key words: education, upbringing philosophy, culture, media education, media industry, national spirit, mentality, informatization, digitalization, spiritual values.

A/logos: An Anomalous Episode in the History of Number

A/logos: An Anomalous Episode in the History of Number Sarah Pourciau (bio) “Mathematics is the science of the infinite” (Weyl, “The Current Epistemological Situation” 123).1 With this pronouncement, the German mathematician Hermann Weyl opens his 1925 diagnostic essay, “The Current Epistemological Situation in Mathematics” (Die heutige Erkenntnislage in der Mathematik), which takes the measure of a contemporary situation identified elsewhere by Weyl as a “foundational crisis” (“On the New Foundational Crisis of Mathematics”). At issue for Weyl, as for many of his fellow mathematicians—whose positions he attempts to reconcile in his paper —is the ongoing battle for dominion over an infinitely divisible continuum. That unbroken flow of experiential time and space, within which, as the Presocratic philosopher Anaxagoras had already observed by the 5th century BC, there is no smallest part of what is small, since there is always a smaller (Curd 38, fragment 3), poses seemingly insurmountable difficulties for an attempt to analyze the world into discrete, and thus calculable or measurable units. On the one hand: to eschew all such analysis is to relinquish the possibility of science, and perhaps even of language, since both activities would appear to depend on an intellectual capacity for delimiting particular phenomena. On the other hand: the contradictions generated by ignoring Anaxagoras’ prohibition against a carved-up continuum (“the things in the one kosmos have not been separated from one another, nor hacked apart with an axe” [Curd 51, fragment 8]) have dogged both philosophers and mathematicians for millenia. Weyl, who [End Page 616] provides a thumbnail history of this “dogging” that runs from Zeno to the traumata of modern set theory, sums up the situation as follows: “One can see how deeply mathematics is tied in its foundations to the general problems of knowledge. The old opposites of realism and idealism, of the Being of Parmenides and the Becoming of Heraclitus, are here again dealt with in a most pointed and intensified form” (“The Current Epistemological Situation” 141).2 Weyl is right to insist (and he is far from alone in doing so) that modern set theoretical arguments are intimately tied to ancient debates about the nature of being and knowledge. His “here again” is deceptive, however, because something actually happens over the course of the late 19th and early 20th centuries—the very something, indeed, that precipitates the “crisis” about which Weyl is writing—that had never happened before in the history of thought. The definition of number undergoes during this period a profound metamorphosis, which calls forth an equally profound metamorphosis in the definition of logical relation. The following article will argue that this double transformation in the definitions of arithmos and logos hangs together with a shift in the mathematical understanding of the role played by anomalous phenomena—and by the concept of the anomalous per se—in the construction of a proper domain for thought.3 The anomaly starts out, via a tradition that harks back to the ancient Greeks and extends well into the 19th century, as a rule-flouting, definition-resisting exception to be explained away or excluded from the system of self-consistent commensurable truths. It then becomes, for a brief, quasi-Hegelian moment prior to the early 20th century axiomatization of set theory, the antithesis that drives the mathematical “thesis” of number toward the telos of an all-encompassing synthesis. From this point onward it transforms again—via a powerful deflation of the Idealist model—to produce the situation that still governs much of contemporary mathematical, [End Page 617] biological, and philosophical thought: the “anomalous” itself becomes associated with nature, while within this default state of chaos and entropy, the orderly systems of reason and life emerge as improbable, negentropic exceptions.4 I The question of what it means to count has always been bound up, also terminologically, with the question of what it means to think. And the question of what it means to be “anomalous” with respect to both activities—to be non-homologous or asymmetrical to the homologies and symmetries of mathematical reason (anomaly, from Gr. anomalia = “inequality, irregularity,” from an “not” + omalos “even, regular,” from homos “one and the same”)—has always been...

ПРОБЛЕМА СОЦИАЛЬНЫХ ФУНКЦИЙ СОВРЕМЕННОГО ГОСУДАРСТВА: ФИЛОСОФСКИЙ АНАЛИЗ

Russian and foreign scientists are increasingly turning to the concept of the social state, its problems and prospects of existence. There are grounds for believing that in addressing issues related to the future of the welfare state and problems of its development, philosophical thought should contribute among others. Scientists set the task of describing and explaining significant changes in the role of the modern state in the management of public affairs (especially in the social sphere). This problem is solved by researchers from different, sometimes opposite, theoretical and methodological positions. Based on the modern scientific theory of the historical process, the paper studies the problem of the implementation of social functions by modern states. It attempts to identify the anthropological foundations of the state and its social function in terms of the philosophical concept of human nature. The author gives his own definition of the social function of the state, which is presented in a wide and narrow sense. The paper proves the idea that the problem of social functions of modern states is a consequence of the crisis of the anthropological foundations of the modern human civilization. The crisis of the homo economicus determines the revision and subsequent optimization of the social obligations of the modern state, the reduction of its social functions. The poverty of the working population, its aging and debt load, job cuts due to the introduction of automated production, deep class differentiation, and other manifestations of this crisis require new approaches to managing the affairs of society. «Departure» of the state from the social sphere inevitably leads to the increased religiosity in society, enhanced role of major international corporations that have a significant potential for the replacement of the state’s social functions. The paper provides basic recommendations and suggests the main ways to overcome the anthropological crisis in modern Russia.

The changing role of continuity and discontinuity in the history of philosophy and mathematics

The aim of this article is to highlight the inevitability of employing discreteness and continuity as primitive (indefinable) modes of explanation in the history of philosophy and mathematics. It embodies the general challenge to account for the coherence of what is unique. Gödel emphasises the coherence of ‘primitive concepts’. Greek philosophy already discovered the spatial whole and/or parts relation with its infinite divisibility. During and after the medieval era philosophers toggled between an atomistic appreciation of the continuum and its opposite, for example found in the thought of Leibniz who postulated his law of continuity (lex continui). The discovery of incommensurability (irrational numbers) by the Greeks caused the first foundational crisis of mathematics, as well as its geometrisation. Leibniz and Newton did not resolve the problems surrounding the limit concept and soon it induced the third foundational crisis of mathematics. It caused Frege and the ‘continuum theoreticians’ to assign priority to the continuum – discreteness is a catastrophe. Recently Smooth Infinitesimal Analysis appreciated what is ‘continuous’ as constituting ‘an unbroken or uninterrupted whole’. Intuitionistic mathematics once more proceeded from an emphasis on the whole and/or parts relation. In spite of alternating attempts to understand continuity exclusively, either in arithmetical or in spatial terms, the history of philosophy and mathematics undeniably confirms that the co-conditioning role of these two modes of explanation remains a constant element in reflections on continuity and discontinuity. (The role of continuity and discontinuity within the disciplines of physics and biology will be discussed in a separate article.)

The Philosophical Implications of Set Theory in Infinity

What does the term “Infinity” mean? There are mathematical, physical and metaphysical definitions of the concept of limitlessness. This study will focus on the scription of the three philosophical foundations of mathematics – formalism, intuitionism and logicism – in set theory. Examples will also be provided of the concept of infinity for these three schools of thought. However, none of them cannot prove whether there is an infinite set or the existence of infinity. It forms the foundational crisis of mathematics. Further elaboration on these schools of philosophy leads to the ideas of actual, potential and absolute boundlessness. These correspond to three basic aforementioned definitions of infinity. Indeed for example, by using Basic Metaphor Infinity, cognitive mechanisms such as conceptual metaphors and aspects, one can appreciate the transfinite cardinals’ beauty fully (Nũnez, 2005). This implies the portraiture for endless is anthropomorphic. In other words, because there is a connection between art and mathematics through infinity, one can enjoy the elegance of boundlessness (Maor, 1986). Actually, in essence this is what mathematics is: the science of researching the limitless.

Theological Underpinnings of the Modern Philosophy of Mathematics.

Abstract The study is focused on the relation between theology and mathematics in the situation of increasing secularization. My main concern in the second part of this paper is the early-twentieth-century foundational crisis of mathematics. The hypothesis that pure mathematics partially fulfilled the functions of theology at that time is tested on the views of the leading figures of the three main foundationalist programs: Russell, Hilbert and Brouwer.