Geared toward undergraduate majors in math, computer science, and computer engineering, this text employs discrete mathematics to introduce basic knowledge of proof techniques. Exercises with hints. 2019 edition.

The study analyzes modern reductivist and antireductivist approaches to understanding the interaction between philosophy and neuroscience. It analyzes the content and grounds for using the concepts of neuroscience and neurosciences, philosophy of neuroscience, and neurophilosophy. The milestones in the development of neuroreductivism, from Patricia Churchland’s arguments in support of intertheoretic reduction through Francis Crick’s eliminativism to John Bickle’s ruthless reductionism, are described. The ontological, methodological, and epistemic grounds for the reduction to neurosciences of other ways of representing mind and body (...) are analyzed. Drawing on the post-Wittgensteinian paradigm of the philosophy of neuroscience of Max Bennett, Peter Hacker, and Andrew Reynolds, the semantic problems that arise in the neurosciences when epistemic reduction is attempted are described and derive from the inability to eliminate the basic metaphorical level of meaning-making and transmission rooted in everyday language and its figures, among which metaphors are fundamental. The descriptivist approach to the language of neurosciences is contrasted with neurorevisionism, an attempt to “correct” established ways of conceptualizing consciousness and corporeality, akin to earlier revisionisms, particularly physicalism, and forced to deal with similar problems. Reduction - the operation of the “return,” itself understood metaphorically - and antireduction, which resists scientific revisionism and “returns” understanding to the level of everyday language and philosophy to descriptive work, is presented as a circular hermeneutical movement necessary for scientific and philosophical understanding, but not leading to disciplinary hegemony or the “victory” of either side. The study concludes with a sketch of the publications included in the rubric. (shrink)

Using the two cases of the Icelandic Health Sector Database and Russian initiatives in biobanking, the article criticizes the view of narratives and imaginaries as a sufficient and unproblematic means of shaping public understanding of genetics and justifying population-wide projects. Narrative representations of national biobanking engage particular imaginaries that are not bound by the universal normative framework of human rights, promote affective thinking, distract the public from recognizing and discussing tangible ethical and socioeconomic issues, and harm trust in science and (...) technology. In the Icelandic case, the presentation of the project in association with national imaginaries concealed its market identity and could lead to the commodification of biodata. In the Russian case, framing in terms of "genetic sovereignty" and "civilizational code" offers pretexts for state securitization. Adherence to normative framework of human rights and public discussion of genetics in an argumentative and factual mode can counter these trends. (shrink)

This research is devoted to the study of scientific and methodological aspects of providing students with physical education. The research is based on the works of Russian teachers who have adopted the experience of the new higher education program for bachelor's degree. The starting point for the development of new concepts is the latest edition of the Federal State Educational Standard for Higher Education. The purpose of the study is to analysis of the scientific and methodological support of physical education (...) of students under the Federal State Educational Standard program. In the course of the research, we study the most important aspects of the formation of physical skills with the help of basic and additional types of interaction between a teacher and students. Scientific novelty lies new look at complex education, which includes an expanded set of methods, technologies for the development of cognitive interest, activity, physical skills and motivation for active recreation, a healthy lifestyle. The design technology of 2021, based on the method of new generation projects by Evgenia Semyonovna Polat, is a separate factor. The result of the study was the definition of the scientific and methodological aspects of providing physical education in the main and additional types of interaction between the teacher and students, including physical culture, sports, elite sports, competitive tests, project technology and distance learning format. (shrink)

The article aims at clarifying the historical status and cognitive potentials of such a genre of contemporary historiography of philosophy as biographical encyclopedia (dictionary). Based on extensive bibliographic material, the author demonstrates that in the late XX – early XXI centuries in the English-speaking countries there was a real outbreak of interest in encyclopedias and dictionaries, compiled from personalized articles about the life and works of philosophers of certain epochs, countries, trends, etc. According to the author, the increasing popularity of (...) this genre can be considered as a logical continuation of the historical and biographical turns that took place in the Anglo-American (analytic) philosophy in the 1980s and 1990s, respectively. The author specifically emphasizes that it caused the appearance of a significant number of encyclopedias and dictionaries, which contain the well-known facts as well as the significant elements of scholar novelty. The article also shows that similar tendencies have taken place in the contemporary Ukrainian historiography of philosophy. It is shown that Ukrainian experts also made their own significant contribution to the development of this genre. They have successfully developed a special approach, which presupposes the focus on life and works of the representatives of a particular academic institution. The intellectual value of this approach is demonstrated by the example of the recently published two-volume encyclopedia “Kyiv Theological Academy in Names: 1819-1924”. It contains a systematic and very informative presentation of the biographies of many representatives of the national philosophy, whose activities were associated with this institution. The author also shows that from the perspective of the historiography of philosophy, the general methodological foundations of this encyclopedic research is a matter of special interest. (shrink)

Traditionally, in the literature on robustness analysis objects are classified as genuine phenomena (natural objects, events, and processes) or artifacts (results produced in error). But much of biological measurement requires the manipulation of local experimental conditions in order to produce new effects. These types of intervention-based regularities are neither natural objects nor artifacts; characterizing them as either fails adequately to address key ontological properties as well as their role in scientific practice. It is argued that a new classification, based on (...) methodological considerations, can be useful in order to characterize experimental productions. Experimentally-useful context-sensitive objects are referred to as ‘artefacts’. To show how the new classification works and why it is instructive for scientific practice, two case studies are discussed. First, the puzzle of arsenic-consuming living organisms is analyzed, where under a set of specific experimental conditions a given organism was found to replace phosphorous with arsenic in its DNA. Second, ecological epigenetic measurement is discussed to show the complexity of variant effects in the context of lab, field, and computer measurements. It is argued that the line between artifacts and artefacts is fluid because theoretical, experimental, and practical considerations vary. (shrink)

The article offers an attempt to understand the present state of Kant’s legacy in Russia on the threshold of the Tercentenary. An explanans is found in the metaphors of “ tabula rasa ” and “unplowed virgin soil,” first used by Leibniz in relation to Russia in his letters and memoranda addressed to tsar Peter I and other members of the Russian elite, which became the country’s “absolute metaphors to live by” up to present time. Several known and unknown episodes from (...) the history of the reception of Kantian ideas, his followers in Russia, and the transformation of the urban environment of Kant’s life in Königsberg, as it was becoming Kaliningrad, are presented through the prism of this metaphor. Without hoping to make specific recommendations of any use from such metaphorical grounds, this study aims to emphasize the depth, interconnectedness, and basic, metaphysical tension of the relationship between Europe and Russia, which cannot be terminated at will by either side, or by a third party. In a situation where the sides are doomed to dialog, Kant, appropriated by Russia as its “subject,” occupies the unique position of mediator of philosophical understanding and peaceful action. (shrink)

In the Club of Rome report Come on! Capitalism, Short-Termism, Population and the Destruction of the Planet (2018) Kant, along with other “old” Enlighteners, is presented as the father of a world-view which led to the destabilisation of the environment in which humanity exists. The authors of the report argue that the “old Enlightenment” with its individualism, faith in the market and a consumerist attitude to nature should be scrapped. I maintain that this assessment of Kant’s philosophy is groundless and (...) that his ideas allow us both to conduct a more profound diagnosis of the crisis and to propose a more solidly founded strategy of overcoming it. First, I sum up the position of the authors concerning the loss of sustainability of development which they attribute to the philosophy of Enlightenment. Next, I outline the history and content of the notion of “sustainable development” and offer an analysis of the sources of progressivist commitment to the conquest of nature which lie outside Modern Times in the idea of the “cultural mandate”. Then I present the Kantian diagnosis of the causes of the crisis which attributes it to humankind’s failure to “mature”. I compare the idea of “the full world” formulated by the authors of the report with the idea of the “the world come of age” and their diagnosis of “capitalism — short-termism — depletion of resources” with the Kantian assessment of the attempts to escape from the predicaments of the present into the past or the future. I draw attention to Kant’s solutions to some of the specific problems indicated in the report. Instead of the strategy of “return of the cultural mandate”, proposed at this time by the authors of the report, the Kant­ian answer to the crisis is a “Copernican turn” and re-direction of the cultivating effort to the inner moral development of the human being. (shrink)

An online game of chess against a human opponent appears to be indistinguishable from a game against a machine: both happen on the screen. Yet, people prefer to play chess against other people despite the fact that machines surpass people in skill. When the philosophers of 1970’s and 1980’s argued that computers will never surpass us in chess, perhaps their intuitions were rather saying “Computers will never be favored as opponents”? In this paper we analyse through the introduced concepts of (...) psychological affordances and psychological interplay, what are the mechanisms that make a human-human interaction more meaningful than a human-computer interaction. We claim that an HH chess game consists of two intertwined, but independent simultaneous games—only one of which is retained in the HC game. To help with the analysis we introduce the thought experiment of a Preferential Engagement Test which is inspired by, but non-equivalent to, the Standard Turing Test. We also explore how the PET can illuminate, and be illuminated by, various philosophies of mind reading: Theory Theory, Simulation Theory and Mind Minding. We propose that our analysis along with the concept of PET could illuminate in a new way the conditions and challenges a machine must face before it can replace humans in a given occupation. (shrink)

A murder of an Afro-American detainee by a policeman at the end of May 2020 caused a public outrage in the United States, which led to a campaign against the monuments to historical figures whose reputation, according to the protesters, was marred by racism. Some German publicists, impressed by the campaign, initiated an analogous search for racists among the national thinkers and politicians of the past. Suddenly Kant emerged as a ‘scapegoat’. This statement is an attempt to assess such reactions (...) from the perspective of Russia’s experience. (shrink)

This article reevaluates the mystical techniques and experiences peculiar to Abraham Abulafia’s Kabbalah and attempts to offer an alternative approach to their dominant understanding, which largely depends on Moshe Idel’s work. Current scholars of Jewish mysticism have a habit of highlighting the “unique character” of Abulafia’s mystical practices while asserting that they cannot be compared with the induction techniques and the psychophysical phenomena typical of hypnosis. While generally agreeing with the scholars discussed that the hyperactivation of the mind found in (...) Abulafian Kabbalah contrasts sharply with the mental relaxation attained through the mystical practices of other religious traditions, the present study takes issue with the current view of Abulafian Kabbalah’s relation to hypnotic procedures, processes, and states. This work addresses the issues present with the current view and offers a more inclusive model for interpreting Abulafia’s Kabbalah, drawing from psychiatrist Roland Fischer. (shrink)

This article explores the domain of legal analysis and its methodologies, emphasising the significance of generalisation in legal systems. It discusses the process of generalisation in relation to legal concepts and the development of ideal concepts that form the foundation of law. The article examines the role of logical induction and its similarities with semantic generalisation, highlighting their importance in legal decision-making. It also critiques the formal-deductive approach in legal practice and advocates for more adaptable models, incorporating fuzzy logic, non-monotonic (...) defeasible reasoning, and artificial intelligence. The potential application of neural networks, specifically deep learning algorithms, in legal theory is also discussed. The article discusses how neural networks encode legal knowledge in their synaptic connections, while the syllogistic model condenses legal information into axioms. The article also highlights how neural networks assimilate novel experiences and exhibit evolutionary progression, unlike the deductive model of law. Additionally, the article examines the historical and theoretical foundations of jurisprudence that align with the basic principles of neural networks. It delves into the statistical analysis of legal phenomena and theories that view legal development as an evolutionary process. The article then explores Friedrich Hayek’s theory of law as an autonomous self-organising system and its compatibility with neural network models. It concludes by discussing the implications of Hayek’s theory on the role of a lawyer and the precision of neural networks. (shrink)

The current state of philosophy of science is characterized by stasis in the struggle between realism and antirealism. In recent years, a number of authors have come out with a program of scientific perspectivism that claims to sublate this great collision and gain the status of a new epistemological paradigm: “perspectivism, or, better, perspectival realism, is one of the newest attempts to find a middle ground between scientific realism and antirealism” [1. P. 2]. Important milestones of the perspective movement were (...) the works of Ronald Giere, Francois Recanati, Bas van Fraassen, Michela Massimi, and others. The thesis of the article is that perspectivism has not yet realized its claims to autonomy, although it has become an important new arena for discussions between realists and antirealists who try to appropriate perspectivist concepts and arguments. The “middle ground,” when thought out consistently and thoroughly, turns out to lie not “between,” but either in the territory of realism or in the territory of antirealism, depending on the presumptions of the author of a particular perspectivist conception. This is demonstrated by the analysis of the conceptions of Giere, Massimi, and Recanati. Giere’s perspectivism is based on the metaphor of color vision, and for him only some (secondary) qualities of real objects turn out to be perspectival, i.e., subject-dependent. Massimi’s perspectivism attempts, on the basis of a visual arts metaphor, to combine the phenomenon of the plurality of scientific theories (“perspectival disagreement” about what an object is) with the general realist attitude of science (agreement about that there is an object). Recanati’s perspectivism syncretizes realism about ordinary objects and relativism about other things. The first two versions of perspectivism rely on a perceptual metaphor: perspective is conditioned by the perceptual constitution of the observer, that is, it arises at the mental or cognitive level. Recanati’s version attempts to derive perspective from contextuality, that is, it is semantic. However, it does not show exactly how perceptual categories are superimposed on theories or how scientific concepts reveal their perspectival character. The isomorphism of perception and theoretical thinking, sensibility and understanding, remains undemonstrated. On the one hand, perspectivist efforts are motivated by an important concern to account for antirealist critique (lack of access to the “view from nowhere,” factual and semantic underdetermination, difficulties with the idea of approaching the truth, the historicity of knowledge, the activeness of the constructing subject, etc.) while preserving the scientific commitment to universality, validity, and truthfulness. On the other hand, the ontological question remains fundamental and unavoidable, and perspectivism (yet?) fails to circumvent it. As we see, all three versions of perspectivism considered in this article turn out to be varieties of realism: Giere and Massimi recognize this explicitly, while Recanati de facto assumes a quite respectable and conservative position of selective realism with respect to ordinary objects. (shrink)

It is shown that the power set of $\kappa$ ordered by the subset relation modulo various versions of the non-stationary ideal can be embedded into the partial order of Borel equivalence relations on $2^\kappa$ under Borel reducibility. Here $\kappa$ is an uncountable regular cardinal with $\kappa^{<\kappa}=\kappa$.

This paper restates and subjects to analysis the polemics in Russian pre-revolutionary Populist and Marxist thought that concerned Kant’s practical philosophy. In these polemics Kantian ideas influence and reinforce the Populist personalism and idealism, as well as Marxist revisionist reformism and moral universalism. Plekhanov, Lenin, and other Russian “orthodox Marxists” heavily criticize both trends. In addition, they generally view Kantianism as a “spiritual weapon” of the reactionary bourgeois thought. This results in a starkly anti-Kantian position of Soviet Marxism. In view (...) of this the 1947 Communist Party decision to preserve Kant’s tomb in Soviet Kaliningrad becomes something of an experimentum crucis that challenges the soundness of the theory. (shrink)

In this article, the potential for Artificial Intelligence (AI) to be appraised as an object of beauty is critically examined through the lens of philosophical thought. Tracing beauty’s evolution from Platonic ideals to contemporary interpretations, the analysis contends that AI’s emergence offers a unique illustration of beauty in the modern age. Confronting the challenge of assigning beauty to entities devoid of consciousness or emotional depth, the argument unfolds to suggest that the intricate design of AI’s algorithms and its technological advancements (...) constitute an emergent form of beauty, one inherently tied to human intellectual endeavor. The article proposes that with time, as with historical art forms, the aesthetic qualities of AI may gain broader acknowledgment, implying that technological advancements necessitate an ongoing revision of established beauty norms. The historical evolution of beauty has been traced in details, and an extended literature review has been provided, serving as the foundation for a comprehensive exploration into the potential for AI to be recognized as an object of beauty. The harmony, elegance, and problem-solving capabilities of AI algorithms have been meticulously evaluated, with a comparison made to classical elements of beauty in an effort to contextually situate AI within longstanding aesthetic traditions. Furthermore, the analysis has been extended to consider the emergence of artificial and digital beauty, alongside an investigation into the parallels drawn between divine and artificial intelligence. As part of a deeper inquiry, the possibility of human emotions, such as awe and love, being authentically directed towards AI has been scrutinized. In conclusion, a reflection has been presented on the transformative role of AI in reimagining the conceptual landscape of beauty, prompting readers to thoughtfully engage with an extended review and the philosophical and cultural implications emerging from AI’s evolving influence on the field of aesthetics. (shrink)

We start by giving a survey to the theory of $${\text {Borel}}^{*}$$ sets in the generalized Baire space $${\text {Baire}}=\kappa ^{\kappa }$$. In particular we look at the relation of this complexity class to other complexity classes which we denote by $${\text {Borel}}$$, $${\Delta _1^1}$$ and $${\Sigma _1^1}$$ and the connections between $${\text {Borel}}^*$$ sets and the infinitely deep language $$M_{\kappa ^+\kappa }$$. In the end of the paper we will prove the consistency of $${\text {Borel}}^{*}\ne \Sigma ^{1}_{1}$$.

Introduction. In conservative political philoso- phy in Germany at the end of the 20th century, there developed two main approaches to social policy. The first one, paternalistic and corporat- ist approach continued the line that had been established in the 19th century and assumed the active participation of the state in regulating social support. The second, the market one, adopted American ideas of the second half of the 20th cen- tury and proposed limiting the scope of the welfare state in (...) order to save resources and avoid a nega- tive impact on the labor market. The purpose of the study is to analyze the argu- ments of the two directions of German conserva- tism at the end of the 20th century, their philo- sophical origin and their significance for politics. Methods. The article is based on the comparative historical approach, analysis of institutions and legal documents, and the hermeneutic method for studying the political, administrative and ideological context of the development of German conserva- tism at the end of the 20th century. Scientific novelty of the research. The article focuses on the intellectual heritage of German theorists, while the main attention of domestic and foreign researchers of conservative political philosophy of the late 20th century was attracted by American and British authors. Results. The key arguments of the paternalistic approach to social issues include pointing out the responsibility of elites for the well-being of the population and a strong state as a means of com- pensating for inequality in society. The arguments of the market approach are based on the appeal to the ideas of civic virtue and the protection of property as key forces that ensure social peace and well-being. Conclusions. In practice, the approach that offered the preservation and expansion of the welfare state prevailed, and favorable economic condi- tions, as well as institutional and ideological inertia, contributed to implementing solutions within the framework of this paradigm. But the ideas of the market approach have not lost their relevance, since the burden on the welfare state increases due to the aging of the population. (shrink)

The aim of this essay is to clarify the meaning and extent of Kant's liberalism by contrasting some of his key ideas to those of Burke, Hobbes, Machiavelli, Nozick, Rawls, and Schmitt. My claim is that Kant's political philosophy navigates the path between the extremes of liberalism and conservatism, just as his theoretical philosophy tries to navigate between dogmatism and skepticism, and that current liberal claim on Kant has important limitations in Kant's letter, as well as in spirit.

Hale proposes a neo-logicist definition of real numbers by abstraction as ratios defined on a complete ordered domain of quantities (magnitudes). I argue that Hale's definition faces insuperable epistemological and ontological difficulties. On the epistemological side, Hale is committed to an explanation of measurement applications of reals which conflicts with several theorems in measurement theory. On the ontological side, Hale commits himself to the necessary and a priori existence of at least one complete ordered domain of quantities, which is extremely (...) implausible because science treats the logical structure of quantities as subject to experimentally and theoretically motivated refinements and revisions. (shrink)

Publication of Taras Lyuty’s book on Nietzsche is a salient event in the philosophical life of Ukraine in 2016. Given the fact that the book covers a great number of different issues, the reviewer decides to focus on those of them which correspond to his own academic interests, related primarily to the history of psychoanalysis and biographical approach within the historiography of philosophy. As a review shows, Lyuty masterfully avoids such a trap as a biographical reductivism. He neither reduces his (...) hero’s teaching to his life, nor isolates the former from the latter. The reviewer pays a special attention to Lyuty’s delineation of intellectual links between the great philosopher and some of his predecessors (such as Ralf Waldo Emerson) and followers (some pioneers of depth psychology). In the end, the reviewer demonstrates that a very deep and systematic analysis of Nietzsche’s biography and philosophical heritage carried out by Lyuty leaves a room for further productive reflections and interpretations. (shrink)

Chaos-related obstructions to predictability have been used to challenge accounts of theory validation based on the agreement between theoretical predictions and experimental data. These challenges are incomplete in two respects: they do not show that chaotic regimes are unpredictable in principle and, as a result, that there is something conceptually wrong with idealized expectations of correct predictions from acceptable theories, and they do not explore whether chaos-induced predictive failures of deterministic models can be remedied by stochastic modeling. In this paper (...) we appeal to an asymptotic analysis of state space trajectories and their numerical approximations to show that chaotic regimes are deterministically unpredictable even with unbounded resources. Additionally, we explain why stochastic models of chaotic systems, while predictively successful in some cases, are in general predictively as limited as deterministic ones. We conclude by suggesting that the way in which scientists deal with such principled obstructions to predictability calls for a more comprehensive approach to theory validation, on which experimental testing is augmented by a multifaceted mathematical analysis of theoretical models, capable of identifying chaos-related predictive failures as due to principled limitations which the world itself imposes on any less-than-omniscient epistemic access to some natural systems. (shrink)