The original proof of the four-color theorem by Appel and Haken sparked a controversy when Tymoczko used it to argue that the justification provided by unsurveyable proofs carried out by computers cannot be a priori. It also created a lingering impression to the effect that such proofs depend heavily for their soundness on large amounts of computation-intensive custom-built software. Contra Tymoczko, we argue that the justification provided by certain computerized mathematical proofs is not fundamentally different from that provided by surveyable (...) proofs, and can be sensibly regarded as a priori. We also show that the aforementioned impression is mistaken because it fails to distinguish between proof search (the context of discovery) and proof checking (the context of justification). By using mechanized proof assistants capable of producing certificates that can be independently checked, it is possible to carry out complex proofs without the need to trust arbitrary custom-written code. We only need to trust one fixed, small, and simple piece of software: the proof checker. This is not only possible in principle, but is in fact becoming a viable methodology for performing complicated mathematical reasoning. This is evinced by a new proof of the four-color theorem that appeared in 2005, and which was developed and checked in its entirety by a mechanical proof system. (shrink)

IMMANUEL KANT GRADUATED IN 1755 from the University of Königsberg on the basis of the dissertation On Fire and with the essay A New Exposition of the First Principles of Metaphysics written specifically for the occasion; he took up a position as lecturer in the same year. In 1756 he wrote a third Latin essay, the Physical Monadology, and applied for a professorship at the Albertina in Königsberg. The application was unsuccessful and, more significantly, the work failed to attract the (...) attention Kant had hoped. He had to wait until 1770—some fourteen years later—for an appointment as full professor in Königsberg, and it was not until the publication of the Critique of Pure Reason in 1781 that he finally established his reputation as a philosopher. (shrink)

In den Kant-Forschungen werden sowohl historisch als auch systematisch orientierte Arbeiten zur Philosophie Immanuel Kants veröffentlicht. Die Bände stellen Funde unbekannter oder verschollen geglaubter Kantischer Autographen und Vorlesungsskripte vor und erörtern Editionsprobleme der Kantischen Vorlesungen und Werke. Sie enthalten darüber hinaus Studien zu Kants Umfeld und zur Kant-Rezeption im 18. Jahrhundert sowie systematisch angelegte Arbeiten zu Architektonik und System der Philosophie Kants.

Konstantin Pollok offers the first book-length analysis of Kant's theory of normativity that covers foundational issues in theoretical and practical philosophy as well as aesthetics. Interpreting Kant's 'critical turn' as a normative turn, he argues that Kant's theory of normativity is both original and radical: it departs from the perfectionist ideal of early modern rationalism, and arrives at an unprecedented framework of synthetic a priori principles that determine the validity of our judgments. Pollok examines the hylomorphism in Kant's theory (...) of normativity and relates Kant's idea of our reason's self-legislation to the 'natural right' tradition, revealing Kant's debt to his predecessors as well as his relevance to contemporary debates on normativity. This book will appeal to academic researchers and advanced students of Kant, early modern philosophy and intellectual history. (shrink)

This article is a commentary on ChatGPT and LLMs (Large Language Models) in general. It argues that this technology has matured to the point where calling systems such as ChatGPT “stochastic parrots” is no longer warranted. But it also argues that these systems continue to have serious limitations when it comes to reasoning. These limitations are much more severe than commonly thought. A large array of examples are given to support these claims.

ArgumentPost-Stalinist reforms resulted in dramatic changes in the ways of operation of Soviet science: one can say that they altered the very understanding of what science was, or should be, in the socialist society. A new vision came about as a result of political and rhetorical efforts of scientists, who pushed forward their various, often conflicting, agendas acting in accordance with specific rules of Soviet polity. The most visible part of the reform came with the 1961 administrative reorganization of the (...) USSR Academy of Sciences. The related series of changes, however, was much broader and comprehensive, modifying the relationships between science and ideology, politicians and academic researchers, and establishing the very division between fundamental and applied research, which had been strongly rejected during the preceding Stalinist period. (shrink)

В книге рассматриваются некоторые попытки построения "Третьего Христианства", очищенного от скверны.

Doctor Stephen Strange and Leo Tolstoy both experienced significant changes in mid‐life, though, that affected their worldviews and led them to reconsider the meaning of life. For his part, Tolstoy developed a strong opposition to violence, even when used in resistance to evil. A central focus of Tolstoy's newfound philosophy is the evil of the violence practiced by humans throughout history. The metaphysical nature of evil is reflected in the amount of time Doctor Strange spends in such realms as the (...) Dream Dimension, fighting the darkness that tries to take over human minds and souls. If Tolstoy were in the world of Doctor Strange, he might open the sacred Book of Vishanti, don the Eye of Agamotto, and become a sorcerer‐defender of our planet from demonic evil. (shrink)

In the article, I analyze Georg Simmel’s essay on individual law and summarize his criticism of the concept of a universal moral law, which was developed by Immanuel Kant. Simmel identifies two ways of conceptualizing the concept of a moral law: as universal, referring to the regulation of the actions of all rational beings, and as individual, including a specific acting person in his integrity and connection with the world, which is, at the same time, absolute only for him. Kant (...) became the personification of the first method for Simmel; Simmel put forward the second method as an alternative to the first. The central characteristic of law for Simmel is its integrity and individuality, not rationality and universality. If Kant understands the moral law through a distraction from personal characteristics and inclinations in favor of impersonal norms that operate for all rational beings, then, for Simmel, the moral law manifests itself as an integral and individual human act, in which the flow of life manifests itself in the whole. Simmel insists that the idea of Kant’s universal law overlooks the very es-sence of moral obligation, which can only be individual, since only in an individual form life manifests itself – a single source of both the real and the proper. The article ends with a criticism of Simmel’s example of an individual law, which, as I show, not only contradicts a number of Simmel’s statements made earlier, but also demonstrates the undeveloped nature of his concept as a whole, namely: Simmel’s insensitivity to the distinction between integrity and totality as well as disregard for the figure of the Other. (shrink)

The article considers A.F. Losev''s philosophy of music in the context ofhis entire religious worldview and as the part of hisChristian-Neoplatonic philosophy. Synthesizing Pythagorean-Platonic andRomantic musical doctrines, Losev concludes: music is the expression ofthe life of numbers, a meonic-hyletic element that rages inside numericconstructions. So it is necessary to analyse the concept of number inthe system of Neoplatonic thought. In the Neoplatonic hierarchy of theuniverse both numeric sphere and music are located at the source of allthe eidei, above them and (...) between the One (the first hypostasis) and theWorld Intelligence (the second hypostasis). Then music is considered inthe context of the relation between the uncreated Absolute (Tetrade A)and the created world (Tetrade B). Losev''s doctrine on the Tetrades Aand B (connected not by essence but by energies) is the importantmodification of Neoplatonism. Finally the article considers Losev''saccount of music in relation to the absolutized individual person. (shrink)

Synchronic norms of theory choice, a traditional concern in scientific methodology, restrict the theories one can choose in light of given information. Diachronic norms of theory change, as studied in belief revision, restrict how one should change one’s current beliefs in light of new information. Learning norms concern how best to arrive at true beliefs. In this paper, we undertake to forge some rigorous logical relations between the three topics. Concerning, we explicate inductive truth conduciveness in terms of optimally direct (...) convergence to the truth, where optimal directness is explicated in terms of reversals and cycles of opinion prior to convergence. Concerning, we explicate Ockham’s razor and related principles of choice in terms of the information topology of the empirical problem context and show that the principles are necessary for reversal or cycle optimal convergence to the truth. Concerning, we weaken the standard principles of agm belief revision theory in intuitive ways that are also necessary for reversal or cycle optimal convergence. Then we show that some of our weakened principles of change entail corresponding principles of choice, completing the triangle of relations between,, and. (shrink)

The article attempts to compare personalist aspects in the works of Vasily Zenkovsky and Vladimir Lossky. It is shown that two types of philosophical personalism (metaphysical and existentialist) in the history of Russian thought set the framework for two types of theological personalism presented respectively by Zenkovsky and Lossky. The philosophy of Lev Lopatin was the important source for the principles of Zenkovsky’s personalist vision. The relevant philosophical background on Lossky’s personalism is provided by Nikolai Berdyaev’s works. The article considers (...) the deep criticism by the French theologian Jean-Claude Larchet, who seeks to demonstrate philosophical and existentialist sources of Lossky’s theological personalism, rather than patristical ones. It is noted that the criticism addressed to Lossky’s theory may slide to challenging the very possibility of an Orthodox theological personalism as a line of thought. It is shown that Zenkovsky’s works, presenting a nonexistentialist type of personalism, do not provoke such criticism. It’s concluded that whereas Lossky’s legacy in its personalistic aspect is challenged, Zenkovsky’s personalism enables another way of conceiving “Orthodox theological personalism.”. (shrink)

We say that two arithmetical formulas A, B have the Σ1-interpolation property if they have an ‘interpolant’ σ, i.e., a Σ1 formula such that the formulas A→σ and σ→B are provable in Peano Arithmetic PA. The Σ1-interpolability predicate is just a formalization of this property in the language of arithmetic.Using a standard idea of Gödel, we can associate with this predicate its provability logic, which is the set of all formulas that express arithmetically valid principles in the modal language with (...) two modal operators, □ for provability in PA and for Σ1-interpolability. In this paper we determine this provability logic .It turns out that this problem appears to be quite similar to the problem of such modal description of relative interpretability, a problem, solved by Berarducci and Shavrukov. However, the present case is sometimes easier. In particular, we prove in this paper the fixed point property and the Craig interpolation property for our modal system ELH. (shrink)

The article addresses the special conditions in Soviet society during the Stalin period that contributed to the emergence of latent ideas about the unique position of the USSR on the map of the world, of Europe in particular. The focus is on pedagogical methods, the theory and practice of cartography, literary and journalistic texts, cinematography, and pop music, all of which present an image of the USSR as the “center of world civilization” and thereby sustain its inculcation in public consciousness. (...) An interesting and significant example is the second edition of the Great Soviet Encyclopedia, launched on Stalin’s initiative and carried out under his patronage. In this context, the logic and the rhetoric of encyclopedia articles on the physical and political geography of Europe must be analyzed as a kind of territorial “crowding out” of Europe to the periphery of the Soviet Union. “Crowding out,” not only by geographical but also by ideological illusions of space, which emphasize and reproduce fairy-tale and epic orientations of social self-knowledge, brings the illusory space clearly into view. These means motivate the cyclical movement from centre to periphery and from periphery to centre. (shrink)

Various publications claim that medical AI systems perform as well, or better, than clinical experts. However, there have been very few controlled trials and the quality of existing studies has been called into question. There is growing concern that existing studies overestimate the clinical benefits of AI systems. This has led to calls for more, and higher-quality, randomized controlled trials of medical AI systems. While this a welcome development, AI RCTs raise novel methodological challenges that have seen little discussion. We (...) discuss some of the challenges arising in the context of AI RCTs and make some suggestions for how to meet them. (shrink)

By taking into account some texts published between the first and the second edition of the Critique of Pure Reason that have been neglected by most of those who have dealt with the deduction of the categories, I argue that the core of the deduction is to be identified as the ‘almost single inference from the precisely determined definition of a judgment in general’, which Kant adumbrates in the Metaphysical Foundations in order to ‘make up for the deficiency’ of the (...) A-deduction. Whereas the first step of the B-deduction is an attempt to show that the manifold of an intuition belongs to the ‘necessary unity of self-consciousness’ by means of the synthesis of the understanding, the second step has the task of showing that the very same synthesis is responsible for the spatio-temporal unity of the manifold. Thus, Kant's ‘answer to Hume’ is that no spatio-temporal objects of experience at all are merely ‘given’, independently of the conceptual activities of the understanding. Against the established view I substantiate the claim that with this ‘almost single inference’ of the second proof step the distinction between judgments of perception and judgments of experience consequently vanished from Kant's thinking. (shrink)

Against the well-established critical rejection of rights a growing literature in the tradition of agonistic democracy asserts their emancipatory role in the struggles for social change. However, agonistic theorists, invested as they are in the idea of democratic innovation as a process of gradual ‘augmentation’ of existing rules, institutions and practices, fail to account for the ruptural capacity, and hence for the full radical potential, of rights. Using the performative approach, I develop a conception of rights claiming as a defiant (...) practice to express the ruptural dimension of certain forms of rights politics. I demonstrate how defiant rights claiming articulates immanent critique by declaring the incapacity of putative duty-bearer institutions and governments to uphold the claimed right due to structural constraints, thereby generating inevitable contradictions within the extant order and creating the necessity for an alternative one. Moreover, in order to fully capture the emancipatory potential and creative capacity of rights, this article argues for understanding certain forms of rights politics both as augmentation and rupture, taking the two to be different dimensions of the same radical democratic practice. I present the creative use of rights discourse by the Landless Workers’ Movement in Brazil and the transnational network of agrarian movements, La Via Campesina, as precisely such a combination of the practice of augmentation and defiant claims, which has led to the transformation of the right to food and land into the right to food sovereignty, demonstration of the structural embeddedness of rights violations in the existing global regime of food production and distribution, and authorisation of an alternative vision of the future. (shrink)

One of the key ethical debates in Russian religious thought, initiated by Leo Tolstoy, concerned the question of nonresistance to evil by force. The purpose of this article is to assess the influence of Kant’s ethics and philosophy of religion on the course of this debate and to determine the place and significance of the arguments and considerations expressed on this issue by Semyon Frank in the early and late periods (1908 and 1940s) of his work. To this end I (...) reconstruct the general course of the debate, notably the positions and arguments of Leo Tolstoy, Vladimir Solovyov, Ivan Ilyin and Nikolai Berdyaev. Beginning with Tolstoy, Russ­ian thinkers introduced the original ethical content of the idea of nonresistance derived from the Gospel into the ethics of duty borrowed from Kant. The Tolstoy version of this idea was challenged mainly from two directions: from the Kantian grounding of the legitimacy of coercion and attempts to bring in styles of moral thinking other than the ethic of duty. Ilyin’s apolo­gia for the use of force in the struggle against evil prompted Russian émigré thinkers to take a closer look at Tolstoy’s ethical concept and pay attention to its positive content. On this basis Berdyaev and especially Frank create their version of the Christ-centered ethic of salvation which, in the perspective of “protecting the world against evil” includes the ethic of duty and links it with the possibility of using force, always a wrongful act, but one justified “in a situation of extreme need”. (shrink)

In this paper, we tackle the widely held view that practice-oriented approaches to ethics are conservative, preserving the moral status quo, and, in particular, that they do not promote any (fundamental) change in our dealings with animals or formulate clear principles that help us to achieve such change. We shall challenge this view with reference to Wittgensteinian ethics. As a first step, we show that moral thought and action rest on basic moral certainties like: equals are to be treated equally (...) and unequals unequally. We then explore the relations between this insight and the notion of the difficulty of reality elaborated by Cora Diamond. Our goal is to show that a Wittgensteinian-Diamondian approach to animal ethics is not necessarily morally conservative. Indeed, it offers a profound practice-oriented approach to animal ethics that is capable of promoting change in human dealings with animals because it is compatible with radical critique. (shrink)

Konstantin Pollok - Kant's Critical Concepts of Motion - Journal of the History of Philosophy 44:4 Journal of the History of Philosophy 44.4 559-575 Muse Search Journals This Journal Contents Kant's Critical Concepts of Motion Konstantin Pollok There are two significant places in Kant's Critical corpus where he discusses the concept of motion. The first is in the Critique of Pure Reason, where in the "Deduction of the Categories" Kant writes: Motion, as an act of the subject , (...) and therefore the synthesis of the manifold in space, first produces the concept of succession—if we abstract from this manifold and attend solely to the act through which we determine the inner sense according to its form. In this passage Kant simply refers to the concept of motion, and the immediate context in which this reference occurs reveals little about what he means by it. In the Metaphysical Foundations of Natural Science, however, motion plays a more significant role, and, concomitantly, it is in his writings on natural science that Kant most fully expresses his thoughts on the subject. For present purposes, the most relevant passage is paragraph 15 of the Preface of the Metaphysical Foundations, where Kant says that the concept of matter had … to be carried through all four of the indicated functions of the concepts of the understanding , where in each a new determination of this concept was added. The.. (shrink)