_Russian Philosophy in the Twenty-First Century: An Anthology_ presents a variety of contemporary philosophic problems found in the works of prominent Russian thinkers, ranging from social and political matters and pressing cultural issues to insights into modern science and mounting global challenges.

The subject of this research is the historical evolution of the three world religions – Buddhism, Christianity, and Islam. The author analyzed the development of these religions based on the model of religious cycle, which in his opinion, is common to the majority of historical religions, in other words, religious systems created after the invention of writing. In accordance with the author’s concept, each of the aforementioned religion has gone through six stages of development: initial, orthodox, classical, reformist, critical, and (...) post-critical; as well as two types of crises – structural and system. The three methods are used in the course of this study: historical, comparative, and method of ascension from abstract to concrete. The main conclusion of the conducted research consists in the statement on the functional identity of historical development of Buddhism, Christianity, and Islam regardless of their doctrine of ritual practice. Author’s special contribution is defined by formulation of the abstract model of religious cycle that he applies to the evolution of the aforementioned religions. (shrink)

The human intestines are constantly under the influence of numerous pathological factors: enteropathogenic microorganisms, food antigens, physico‐chemical stress associated with digestion and bacterial metabolism, therefore it must be provided with a system of protection against adverse impact. Recent studies have shown that Paneth cells play a crucial role in maintaining homeostasis of the small intestines. Paneth cells perform many vital functions aimed at maintaining a homeostatic balance between normal microbiota, infectious pathogens and the human body, regulate the qualitative composition and (...) number of intestinal microorganisms, prevent the introduction of potentially pathogenic species, and protect stem cells from damage. Paneth cells take part in adaptive and protective‐inflammatory reactions. Paneth cells maintain dynamic balance between microbial populations, and the macroorganism, preventing the development of intestinal infections and cancer. They play a crucial role in gastrointestinal homeostasis and may be key factors in the etiopathological progression of intestinal diseases. (shrink)

In _Theory of Religious Cycles: Tradition, Modernity and the Bahá’í Faith_ Mikhail Sergeev offers a new interpretation of the Soviet period of Russian history by developing a theory of religious cycles, which he applies to modernity and all major world religions.

The contributors to this anthology represent Russian-speaking communities from eight countries of the world, located on three continents: The United States, Germany, Italy, Sweden, Switzerland, Ukraine, China and Israel. Most of the authors also represent different waves of Russian emigration that took place in the last quarter of the 20th century. The book opens with an interview with one of the legendary figures of the Russian diaspora, Russian-American historian Alexander Yanov, and is followed by articles from such prominent thinkers as (...) Igor Smirnov, Anatoly Akhutin and Fr. Vladimir Zelinsky, Boris Groys and Karen Swassjan, Mikhail Epstein and Alexander Genis. Issues raised in these essays cover the whole range of modern philosophical discourse-from epistemology, ontology and philosophical anthropology, to the philosophy of culture, religion, and social and political philosophy. (shrink)

Depending upon their epistemological foundations philosophical systems can be divided into five types: empiricist (Locke), rationalist (Descartes), intuitivist (Bergson), traditionalist (Confucius), and scriptural (Aquinas). In the history of philosophy there were five major waves of scriptural reasoning-Hindu, Buddhist, Jewish, Christian, and Muslim. In this context Bah ' philosophy represents the sixth wave, and it finds itself in a fruitful dialogue not only with the traditional forms of religious philosophy but also with modern Western thought which is based solely on reason (...) and empirical observation. In this collection the reader will find articles on various aspects of Bah ' philosophy-philosophical anthropology, philosophy of science, philosophy of culture, epistemology, ethics, philosophy of religion, comparative and political philosophy, and, finally, history of philosophy. The authors of those articles-Bah ' and non-Bah ' scholars-reflect global aspirations of this religion by representing diverse countries of the world-USA, Canada, France, Italy, and Sweden. This collection of articles also introduces a Global Faith Book Series which publishes works on various aspects of the Bah ' Faith and globalization. (shrink)

Pendant près de deux siècles, la " question sociale"s'est confondue avec la question de la propriété, ou plus exactement avec celle de sa légitimité. Tel auteur affirme que c'est l'âme de la législation. Tel autre que c'est le vol. On dispute de ses origines et de ses limites, parfois de son abolition. Mais à travers la violence de la querelle, partisans et détracteurs de l'institution s'en font la même idée : un droit absolu d'une personne sur une chose. Or il (...) se trouve que cette définition, empruntée à la dogmatique juridique, est devenue largement inopérante. Les spécialistes préfèrent désormais parler de secret, d'exclusivité ou de faisceau de droits, et certains suggèrent même la " désintégration " de la propriété. Il reste que si un dogme propriétaire s'est désintégré, la chose elle-même, sous quelque forme que ce soit, se porte fort bien, et continue de poser d'épineuses questions de justice - sociale notamment. C'est dire que s'offre enfin la chance que soit posée, dans toute sa radicalité conceptuelle, la question de savoir ce qu'est la propriété. Pour y répondre, une enquête est menée dans ce livre aux sources du droit de propriété moderne, du côté des premiers commentateurs du Code Napoléon. Au-delà des déclamations idéologiques des préfaces, elle s'aventure là où opère vraiment la créativité conceptuelle des juristes, dans l'élément technique du droit. Il apparaît alors que la propriété désigne soit une maîtrise souveraine, droit réel et absolu de l'esprit sur la matière, soit l'appartenance patrimoniale, rapport d'identité pensé dans les termes de l'avoir, soit enfin une réservation de jouissance, monopole d'exploitation octroyé en rémunération d'une activité productrice de valeur. (shrink)

The Mathematical Intelligencer recently published a note by Y. Sergeyev that challenges both mathematics and intelligence. We examine Sergeyev’s claims concerning his purported Infinity computer. We compare his grossone system with the classical Levi-Civita fields and with the hyperreal framework of A. Robinson, and analyze the related algorithmic issues inevitably arising in any genuine computer implementation. We show that Sergeyev’s grossone system is unnecessary and vague, and that whatever consistent subsystem could be salvaged is subsumed entirely within a stronger and (...) clearer system. Lou Kauffman, who published an article on a grossone, places it squarely outside the historical panorama of ideas dealing with infinity and infinitesimals. (shrink)

The aim of the dissertation is to formulate a research program in moral cognition modeled on aspects of Universal Grammar and organized around three classic problems in moral epistemology: What constitutes moral knowledge? How is moral knowledge acquired? How is moral knowledge put to use? Drawing on the work of Rawls and Chomsky, a framework for investigating -- is proposed. The framework is defended against a range of philosophical objections and contrasted with the approach of developmentalists like Piaget and Kohlberg. (...) ;One chapter consists of an interpretation of the analogy Rawls draws in A Theory of Justice between moral theory and generative linguistics. A second chapter clarifies the empirical significance of Rawls' linguistic analogy by formulating a solution to the problem of descriptive adequacy with respect to a class of commonsense moral intuitions, including those discussed in the trolley problem literature originating in the work of Foot and Thomson. Three remaining chapters defend Rawls' linguistic analogy against some of its critics. In response to Hare's objection that Rawls' conception of moral theory is too empirical and insufficiently normative, it is argued that Hare fails to acknowledge both the centrality of the problem of empirical adequacy in the history of moral philosophy and the complexity of Rawls' approach to the problem of normative adequacy. In response to Nagel's claim that the analogy between moral theory and linguistics is false because whatever native speakers agree on is English, but whatever ordinary men agree in condemning is not necessarily wrong, it is argued that the criticism ignores both Rawls' use of the competence-performance distinction and the theory-dependence of the corresponding distinction in linguistics. In response to Dworkin's claim that Rawls' conception of moral theory is incompatible with naturalism and presupposes constructivism, it is argued that Dworkin's distinction between naturalism and constructivism represents a false antithesis; neither is an accurate interpretation of the model of moral theory Rawls describes in A Theory of Justice. The thesis concludes by situating Rawls' linguistic analogy within the context of broader debates in metaethics, democratic theory, natural law theory, and the theory of moral development. (shrink)

Is the science of moral cognition usefully modelled on aspects of Universal Grammar? Are human beings born with an innate 'moral grammar' that causes them to analyse human action in terms of its moral structure, with just as little awareness as they analyse human speech in terms of its grammatical structure? Questions like these have been at the forefront of moral psychology ever since John Mikhail revived them in his influential work on the linguistic analogy and its implications for (...) jurisprudence and moral theory. In this seminal book, Mikhail offers a careful and sustained analysis of the moral grammar hypothesis, showing how some of John Rawls' original ideas about the linguistic analogy, together with famous thought experiments like the trolley problem, can be used to improve our understanding of moral and legal judgement. (shrink)

This paper discusses the role of Law and Legal Thinking in Critical Theory with specific reference to the arguments that Michael Hardt and Antonio Negri offer in their book Commonwealth. The core idea is that Critical Theory is no less radical, but much more concrete, when it is performing not only an external, but also an internal critique of the Law. It shows that the role of the law in critical theory emerges as a problem when the latter claims that (...) ‘there is no outside’ and that ‘the legal base of the system structures our lives.’ It then discusses optimistic and pessimistic strategies to overcome the problem, and argue for a demanding strategy which consist in articulating the external and the internal critique of the law. To make this point, the paper goes back to the epistemic context in which critical attitudes are deployed (the ‘Conflict of the Faculties’), describes the four theoretical moves constitutive of the historical moment in which, at the end of the 18th Century, modern law as we know it was conceived of and founded; and sketches the key moments of the history of the internal critique of the law. It then illustrates the demanding strategy with examples taken from the field of Intellectual Property, and concludes that the Law is malleable and open enough to allow the thinking and practicing of radical alternatives from within the legal system and also that alternatives spoken in the language of the law are no less radical, but certainly, more concrete than others. (shrink)

This groundbreaking work by one of the world's foremost theoreticians of Russian literature, culture, and thought gives for the first time an extensive and detailed examination of the development of Russian thought during the late Soviet period. Countering the traditional view of an intellectual wilderness under the Soviet regime, Mikhail Epstein offers a systematic account of Russian thought in the second half of the 20th century. In doing so, he provides new insights into previously ignored areas such as Russian (...) liberalism, personalism, structuralism, neo-rationalism, and culturology. Epstein shows how Russian philosophy and culture has long been trapped in an intellectual prison of its own making as it sought to create its own utopia. However, he demonstrates that it is time to reappraise Russian philosophical thought and cultural theory, now freed from the bonds of totalitarianism. We are left with not only a new and exciting interpretation of Russian thought, but also an opportunity to rethink our own intellectual heritage. (shrink)

The academic community in the West tends to be suspicious of Russian philosophy, often relegating it to another category, such as “ideology” or “social thought.” But what is philosophy? There is no simple universal definition, and many thinkers consider it impossible to formulate one. The most credible attempt is nominalistic: philosophy is the practice in which Plato and Aristotle were involved. As Alfred North Whitehead wrote, “The safest general characterization of the European philosophical tradition is that it consists of a (...) series of footnotes to Plato.”If so, then Russian thought needs to be understood as an important part of the Western philosophical heritage, given that it offers perhaps the most elaborate set of footnotes to Plato's most mature and comprehensive dialogues: the Republic and the Laws. The status of ideas in Russian philosophy mirrors Plato's vision of them as ontological and political entities, “laws,” or ideal principles—as distinct from mere epistemic units or tools of cognition. The Platonic tendency to integrate and implement religious, philosophical, and political teachings culminated in twentieth-century Russia. In the Soviet state, perhaps more than anywhere else in history, philosophy became a supreme legal and political institution, acquiring the power of a suprapersonal, universal reason. Hence thought itself, in the moment of its triumph, became a prisoner in the social structures that Soviet ideocracy erected on a philosophical foundation. In discussing Russian philosophy, we inevitably consider the practical application of Platonic conceptions by the Soviet ideocracy to a state in which philosophy was called upon to rule.According to Sergei Averintsev, the emphasis on Platonism in the Russian intellectual tradition is nothing to be proud of; it should rather be lamented and repented. Despite the obvious Platonic preferences of Russian thinkers (from Ivan Kireyevsky to Aleksei Losev), Averintsev asks whether even now we might be able to reorient the tradition toward Aristotle instead—toward a more secular, tolerant, and analytic philosophy of human nature. “If Plato is the first utopian,” Averintsev writes, “Aristotle is the first thinker to look the spirit of utopia right in the eye and overcome it.... Aristotle's technique of thought is more neutral toward religion than is Plato's ecstasy.” Characteristically, the name index to the Palgrave Handbook of Russian Thought contains almost twice as many mentions of Plato as of Aristotle.Each national tradition has its own “strange attractor,” as they say now in complexity theory. English empiricism, French rationalism, German Idealism, American pragmatism... However stereotypical these generalizations are, they help to clarify the nations’ distinctive contributions to philosophy. Where does Russia stand in this row? I think that Caryl Emerson is correct to pinpoint, among the most distinctive features of the Russian intellectual tradition, the striving for “wholeness” (tselostnost’). Many Russian thinkers seem to evade definitive and particular “isms,” preferring to find ways of complementing (and thus diluting) those that are on offer. Faced with the claims for rationalism, for example, the Russian response tends to be that true rationality is or should be coupled with fullness of feeling. The characteristic Russian “ism” is at best “holism,” at worst “totalitarianism,” and is usually directed against Western thought. Kireyevsky declares: There [in the West] is a bifurcation [razdvoenie] of the spirit, a bifurcation of thoughts, a bifurcation of the sciences, a bifurcation of the state, a bifurcation of estates, a bifurcation of society, a bifurcation of family rights and duties, a bifurcation of morality and the heart.... In Russia, on the contrary, there is a predominant tendency toward the wholeness of the inner and the outer, of public and moral being.Vladimir Solovyov held that the goal of all knowledge was to comprehend “total unity” and to overcome all kinds of unilateralism, which he referred to as “abstract elements” (otvlechennye nachala). These one-sided elements included Realism, rationalism, empiricism, and positivism, all of which had been advanced by Western philosophical movements.Reading the Handbook, I was struck by how steadily, from one thinker to another, the concept of “unity” is reiterated in various synonyms and contexts: “all-unity,” “wholeness,” “totality,” “integrity,” “edinstvo,” “tsel'nost,’” “tselostnost,” “sobornost,” and so forth. Russian thinkers endeavor not to create something original and special but to unify everything that has already been done and known. Consider opponents, like the Slavophiles and Westernizers; take Petr Chaadaev and Vissarion Belinsky, Kireyevsky and Alexander Herzen, Dostoevsky and Solovyov—all are united by this “super-idea,” proclaiming its embodiment to be the all-embracing vocation of the Russian people. At the same time, they sharply reject all “private principles” and “trashy certainty” (Belinsky's driannaia opredelennost’)—anything that restricts and divides individuals or nations. All these forms of privacy and particularity must be overcome on the way to a universal whole that is even greater in scale than Western Catholicism. According to this logic of totality, we would be better off left with nothing than to be content with the particular and the limited. The first original Russian thinker, Chaadaev (1794–1856), makes the salto mortale of declaring Russia a country that has given nothing to the world, then proclaiming that Russia's destiny is to rise above the rest of the world and resolve all its contradictions. From nothing to everything: such are the philosophical foundations for the totalitarian aspiration of Russian thought, which eventually expressed itself in the revolutionary movements and communist experiments of the twentieth century.As is well known, Russian literature is considered in the West a far more powerful and original expression of philosophical ideas than Russian philosophy as such. Characteristically, then, almost half of the Handbook, its entire second part, is devoted to the dialogue of Russian philosophy with literature and art. As M. N. Forster remarks in the Handbook's concluding essay: “It is natural to wonder why this striking asymmetry between relatively modest achievements in pure philosophy and spectacularly high achievements in literature came about.” To the literary focus of Russian philosophy, we can add a political focus. At least a third of part one of the Handbook is devoted to Russian political and revolutionary philosophy, to Lenin and other Marxists, to Ivan Ilyin, and so on. In this context, both literature and politics assumed philosophical dimensions, often overshadowing philosophy itself.Bertrand Russell lamented that the system of philosophical categories in the West featured mostly nouns (being, consciousness, idea, matter, substance, and so forth), omitting adjectives, verbs, prefixes, and other parts of speech. This criticism should be applied to the category philosophy itself. Why the noun philosophy rather than the adjective philosophical, which can be applied to many areas of activity and creativity, including literature and politics?In Russian intellectual history, the philosophical, rather than philosophy, is the predominant category. The state, ideology, economics, politics and geopolitics, literature, art, warfare, space exploration—all these spheres in Russia and the USSR have been and remain abundantly philosophical, subordinated to certain philosophical tasks, though philosophy as such has never been as developed and sophisticated as in the West. As a discipline, Western philosophy “outsourced” itself to Russian disciples, leaving it to Dostoevsky and Tolstoy, Lenin and Trotsky, to test in literary and political practices a host of Western philosophical ideas, from those of Plato, Rousseau, and Hegel to those of Feuerbach, Marx, and Nietzsche.Likewise, the verb to philosophize is used in ways unusual and awkward in the West. “It is characteristic of the Russian people to philosophize [filosofstvovat'],” as Nikolai Berdyaev observed: “An illiterate Russian peasant likes to pose questions of a philosophical nature—about the meaning of life, about God, about eternal life, about evil and untruth, about how to realize the Kingdom of God.” The philosophical and philosophizing, as attributes and actions of the state and society, overpowered philosophy as a noun—as an academic discipline, if you will. Russian philosophy has had a very modest impact on the West, but the impact of the philosophical has been immense. Nineteenth-century Russian literature influenced Western culture with its philosophical interrogations and existential dilemmas, just as, in the twentieth century, the USSR influenced the West with the philosophical ideas (Marxism, materialism, dialectics, collectivism, socialism, communism) that determined Soviet ideology, politics, and economics.In the USSR of the 1920 and 1930s, for instance, philosophy as an independent academic subject was in a subdued position, as a servant of party ideology. But, meanwhile, the sphere of the philosophical spread to such distant domains as theater (Stanislavsky), physiology (Pavlov), and agriculture (Michurin), with all such activities glorified and sponsored by the state as “philosophically correct”—as faithful to “materialism” and “Realism.” Paradoxically, in the quintessentially philosophical state that was the USSR, the state of philosophy, with the repression of all independent thought and thinkers, was miserable. The fateful and often disastrous originality of Russian philosophy consisted precisely in its dissemination to other areas, in an act of kenosis or self-transcendence that can be viewed both as an aggressive philosophical appropriation of politics, economics, ideology, and literature—and as philosophy's sacrificial devotion to the world beyond its professional boundaries.So there are three features that make Russian thought relevant and dangerous: its Platonic utopian aspiration; its spirit of totality; and its tendency to transcend the boundaries of academic philosophy and to philosophize society, politics, and life in general. Russian philosophy has not been as good at explaining the world as at changing it, sometimes ethically and poetically, sometimes violently and aggressively. Teachers and students of Russian culture should be deeply motivated to draw more attention to the philosophical in Russia and to raise its status in the Western academy. In my view, we would do better service to Russian philosophy if we are frank enough to qualify it as dangerous, sometimes very toxic and addictive, fraught with totalistic tendencies. This philosophy is the voice of the “underground,” both in the Dostoevskian and Leninist senses.At the same time, however, the antidotes concocted in the Russian metaphysical laboratory are of enormous value: the Russian versions of personalism, existentialism, secular and religious liberalism, neorationalism, culturology, conceptualism, and postmodernism. These movements, which counteract totalization, need to be studied precisely because they were cooked up and tested under the same extreme conditions in which the most dangerous intellectual poisons have been produced. (shrink)

This book is not only a major twentieth-century contribution to Dostoevsky’s studies, but also one of the most important theories of the novel produced in our century. As a modern reinterpretation of poetics, it bears comparison with Aristotle.“Bakhtin’s statement on the dialogical nature of artistic creation, and his differentiation of this from a history of monological commentary, is profoundly original and illuminating. This is a classic work on Dostoevsky and a statement of importance to critical theory.” Edward Wasiolek“Concentrating on the (...) particular features of ‘Dostoevskian discourse,’ how Dostoevsky structures a hero and a plot, and what it means to write dialogically, Bakhtin concludes with a major theoretical statement on dialogue as a category of language. One of the most important theories of the novel in this century.” The Bloomsbury Review. (shrink)

Is a human more conscious than an octopus? In the science of consciousness, it’s oftentimes assumed that some creatures (or mental states) are more conscious than others. But in recent years, a number of philosophers have argued that the notion of degrees of consciousness is conceptually confused. This paper (1) argues that the most prominent objections to degrees of consciousness are unsustainable, (2) examines the semantics of ‘more conscious than’ expressions, (3) develops an analysis of what it is for a (...) degreed property to count as degrees of consciousness, and (4) applies the analysis to various theories of consciousness. I argue that whether consciousness comes in degrees ultimately depends on which theory of consciousness turns out to be correct. But I also argue that most theories of consciousness entail that consciousness comes in degrees. (shrink)

La Meditación de la técnica contiene las reflexiones de José Ortega y Gasset sobre un fenómeno de invasora presencia en el mundo contemporáneo. Trata, en suma, de inscribir el hecho de la técnica en el marco de una antropología filosófica, fundada en el sistema orteguiano, para así contribuir a la comprensión del momento histórico contemporáneo. El volumen incluye, además del curso ¿Qué es la técnica?, desarrollado en 1933 en la Universidad de Santander, otros textos afines: la conferencia El mito del (...) hombre allende a la técnica pronuncida en Darmstadt y varios ensayos sobre el conocimiento científico, que prueban la permanente atención que Ortega prestó a las novedades de la ciencia contemporánea. En esta nueva edición el texto se ha revisado y corregido conforme a los manuscritos originales o las primeras ediciones. La principal novedad es una Introducción al curso ¿Qué es la técnica?, sólo editada póstumamente. (shrink)

Scientists from various disciplines have begun to focus attention on the psychology and biology of human morality. One research program that has recently gained attention is universal moral grammar (UMG). UMG seeks to describe the nature and origin of moral knowledge by using concepts and models similar to those used in Chomsky's program in linguistics. This approach is thought to provide a fruitful perspective from which to investigate moral competence from computational, ontogenetic, behavioral, physiological and phylogenetic perspectives. In this article, (...) I outline a framework for UMG and describe some of the evidence that supports it. I also propose a novel computational analysis of moral intuitions and argue that future research on this topic should draw more directly on legal theory. (shrink)

My primary aims in this paper are to explain what exploitation is, when it’s wrong, and what makes it wrong. I argue that exploitation is not always wrong, but that it can be, and that its wrongness cannot be fully explained with familiar moral constraints such as those against harming people, coercing them, or using them as a means, or with familiar moral obligations such as an obligation to rescue those in distress or not to take advantage of people’s vulnerabilities. (...) Its deepest wrongness, I argue, lies in our moral obligation not to extract excessive benefits from people who cannot, or cannot reasonably, refuse our offers. (shrink)

Mikhail Lifshitz is a major forgotten figure in the tradition of Marxist philosophy and art history. _The Crisis of Ugliness_, published here in English for the first time, is a compact broadside against modernism in the visual arts that resists the dogmatic complacencies of Stalinist aesthetics.

This book provides brief expositions of the central concepts in the field of Global Studies. Former President of the Soviet Union Mikhail Gorbachev says, “The book is intelligent, rich in content and, I believe, necessary in our complex, turbulent, and fragile world.” 300 authors from 50 countries contributed 450 entries. The contributors include scholars, researchers, and professionals in social, natural, and technological sciences. They cover globalization problems within ecology, business, economics, politics, culture, and law. This interdisciplinary collection provides a (...) basis for understanding the concepts and methods within global studies and for accessing lengthier and more technical research in the field. The articles treat such important topics as the biosphere, ozone depletion, land resources and pollution, world health challenges, education, global modeling, sustainable development, war, weapons of mass destruction, and terrorism. The book also promotes academic cooperation, political dialogue, and mutual understanding across diverse traditions and national identities that are needed to engage successfully the many daunting challenges of globalization. (shrink)

When is it immoral to take advantage of another person for one's own benefit? For some, such as Ruth Sample, John Roemer, and Will Kymlicka, the answer at least partly depends on whether what one takes advantage of is the fact that this person is, or has been, the victim of injustice. I argue, however, that whether person A wrongly exploits person B is wholly unrelated to whether A takes advantage of the fact that B is, or was, the victim (...) of injustice. I also develop a positive account regarding which personal attributes one should not exploit for personal gain. (shrink)

In this paper, the predicate counterparts, defined both axiomatically and semantically by means of Kripke frames, of the modal propositional logics $\textbf {GL}$, $\textbf {Grz}$, $\textbf {wGrz}$ and their extensions are considered. It is proved that the set of semantical consequences on Kripke frames of every logic between $\textbf {QwGrz}$ and $\textbf {QGL.3}$ or between $\textbf {QwGrz}$ and $\textbf {QGrz.3}$ is $\Pi ^1_1$-hard even in languages with three (sometimes, two) individual variables, two (sometimes, one) unary predicate letters, and a single (...) proposition letter. As a corollary, it is proved that infinite families of modal predicate axiomatic systems, based on the classical first-order logic and the modal propositional logics $\textbf {GL}$, $\textbf {Grz}$, $\textbf {wGrz}$ are not Kripke complete. Both $\Pi ^1_1$-hardness and Kripke incompleteness results of the paper do not depend on whether the logics contain the Barcan formula. (shrink)

Adequality, or παρισóτης (parisotēs) in the original Greek of Diophantus 1 , is a crucial step in Fermat’s method of finding maxima, minima, tangents, and solving other problems that a modern mathematician would solve using infinitesimal calculus. The method is presented in a series of short articles in Fermat’s collected works (1891, pp. 133–172). The first article, Methodus ad Disquirendam Maximam et Minimam 2 , opens with a summary of an algorithm for finding the maximum or minimum value of an (...) algebraic expression in a variable A. For convenience, we will write such an expression in modern functional notation as f (a). 3 The algorithm can be broken up into six steps in the following way:Introduce an auxiliary .. (shrink)