Empirical claims are factual claims validated by the methods of science. Conceptual claims involve matters of sense. Empirical inquiry that proceeds from conceptual confusion can never yield fruitful results (i.e., knowledge). John Mikhail's speculations about UMG are an example of conceptual confusions that lead not to knowledge but to claims and assertions that lack sense.

Many historians of the calculus deny significant continuity between infinitesimal calculus of the seventeenth century and twentieth century developments such as Robinson’s theory. Robinson’s hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, (...) Robinson regards Berkeley’s criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley’s criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz’s infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz’s defense of infinitesimals is more firmly grounded than Berkeley’s criticism thereof. We show, moreover, that Leibniz’s system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz’s strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity. (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)

In relation to a thesis put forward by Marx Wartofsky, we seek to show that a historiography of mathematics requires an analysis of the ontology of the part of mathematics under scrutiny. Following Ian Hacking, we point out that in the history of mathematics the amount of contingency is larger than is usually thought. As a case study, we analyze the historians’ approach to interpreting James Gregory’s expression ultimate terms in his paper attempting to prove the irrationality of \. Here (...) Gregory referred to the last or ultimate terms of a series. More broadly, we analyze the following questions: which modern framework is more appropriate for interpreting the procedures at work in texts from the early history of infinitesimal analysis? As well as the related question: what is a logical theory that is close to something early modern mathematicians could have used when studying infinite series and quadrature problems? We argue that what has been routinely viewed from the viewpoint of classical analysis as an example of an “unrigorous” practice, in fact finds close procedural proxies in modern infinitesimal theories. We analyze a mix of social and religious reasons that had led to the suppression of both the religious order of Gregory’s teacher degli Angeli, and Gregory’s books at Venice, in the late 1660s. (shrink)

The article discusses the philosophical underpinnings of Mikhail Yu. Lermontov's poetry as chiefly expressed in the antithesis of heaven and earth. It is argued that in Russian spiritual culture, Lermontov was the first to bring together the opposed poles of God and man in the sphere of the God-man.

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.

The article focuses on one highly idiosyncratic trait of Lifshits’ reading of Hegel, namely his assertion that the epoch of Restoration during which Hegel produced his main works was analogous to the period of the 1930s in the USSR. In both cases, “constructive” tasks came to the fore as the fermentation of the revolutionary era waned. On this assumption, Lifshits built up his idea of a Restauratio magna, which should serve as the guiding star of cultural politics. In fact, Lifshits (...) came very near to rehabilitating of Edmund Burke’s views about the conservation of cultural heritage, which is highly problematic in light of his initial Marxist convictions. (shrink)

One of the most influential scientific treatises in Cauchy's era was J.-L. Lagrange's Mécanique Analytique, the second edition of which came out in 1811, when Cauchy was barely out of his teens. Lagrange opens his treatise with an unequivocal endorsement of infinitesimals. Referring to the system of infinitesimal calculus, Lagrange writes:Lorsqu'on a bien conçu l'esprit de ce système, et qu'on s'est convaincu de l'exactitude de ses résultats par la méthode géométrique des premières et dernières raisons, ou par la méthode analytique (...) des fonctions dérivées, on peut employer les infiniment petits comme un instrument sûr et commode pour abréger et simplifier les demonstrations.Lagrange's renewed enthusiasm for .. (shrink)

We address Turkheimer’s argument that genome-wide association studies of behaviors and psychiatric traits will fail to produce coherent explanations. We distinguish two major sources of potential i...

In this paper we attempt to prove that it was Ludwig Feuerbach’s anthropology that influenced Bakunin’s philosophical path. Following his example Bakunin turned against religion which manipulates, as Hegelianism does, the only priority human being has—another human being. Although Feuerbach’s philosophy did not involve social problems present at Bakunin’s works, we would like to show that it was Feuerbach himself who laid foundation for them and that Bakunin’s criticism of the state was the natural consequence of Feuerbach’s struggle for the (...) individual. Mikhail Alexandrovich Bakunin proved that Feuerbach’s attempts to rise anthropology to the rank of theology are not sufficient to free the individual from the power of abstractions as in his opinion it is not only God (religion) that should be overthrown but also the state. (shrink)

This essay describes some of the literary, psychological, and historical causes of Russia’s war in Ukraine (2022) based on observations of the national character found in the fiction of Aleksandr Pushkin and Fyodor Dostoevsky and in philosophical and psychological essays of Petr Chaadaev, Sergei Askol’dov, and Sigmund Freud. The political ideology that stands behind the war can be characterized as schizofascism, or schizophrenic fascism that embraces the contradiction between archaic myths, chauvinism, and xenophobia, on the one hand, and corruption and (...) cynicism, on the other. Citing the controversial results of sociological polls indicating both Russians’ aspiration for friendship with Ukraine and their support for the aggressive war, the author explores the deep ambivalence inherent in the psychology of Russians as historical successors of the Golden Horde and the Moscovite State, incorporating the legacy of nomadism, militarism, messianism, and autarky. (shrink)

The first half of the 17th century was a time of intellectual ferment when wars of natural philosophy were echoes of religious wars, as we illustrate by a case study of an apparently innocuous mathematical technique called adequality pioneered by the honorable judge Pierre de Fermat, its relation to indivisibles, as well as to other hocus-pocus. André Weil noted that simple applications of adequality involving polynomials can be treated purely algebraically but more general problems like the cycloid curve cannot be (...) so treated and involve additional tools–leading the mathematician Fermat potentially into troubled waters. Breger attacks Tannery for tampering with Fermat’s manuscript but it is Breger who tampers with Fermat’s procedure by moving all terms to the left-hand side so as to accord better with Breger’s own interpretation emphasizing the double root idea. We provide modern proxies for Fermat’s procedures in terms of relations of infinite proximity as well as the standard part function. (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)

Already in his Logical Investigations Husserl is opposing consciousness and the world and raising the question of an objective, “true” existence of the world beyond phenomenological research. This opposition becomes increasingly radical in Husserl's subsequent works, especially in his early and mature periods. For Husserl, phenomenology is not simply about “bracketing” any conditions concerning the existence or nonexistence of the world; it is also designed to carry out a kind of “deworlding” of consciousness, which allows for revealing it not as (...) a thing or a part of the world, but as a nonobjective condition for any real existence. The critical question from which the author proceeds is the extent to which the opposition of consciousness and the world understood in the above way could be retained in situations where the main topic of phenomenology becomes the primordial relatedness of consciousness and the world or of the world a... (shrink)

We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...) Bos and Laugwitz seek to explore Eulerian methodology, practice, and procedures in a way more faithful to Euler’s own. Euler’s use of infinite integers and the associated infinite products are analyzed in the context of his infinite product decomposition for the sine function. Euler’s principle of cancellation is compared to the Leibnizian transcendental law of homogeneity. The Leibnizian law of continuity similarly finds echoes in Euler. We argue that Ferraro’s assumption that Euler worked with a classical notion of quantity is symptomatic of a post-Weierstrassian placement of Euler in the Archimedean track for the development of analysis, as well as a blurring of the distinction between the dual tracks noted by Bos. Interpreting Euler in an Archimedean conceptual framework obscures important aspects of Euler’s work. Such a framework is profitably replaced by a syntactically more versatile modern infinitesimal framework that provides better proxies for his inferential moves. (shrink)

Mikhail Bulgakov's novel The Master and Margarita was written between 1929 and 1940. Although delayed for a quarter of a century, it quickly found a stable place in our life as soon as it was published [for the first publication of the novel see: Moskva, 1966, no. 11; 1967, no. 1]. It is usually classified as a satirical philosophical novel. The satirical element puts it in the same family as such well-known works of the end of the '20s as (...) the novels of I. Il'f and E. Petrov, Twelve Chairs [Dvenadtsat' stul'ev] and The Golden Calf [Zolotoi telenok], but its emphatically philosophical orientation makes it all but a unique phenomenon in the history of Soviet literature. The novel's philosophical aspects have already been examined in a number of essays. Thus, for example, N. P. Utekhin analyzes the reflection of certain general philosophical categories in the novel. G. Chernikova and I. L. Galinskaia have endeavored to determine the concrete literary sources of the novel's philosophy [Chernikova 1971, pp. 213-219; Galinskaia 1986]. (shrink)

Georges Gurvitch, from the 1920s to the end of his life, was solving the problem of combining unity and plurality in the justification of society. He believed that individualism and collectivism represented social processes in a limited way because they were based on the preconception that the binding power of law derives respectively from a private or corporate actor's will. Gurvitch contrasted individual law with the social one, which was intended to overcome the opposition between individualism and collectivism. Social law (...) bases on legal sociology's assumption that social interactions as such are already legal relations. This conclusion allows Gurvitch to consider any social interaction as a source of law and to assert legal pluralism as a way of constructing society. The integrity of the latter is a condition for the mutual correlation of the multiplicity of legal regulations generated by internal social interactions into the unified structure of social law. In a holistic approach to comprehending social interactions, Gurvitch, in his Russian-language works in the migr period, uses the philosophical-legal interpretation of sobornost to describe society's integrity. In French- and English-language works from the 1930s, Gurvitch uses the term "totality," which he learned from Marcel Mauss, to describe social integrity. This article compares sobornost and totality as variants of denoting social integrity in Gurvitch's social law doctrine. The researcher determines that Gurvitch, using the concepts of sobornost and totality, interpreted society's development differently, 1) as anti-hierarchical sobornost equality, and 2) as a hierarchical inordination of totalities. Having analyzed the peculiarities of the interpretation of sobornost and totality in Gurvitch's works, the author concludes that these concepts should be considered multilingual equivalents in denoting communal unity as sources of law, which reflect changes in the interpretation of society in Gurvitch's social law doctrine. (shrink)

Cold-War Twins: Mikhail Alpatov's a Universal History of Arts and Ernst Gombrich's the Story of Art This article deals with the "afterlife" of a methodological disagreement in the Vienna School of Art History between the positions of Alois Riegl and Julius von Schlosser in Mikhail Alpatov's and Ernst Gombrich's art history survey texts published during the Cold War on different sides of the Iron Curtain. Though these surveys are methodological antipodes, the difference itself, I argue, is possible only (...) within the framework of the larger art historical discourse they share. In addition, I will draw on the radical ideological critique of Alpatov's survey inside the Soviet Union and the case of the Stalinist survey meant to replace it, in order to address the ideological commonality between Alpatov's and Gombrich's surveys. (shrink)

All of Mikhail Bakhtin’s work stands under the sign of plurality, the mystery of the one and the many. Unlike the third eye of Tibetan Buddhism, which gives those who possess it a vision of the secret unity holding creation together, Bakhtin seems to have had a third ear that permitted him to hear differences where others perceived only sameness, especially in the apparent wholeness of the human voice. The obsessive question at the heart of Bakhtin’s thought is always (...) “Who is talking?” It was his sense of the world’s overwhelming multiplicity that impelled Bakhtin to rethink strategies by which heterogeneity had traditionally been disguised as a unity. In his several attempts to find a single name for the teeming forces which jostled each other within the combat zone of the word—whether the term was “polyphony,” “heteroglossia,” or “speech communion”—Bakhtin was at great pains never to sacrifice the tension between identity and difference that fueled his enterprise. He always sought the minimum degree of homogenization necessary to any conceptual scheme, feeling it was better to preserve the heterogeneity which less patient thinkers found intolerable—and to which they therefore hurried to assign a unitizing label.Bakhtin’s metaphysical contrariness has the effect of making at times appear to be indiscriminate, as when he refused to recognize borders between biography and autobiography or, more notoriously, between speaking and writing. But, as I hope to show, these apparently cardinal distinctions are for Bakhtin only local instances of unity that participate in and are controlled by a fare more encompassing set of oppositions and differences. All this places an extra burden on those who seek an overarching design in Bakhtin’s legacy: the apparently unitizing term “Bakhtin” proves to be as illusory—or more illusory—in its ability to subsume real distinctions as any other, if we submit it to a Bakhtinian analysis. Michael Holquist is professor and chairman of the department of Slavic languages and literatures a Indiana University. With his wife, Katerina Clark, he has just completed Mikhail Bakhtin, a study of Bakhtin’s life and works, forthcoming in the autumn of 1984. He is currently working in Moscow. (shrink)

Proposing his conception of narrative identity in Oneself as Another, Paul Ricoeur holds that human life is comprehensible, once the story of a man’s life has actually been told, and it is the narrative of one’s life which constructs one’s identity. Developing his theory of heteroglossia and the polyphony of human speech, explicated chiefly in Speech Genres and The Dialogic Imagination, Mikhail Bakhtin recognizes the intrinsically intertwining character of utterance and response. According to him, utterance is always addressed to (...) someone and antedates an answer. Bakhtin’s “addressivity,” as well as his view of discourse as fundamentally dialogic, are convergent with Ricoeur’s elucidation both of man’s answerability to the Other and of narrative identity. The dynamic character of narrative identity, as construed by Ricoeur, converges with the dynamic nature of language as viewed by Bakhtin. The aim of this article is to study the intersections of Ricoeur’s narrative theory and Bakhtin’s recognition of the polyphonic nature of speech. I view these as inherently interrelated, and as testifying, respectively, to the philosophical and linguistic aspects of one and the same phenomenological vision. That vision accounts for selfhood, understood as vulnerable and contextualized, while also recognizing that it is conveyed by means of language with its essentially dialogic openness. (shrink)

This is an examination of two essays on minimal religion by Mikhail Epstein (1982 and 1999), assessing the usefulness of the term ‘minimal religion’ for the analysis of religion in contemporary Russia.