Mikhail L. Gasparov. Intertextual analysis today. The paper provides a discussion about recent results and perspectives of intertextual analysis — the method that has been a contemporary with Tartu-Moscow school. The connections between the classical philological methods and intertextual analysis are described, together with specifying the concept of intertext and emphasizing the need for the correctness of a researcher, because such an analysis always carries a danger of overinterpretation. Several examples are used to illustrate how the imagination of a (...) researcher can create arbitrary allusions that are not based on the original text and are usually misleading. As a result, the text under study will not become more clear, vice versa, it turns to be less understandable. (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 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)

Most of the time our utterances are automatically interpreted as speech acts: as assertions, conjectures and testimonies; as orders, requests and pleas; as threats, offers and promises. Surprisingly, the cognitive correlates of this essential component of human communication have received little attention. This book fills the gap by providing a model of the psychological processes involved in interpreting and understanding speech acts. The theory is framed in naturalistic terms and is supported by data on language development and on autism spectrum (...) disorders. Mikhail Kissine does not presuppose any specific background and addresses a crucial pragmatic phenomenon from an interdisciplinary perspective. This is a valuable resource for academic researchers and graduate and undergraduate students in pragmatics, semantics, cognitive linguistics, psycholinguistics and philosophy of language. (shrink)

Mikhail Bakhtin is one of the most influential theorists of philosophy as well as literary studies. His work on dialogue and discourse has changed the way in which we read texts – both literary and cultural – and his practice of philosophy in literary refraction and philological exploration has made him a pioneering figure in the twentieth-century convergence of the two disciplines. In this book, Graham Pechey offers a commentary on Bakhtin’s texts in all their complex and allusive ‘textuality’, (...) keeping a sense throughout of the historical setting in which they were written and of his own interpretation of and response to them. Examining Bakhtin’s relationship to Russian Formalism and Soviet Marxism, Pechey focuses on two major interests: the influence of Eastern Orthodox Christianity upon his thinking; and Bakhtin’s use of literary criticism and hermeneutics as ways of ‘doing philosophy by other means’. (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)

In his late works Husserl interprets the crisis of European sciences as the loss of their meaning for life. The diagnosis seems to suggest therapeutic strategy: to overcome the crisis, phenomenology must return to the evidences of the life-world. The article argues that the husserlian strategy of overcoming the crisis consists not in the elimination of the break with the prescientific evidences of the natural attitude, but, on the contrary, in the radicalization of the breach. Thus, I want to show (...) that Husserl seeks to overcome the crisis of sciences by means of more radical crisis of phenomenology. In Husserl’s view, phenomenology must become the only science, which does not presuppose the life-world, since it problematizes it. I am going to argue also, that the counterintuitive strategy is not just of the historico-philosophical interest, but is meaningful for the actual philosophical understanding of the life-world. To justify those claims, I will proceed in three stages. In the first section of the article, I analyze the difference between the objective world and the life-world, which is the point of departure of husserlian interpretation of the crisis of sciences in Crisis. Bringing into correlation the difference between the objective world and the life-world in Crisis with the distinction of the ideal world and the real one in Ideas I, I disclose the ambiguity of husserlian interpretation of the crisis of European sciences. According to Husserl, the crisis arises, when science transcends the life-world through the idealizations, and, at the same time, presupposes the immediate prescientific evidences as something that is taken for granted. In the second section, I argue that the strategy of overcoming the crisis in Crisis is based on the phenomenological epoche, which allows for the porblematization of the life-world without presupposing it, Within this context I demonstrate the motivational unity of two reductions, performed by Husserl in Crisis—the reduction to the life-world, stripping the reality of the garb of ideas mistakingly taken to be the reality itself, and the reduction of the life-world, turning it into horizon and depriving phenomenologist of a right of relying on the life-worldly evidences, which is taken for granted in the natural science and renders it possible. The unity of the reductions indicates that phenomenological descent back down to the life-world is treated by Husserl as the radical break with the evidences of the natural life. The third section discusses the question, whether the problematical character of the life-world can be revealed only from the point of view of disinterested spectator, or it can be discovered, in a way, from within, in pretheoretical experience, which capacitates the life to problematizing itself and motivates phenomenological epoche. I argue that, although the question is not answered in a suitable way within husserlian analyses of the motivation for the epoche, the key to the solution of the problem is provided by the genetic phenomenology, since it thematizes the historicity of the life-world. I interpret the historicity as the ambivalent pretheoretical experience, constituting both the self-evidence and the problematical character of the life-world. (shrink)

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)

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)

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)

This essay analyses the contribution of the knowledge of Greek culture in Antiquity for Mikhail Bakhtin’s achievement. It shows how the Socratic dialogue and serious-comic genres contributed to forming the novel – according do Bakhtin’s conceptions – by developing its carnavalized line. It concludes that, although Bakhtin was not properly a Hellenist, he has contributed to Ancient Greece studies, by exploring the literary creativity of Hellenist period.

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 language theory of Mikhail Bakhtin does not fall neatly under any single rubric - 'dialogism,' 'marxism,' 'prosaics,' 'authorship' - because the philosophic foundation of his writing rests ambivalently between phenomenology and Marxism. The theoretical tension of these positions creates philosophical impasses in Bakhtin's work, which have been neglected or ignored partly because these impasses are themselves mirrored by the problems of antifoundationalist and materialist tendencies in literary scholarship. In Mikhail Bakhtin: Between Phenomenology and Marxism Michael Bernard-Donals examines (...) various incarnations of phenomenological and materialist theory - including the work of Jauss, Fish, Rorty, Althusser, and Pecheux - and places them beside Bakhtin's work, providing a contextualised study of Bakhtin, a critique of the problems of contemporary critics, and an original contribution to literary theory. (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)

Could a computer be programmed to make moral judgments about cases of intentional harm and unreasonable risk that match those judgments people already make intuitively? If the human moral sense is an unconscious computational mechanism of some sort, as many cognitive scientists have suggested, then the answer should be yes. So too if the search for reflective equilibrium is a sound enterprise, since achieving this state of affairs requires demarcating a set of considered judgments, stating them as explanandum sentences, and (...) formulating a set of algorithms from which they can be derived. The same is true for theories that emphasize the role of emotions or heuristics in moral cognition, since they ultimately depend on intuitive appraisals of the stimulus that accomplish essentially the same tasks. Drawing on deontic logic, action theory, moral philosophy, and the common law of tort, particularly Terry's five-variable calculus of risk, I outline a formal model of moral grammar and intuitive jurisprudence along the foregoing lines, which defines the abstract properties of the relevant mapping and demonstrates their descriptive adequacy with respect to a range of common moral intuitions, which experimental studies have suggested may be universal or nearly so. Framing effects, protected values, and implications for the neuroscience of moral intuition are also discussed. (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 comment on Joshua Greene's essay, The Secret Joke of Kant's Soul, I argue that a notable weakness of Greene's approach to moral psychology is its neglect of computational theory. A central problem moral cognition must solve is to recognize (i.e., compute representations of) the deontic status of human acts and omissions. How do people actually do this? What is the theory which explains their practice?

We propose and investigate a uniform modal logic framework for reasoning about topology and relative distance in metric and more general distance spaces, thus enabling the comparison and combination of logics from distinct research traditions such as Tarski’s for topological closure and interior, conditional logics, and logics of comparative similarity. This framework is obtained by decomposing the underlying modal-like operators into first-order quantifier patterns. We then show that quite a powerful and natural fragment of the resulting first-order logic can be (...) captured by one binary operator comparing distances between sets and one unary operator distinguishing between realised and limit distances . Due to its greater expressive power, this logic turns out to behave quite differently from both and conditional logics. We provide finite axiomatisations and ExpTime-completeness proofs for the logics of various classes of distance spaces, in particular metric spaces. But we also show that the logic of the real line is not recursively enumerable. This result is proved by an encoding of Diophantine equations. (shrink)

This article argues that combining elements of the sociological theories of Johann Arnason and Peter Wagner can contribute to an understanding of the causes of the ‘new Cold War’ on the European continent. Comparisons of today’s confrontation between Russia and the West with the original Cold War are largely misleading since the Soviet model of modernity represented a radical alternative to its liberal western version. Unlike the original Cold War, the current ideological confrontation is not connected with a clash of (...) different forms of modernity. Today’s Russia lacks a clear civilizational identity and does not follow an alternative project of modernity. The recent ‘conservative turn’ in Russian politics largely draws on a specific interpretation of European modernity. (shrink)

I argue against the view that there is intrinsic value in making one's own decisions about the direction and shape of one's life.

Mikhail Lifshits’ interpretation of the scholarly work of the Italian philosopher Giambattista Vico is analysed against the background of other Soviet interpretations. M. Lifshits authored the introductory article for the first complete translation of Vico’s Scienza Nuova in 1940. In the second half of the 1930s, interest in Vico’s ‘historical theory of knowledge’ was important for the struggle against so-called ‘vulgar sociology’ in the field of aesthetics and literary criticism. Besides this, Vico’s theory of the ‘historical cycle’ was close (...) to the interests M. Lifshits and G. Lukács and their circle in Stalin-era Moscow. This interest was connected with discussions about the preservation of the revolutionary impulse under the conditions of state socialism. However, such an interpretation of Vico restricted a wide spectrum of his scholarly work. In particular, Lifshits, as an opponent of social-constructivism tradition, ignored Vico’s well-known doctrine of verum factum. (shrink)

The Dirac δ function has solid roots in nineteenth century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac’s discovery by over a century, and illuminating the nature of Cauchy’s infinitesimals and his infinitesimal definition of δ.

In this guest column, Epstein offers “a new sign” that, he argues, resolves difficulties that have arisen in many theories and practices, including linguistics, semiotics, literary theory, poetics, aesthetics, ecology, ecophilology, eco-ethics, metaphysics, theology, psychology, and phenomenology. The new sign, a pair of quotation marks around a blank space, signfies the absence of any sign. Most generally, “ ” relates to the blank space that surrounds and underlies a text; by locating “ ” within the text, the margins are brought (...) inside and can become the focus of attention. Not only the margins but also the material background of a text (the page or screen) can be brought forward and focused on through the transparency of the sign “ ”, in which case “ ” becomes a sign of itself. Consubstantial with its medium, therefore, this sign is both relative and universal: “ ” is the same everywhere, on every surface, in every language, and also in the arts. Epstein analyzes works by Rauschenberg, Malevich, Ilya Kabakov, and Vasilisk Gdenov in the visual arts, as well as music by John Cage, to demonstrate the usefulness of his new sign for aesthetics and art criticism. Each discipline, he argues, has its own nonspeakable conditions and assumptions that it needs to bring inside disciplinary frontiers. At the frontier of language, “ ” is both inside and outside, and therefore can express the nonspeakable condition of speakability. In concluding, Epstein suggests that the task of the avant-garde in theory today is to develop a “negative semiotics”: a semiotics of nonsigns, modeled on negative (apophatic) theology. (shrink)

One of the most influential arguments in contemporary philosophy and cognitive science is Chomsky's argument from the poverty of the stimulus. In this response to an essay by Chandra Sripada, I defend an analogous argument from the poverty of the moral stimulus. I argue that Sripada's criticism of moral nativism appears to rest on the mistaken assumption that the learning target in moral cognition consists of a series of simple imperatives, such as "share your toys" or "don't hit other children." (...) In fact, the available evidence suggests that the moral competence of adults and even young children is considerably more complex and exhibits many characteristics of a well-developed legal code, including abstract theories of crime, tort, contract, and agency. Since the emergence of this knowledge cannot be explained by appeals to explicit instruction, or to any known processes of imitation, internalization, socialization and the like, there are grounds for concluding it may be innate. Simply put, to explain the development of intuitive jurisprudence in each individual, we must attribute unconscious knowledge and complex mental operations to her that go well beyond anything she has been taught. (shrink)

This article argues that the key elements of the prima facie case of harmful battery may form critical building blocks of moral cognition in both humans and nonhuman animals. By contrast, at least some of the rules and representations presupposed by familiar justifications to battery appear to be uniquely human. The article also argues that many famous thought experiments in ethics and many influential experiments in moral psychology rely on harmful battery scenarios without acknowledging this fact or considering its theoretical (...) or empirical implications. The unifying factor in all these studies is goal-directed harmful contact, inflicted without consent or justification. (shrink)

In the paper, the authors explore the relations between educational technology and educational ideology through the lens of philosophical inquiry. The optics of critical analysis is applied to review the instructional tools, services and systems which compose the complex picture of contemporary educational technology. The authors claim that even when initially established in the ideological domain of educational anarchism most educational technologies when being applied systemically can end up on the more oppressive side of the ideological spectrum close to educational (...) totalitarianism. They focus on the risks of technology that are growing with the social change brought by the lifelong learning paradigm in education. (shrink)

In what sense do people doubt their understanding of reality when subject to gaslighting? I suggest that an answer to this question depends on the linguistic order at which a gaslighting exchange takes place. This marks a distinction between first-order and second-order gaslighting. The former occurs when there is disagreement over whether a shared concept applies to some aspect of the world, and where the use of words by a speaker is apt to cause hearers to doubt their interpretive abilities (...) without doubting the accuracy of their concepts. The latter occurs when there is disagreement over which concept should be used in a context, and where the use of words by a speaker is apt to cause hearers to doubt their interpretive abilities in virtue of doubting the accuracy of their concepts. Many cases of second-order gaslighting are unintentional: its occurrence often depends on contingent environmental facts. I end the article by focusing on the distinctive epistemic injustices of second-order gaslighting: metalinguistic deprivation, conceptual obscuration, and perspectival subversion. I show how each reliably has sequelae in terms of psychological and practical control. (shrink)

A popular view among autonomy theorists is that facts about the history of a person's desires, and specifically facts about how they were formed or acquired, matter crucially to her autonomy. I argue that while there is an important relationship between a person's autonomy and the history of her desires, a person's autonomy does not depend on how her desires were formed or acquired. I argue that a desire's autonomy lies not in its origins but in whether its bearer has (...) a history of having engaged with it in the right sort of way. I argue that this view has important advantages, and no obvious disadvantages, over its historical and its non-historical rivals. (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 first English-language philosophical study of Mikhail Bakunin, this book examines the philosophical foundations of Bakunin?

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)

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.

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.

We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...) Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace −∫ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy. (shrink)