This paper offers an analysis of Kant’s account of the mathematical sublime with reference to his claim that ‘Nature is thus sublime in those of its appearances the intuition of which brings with them the idea of its infinity’. In undertaking this analysis I challenge Paul Crowther’s interpretation of this species of aesthetic experience, and I reject his interpretation as not being reflective of Kant’s actual position. I go on to show that the experience of the (...) class='Hi'>mathematical sublime is necessarily connected with the progression of the imagination in its move towards the infinite. View HTML Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.Kant’s Mathematical Sublime and the Role of the Infinite: Reply to CrowtherVolume 20, Issue 1Simon D. Smith DOI: https://doi.org/10.1017/S1369415414000302Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. Kant’s Mathematical Sublime and the Role of the Infinite: Reply to CrowtherVolume 20, Issue 1Simon D. Smith DOI: https://doi.org/10.1017/S1369415414000302Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. Kant’s Mathematical Sublime and the Role of the Infinite: Reply to CrowtherVolume 20, Issue 1Simon D. Smith DOI: https://doi.org/10.1017/S1369415414000302Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation. (shrink)

According to Kant’s Critique of the Power of Judgement, in the end all estimation of magnitude is sensible, or ‘aesthetic’, and the absolutely great in aesthetic estimation is called ‘the mathematical sublime’. This article identifies the relevant sensible element with an inner sensation of a temporal tension: in aesthetic comprehension, the imagination encounters an inevitable tension between the successive reproduction of a magnitude’s individual parts and the simultaneous unification of these parts. The sensation of this tension varies in (...) degree and facilitates aesthetic estimation in general. But in the special case where it comes to involve a sense of exceeding our imagination’s limit, we judge a magnitude to be mathematically sublime. Pace Kant, I argue that this limit is private and contingent rather than transcendental, such that the judgement of the mathematical sublime is neither universal a priori nor necessary. (shrink)

Kant argues in the Critique of Judgment (CJ) that there are two distinct modes of the sublime. This essay will concentrate on the mathematical mode. It is helpful to begin an examination of the mathematical sublime by elucidating the difference between logical estimation and aesthetic estimation; it is aesthetic estimation under strain, so Kant argues, that instigates the moment of the sublime. Logical estimation forms the cognitive basis of scientific calculations. He argues that scientific enquiry (...) only requires an understanding of the logical relationship of numbers and so does not require an aesthetic experience of those numbers. (shrink)

Immanuel Kant’s work on the sublimity of aesthetic experience lends itself to puzzlement, if not misclassification. Complicating matters, Kant distinguishes between two kinds of sublimity: respectively, the “mathematical” and “dynamical” sublime. More mystifying is that the sublime is ineffable, beyond the ken of human comprehension. These perplexities notwithstanding, Kant argues that sublime sentiment produces a feeling of supersensible comfort. Commentators identify this comfort emanating most strongly from the dynamical sublime. However, in this paper I draw (...) from the unity of reason thesis to offer a plausible account of how the mathematical sublime is equally capable of providing the same feeling of supersensible comfort. (shrink)

In this paper, I elaborate the difference between the concept of infinity and the idea of infinity through Cantor's diagonalization proof to illuminate a passage in Kant's Critique of Judgment. Taking Lyotard's analysis of aesthetic judgments as the basis for my own project, I focus on the idea of a collapse of temporality required for objective cognition and its concomitant preclusion of cognitive subjectivity. Finally, after borrowing language from Hegel's Phenomenology of Spirit, I show that even though there is not (...) a cognitive subject in judgments of the sublime, there is nevertheless a subjectivity that consciousness is tasked with, even if it never fulfills this task when it is confronted with a mathematically sublime object, and it is an subjectivity that would transcend time in order to know the object in-itself. (shrink)

The aesthetic tradition has identified as paradigmatically sublime such objects as imposing mountains and intense storms, as well as monumental art. But the tradition also acknowledges less paradigmatic cases, including sometimes mathematical structures or abstract concepts. In this paper, we argue that there is also a case for considering phenomenal consciousness – the experiential quality of subjective awareness – as a sublime phenomenon. One appreciates this, we argue, when one is struck by (fitting) awe upon contemplating (a) (...) the perplexing existence of something like phenomenal consciousness in an otherwise completely material universe and (b) the role of consciousness in injecting meaning and value in an otherwise brutally factual reality. (shrink)

I defend an interpretation of the first Critique’s category of totality based on Kant’s analysis of totality in the third Critique’s Analytic of the mathematical sublime. I show, firstly, that in the latter Kant delineates the category of totality — however general it may be — in relation to the essentially singular standpoint of the subject. Despite the fact that sublime and categorial totality have a significantly different scope and function, they do share such a singular baseline. (...) Secondly, I argue that Kant’s note (in the first Critique’s metaphysical deduction) that deriving the category of totality requires a special act of the understanding can be seen as a ‘mark’ of that singular baseline. This way, my aesthetical ‘detour’ has the potential of revealing how the subjective aspects of object-constitution might be accounted for in the very system of the categories (of quantity) itself. (shrink)

There is a long tradition, in the history and philosophy of science, of studying Kant’s philosophy of mathematics, but recently philosophers have begun to examine the way in which Kant’s reflections on mathematics play a role in his philosophy more generally, and in its development. For example, in the Critique of Pure Reason , Kant outlines the method of philosophy in general by contrasting it with the method of mathematics; in the Critique of Practical Reason , Kant compares the Formula (...) of Universal Law, central to his theory of moral judgement, to a mathematical postulate; in the Critique of Judgement , where he considers aesthetic judgment, Kant distinguishes the mathematical sublime from the dynamical sublime. This last point rests on the distinction that shapes the Transcendental Analytic of Concepts at the heart of Kant’s Critical philosophy, that between the mathematical and the dynamical categories. These examples make it clear that Kant's transcendental philosophy is strongly influenced by the importance and special status of mathematics. The contributions to this book explore this theme of the centrality of mathematics to Kant’s philosophy as a whole. This book was originally published as a special issue of the Canadian Journal of Philosophy. (shrink)

Kant’s account of the sublime in the Critique of Judgment has been extremely influential, prompting extensive discussion of the psychology, affect, moral significance, and relevance to artistic representation of the sublime on his provocative view. I focus instead on Kant’s account of the mathematical sublime in connection to his theoretical critical project, namely his attempt to characterize human cognitive powers and to limit human pretensions to knowledge of the supersensible. I argue, first, that his account of (...) the psychology of the sublime is designed to explain not just its affective character, but also to address challenges concerning the coherence of an experience of something as transcending one’s cognitive abilities. Thereby, I argue moreover, Kant provides an alternative, demystifying account of mystical experiences, in which humans might take themselves to intuit that which is beyond human understanding or reason, and thus to claim that they have special cognitive access to the supersensible, transcending the limits Kant claims to establish for human cognition. Kant’s account of the mathematical sublime is not merely so reductive of mystical experience, however; it also, I suggest, describes the aesthetic of Kantian critique itself. (shrink)

The sublime has been a relatively neglected topic in recent work in philosophical aesthetics, with existing discussions confined mainly to problems in Kant's theory.1 Given the revival of interest in his aesthetic theory and the influence of the Kantian sublime compared to other eighteenth-century accounts, this focus is not surprising. Kant's emphasis on nature also sets his theory apart from other eighteenth-century theories that, although making nature central, also give explicit attention to moral character and mathematical ideas (...) and generally devote more discussion to art and artifacts than Kant did.2 Recent postmodern and poststructuralist theories of the sublime tend to concentrate on the concept in art and .. (shrink)

The Kantian approach to the sublime in the Critique of the Power of Judgment is based on an antagonism between two faculties, Imagination and Reason. In order to understand this conflict under new conceptual coordinates, and pursuing a triple exegetical, aesthetical and political interest, the aim of the present paper is to develop the brutal character proper to the conceptual dynamics deployed in such an approach. Reconstructing this mouvement from the incidences of the term Gewalt, under a brutalism of (...) the sublime, we focus on the inquiry of the violence that the Imagination experiences in its mathematical determination and, on the other hand, of the power that Reason holds according to the dynamic determination of the sublime. Thus, under such a perspective, violence, power and subjective impotence will appear as constitutive characters of the genesis of the feeling of the sublime within the horizon of transcendental philosophy. (shrink)

In their recent work, L. Graham and J.-M. Kantor discuss a remarkable connection between diverging conceptions of the mathematical infinite in Russia and France at the beginning of the twentieth century and the religious convictions of their respective authors. They expand much more on the Russian side of the cultural equation they propose; I do believe, however, that the French (or rather ‘West European’) side is more complex than it seems, and that digging deeper into it is worthwhile. In (...) this paper I shall therefore broaden the path laid out in Graham and Kantor’s work, by connecting two different strands of research concerning the origin of what I loosely call ‘formal’ ideas: firstly, the rich but complex relation between logic and rhetoric throughout European cultural history, and secondly, the impact of religious convictions on the formation of certain mathematical and scientific ideas during Renaissance and Early Modernity, especially but not exclusively in France. (shrink)

There is a long tradition, in the history and philosophy of science, of studying Kant’s philosophy of mathematics, but recently philosophers have begun to examine the way in which Kant’s reflections on mathematics play a role in his philosophy more generally, and in its development. For example, in the Critique of Pure Reason , Kant outlines the method of philosophy in general by contrasting it with the method of mathematics; in the Critique of Practical Reason , Kant compares the Formula (...) of Universal Law, central to his theory of moral judgement, to a mathematical postulate; in the Critique of Judgement , where he considers aesthetic judgment, Kant distinguishes the mathematical sublime from the dynamical sublime. This last point rests on the distinction that shapes the Transcendental Analytic of Concepts at the heart of Kant’s Critical philosophy, that between the mathematical and the dynamical categories. These examples make it clear that Kant's transcendental philosophy is strongly influenced by the importance and special status of mathematics. The contributions to this book explore this theme of the centrality of mathematics to Kant’s philosophy as a whole. This book was originally published as a special issue of the Canadian Journal of Philosophy. (shrink)

If the cliché about garbage – ‘Out of sight, out of mind’ – is true, its inverse, unfortunately, is not. Heaps and masses of garbage brought into direct view still somehow manage to escape acute recognition, let alone social responsibility or global political activism. This article investigates this trend as a growing problem between the human world and representation. Focusing on historical and contemporary landscape photography, the article questions whether data visualization trends, particularly those that attempt to visualize the post-industrial (...) consumer landscape, help or hinder our capacity to understand our environment, and possibly even ecological endeavors. The article charts the history of photography’s landscape genre, mapping the contours of a shift from the classical ‘nature’ aesthetic, to an industrial, post-industrial, and eventually a mathematical aesthetic contingent on emergent techniques and data visualization in the attempt to depict ever amassing magnitudes of environmental despoliation. (shrink)

Show more ▾ There are various dichotomies in Kant’s philosophy: sensibility vs. rationality, nature vs. freedom, cognition vs. morality, noumenon vs. phenomenon, among others. There are also different ways of mediating these dichotomies, which is the systematic undertaking of Kant’s Critique of the Power of Judgment. One of the most important concepts in this work is the sublime, which exemplifies the connections between the different dichotomies; this fact means the concept’s construction is full of tension. On the one hand, (...) as a pure reflection of aesthetic judgment the sublime must be without interest or purpose, but on the other hand it is “based on the concept of reason” (KU AA:292). On the one hand, the sublime “represents merely the subjective play of the powers of the mind (imagination and reason) as harmonious” (KU AA5:258), but on the other hand, reason “exercises dominion over sensibility” and the imagination is “purposively determined in accordance with a law” of reason (KU AA5:268f). Taking into account these problems concerning the essential definition the sublime, this paper will first illustrate how the sublime embodies the a priori principle of aesthetic judgment through contrasting the judgment of the sublime with the judgment of taste in order to establish a basic logical frame for the judgment of the sublime. Second, this paper redefines the boundary between the mathematically and dynamically sublime in order to reveal both the coexistence of contemplation and movement within the sublime and the unrevealed function of reason and imagination. Finally, contrasting the sublime with moral feeling, this paper elaborates the turning-structure (from sensibility to rationality and from object-intuition to idea-exhibition) of the sublime. (shrink)

For the purposes of this monograph, "by a degree" is meant a degree of recursive unsolvability. A degree [script bold]m is said to be minimal if 0 is the unique degree less than [script bold]m. Each of the six chapters of this self-contained monograph is devoted to the proof of an existence theorem for minimal degrees.

Kurt Gdel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gdel's writings. The first three volumes, already published, consist of the papers and essays of Gdel. The final two volumes of the set deal with Gdel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and (...) updated by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

Introduction -- The symbolic form of art -- Kant's theory of the mathematical sublime and the boundlessness of the symbolic form of art -- The classical sublimity of Judaism -- The classical form of art -- The original epic -- The ideal -- The transition to the revealed religion and the romantic form of art -- The revealed religion -- Representational thought and the romantic form of art -- Traces of left-hegelianism in Hegel's lectures on aesthetics -- The (...) end of mythology -- The significance of Kierkegaard's interpretation of Don Giovanni in relation to Hegel's theory of the end of art -- The end of art -- The opera as a modern art form -- Hegel and Lukács's on the possibility of a modern epic -- The problem of a modern epic -- The modern epic and history -- Civil society as the background to the modern epic -- Myth and society : a common theme in the thought of Hegel and Sorel -- Sorel's myth of the general strike -- Myth and modern ethical life. (shrink)

Author: Werner Maria Title: VICTOR BASCH’S INTERPRETATION OF KANTIAN THEORY OF THE SUBLIME (Victora Bascha interpretacja Kantowskiej teorii wzniosłości) Source: Filo-Sofija year: 2005, vol:.5, number: 2005/1, pages: 189-201 Keywords: BASCH, KANT, THEORY OF THE SUBLIME Discipline: PHILOSOPHY Language: POLISH Document type: ARTICLE Publication order reference (Primary author’s office address): E-mail: www:The article shows the critical analysis of the analytics of the sublime from Kant’s Critique of Judgment, presented by V. Basch. In his work Essai critique sur l’esthetique (...) de Kant Basch tries to prove Kantian division between the mathematical and dynamically sublime superfluous. In his interpretation of the problem also other aspects of Kant’s theory of the sublime (such as referring to the idea of the infinity and his description of the process of ‘grasping and uniting’ in the experience of mathematical sublime) are needless. On the grounds of his criticism Basch gives his own theory of the sublime. According to it the very nature is sublime, and the glorification of human nature is given not in calling to the ideas of reason, but in the uniting with nature. (shrink)

In contrast with Kant's "Theory of Beauty" his "Analytics of the Sublime" has till now been paid meager systematic attention. This essay on the architectonics of the sublime proves three theses. (1) Beauty and sublime are not experiences of two different object classes, but of two contrary moods of mind. (2) Kant's exposition of the "mathematical-sublime" is based on not immediately evident premises. But these difficulties concerning the "comprehensio aesthetica" can be explained retrospectively from the (...) "dynamical-sublime". For only in view of a symbolically threatening nature its mere "extensively" immeasurable oversize is apperceived asan "intensively" overwhelming power, which evokes the feeling of reluctance. And even the (strictly thought) absurd idea of a "totallygiven infinity" is the playing retort of the imaginative power, by which a reversal of the proportions, a belittling of nature, and the restoration of pleasure is accomplished. (3) The symmetry of the fourmoments of judgment is novel, but plausible. (shrink)

Abstract.There is ample evidence that humans (and other primates) possess a knowledge instinct—a biologically driven impulse to make coherent sense of the world at the highest level possible. Yet behavioral decision‐making data suggest a contrary biological drive to minimize cognitive effort by solving problems using simplifying heuristics. Individuals differ, and the same person varies over time, in the strength of the knowledge instinct. Neuroimaging studies suggest which brain regions might mediate the balance between knowledge expansion and heuristic simplification. One region (...) implicated in primary emotional experience is more activated in individuals who use primitive heuristics, whereas two areas of the cortex are more activated in individuals with a strong knowledge drive: one region implicated in detecting risk or conflict and another implicated in generating creative ideas. Knowledge maximization and effort minimization are both evolutionary adaptations, and both are valuable in different contexts. Effort minimization helps us make minor and routine decisions efficiently, whereas knowledge maximization connects us to the beautiful, to the sublime, and to our highest aspirations. We relate the opposition between the knowledge instinct and heuristics to the biblical story of the fall, and argue that the causal scientific worldview is mathematically equivalent to teleological arguments from final causes. Elements of a scientific program are formulated to address unresolved issues. (shrink)

There is ample evidence that humans (and other primates) possess a knowledge instinct—a biologically driven impulse to make coherent sense of the world at the highest level possible. Yet behavioral decision-making data suggest a contrary biological drive to minimize cognitive effort by solving problems using simplifying heuristics. Individuals differ, and the same person varies over time, in the strength of the knowledge instinct. Neuroimaging studies suggest which brain regions might mediate the balance between knowledge expansion and heuristic simplification. One region (...) implicated in primary emotional experience is more activated in individuals who use primitive heuristics, whereas two areas of the cortex are more activated in individuals with a strong knowledge drive: one region implicated in detecting risk or conflict and another implicated in generating creative ideas. Knowledge maximization and effort minimization are both evolutionary adaptations, and both are valuable in different contexts. Effort minimization helps us make minor and routine decisions efficiently, whereas knowledge maximization connects us to the beautiful, to the sublime, and to our highest aspirations. We relate the opposition between the knowledge instinct and heuristics to the biblical story of the fall, and argue that the causal scientific worldview is mathematically equivalent to teleological arguments from final causes. Elements of a scientific program are formulated to address unresolved issues. (shrink)

1936 was a watershed year for computability. Debates among Gödel, Church and others over the correct analysis of the intuitive concept “human effectively computable”, an analysis at the heart of the Incompleteness Theorems, the Entscheidungsproblem, the question of what a finite computation is, and most urgently—for Gödel—the generality of the Incompleteness Theorems, were definitively set to rest with the appearance, in that year, of the Turing Machine. The question I explore here is, do the mathematical facts exhaust what is (...) to be said about the thinking behind the “confluence of ideas in 1936”? I will argue for a cultural role in Gödel’s, and, by extension, the larger logical community’s absorption of Turing’s 1936 model. As scaffolding I employ a conceptual framework due to the critic Leo Marx of the technological sublime; I also make use of the distinction within the technological sublime due to Caroline Jones, between its iconic and performative modes—a distinction operating within the conceptual art of the 1960s, but serving the history of computability equally well. (shrink)

The Sublime is a framework for overwhelming emotions in a neuronalphysiologic und psychological sense. And since Burke’s Enquiry it has been established as a constitutive part of the discourse of aesthetics. With Kant, his empirical exposition took a decisive transcendental turn, unfolding the dichotomy of the Mathematically and the Dynamically Sublime. Whereas in the former case, we are stunned by the incomprehensible vastness of impression, in the latter we enjoy the mighty, threatening and extinguishing power of nature once (...) we ourselves are safe. Both feelings are generated by the cinema as a dispositive of artificial experience in which it becomes sensually evident why imagination fails in its ability to comprehend the whole. But although perceiving its diminutiveness, the subject masters this failure by raising itself up in being able to think - as opposed to imagining - the Greatness. Lyotard interprets this hubris as an act of self-empowerment, tending to extinguish the experience of nature. Therefore, his interest in the Sublime bears on abstract, amorphous art and lighting installations. This article, however, argues that especially with regard to the film as mass media, the categories and concepts of the sublime as deployed in the 18. (shrink)

This volume builds on two recent developments in philosophy on the relationship between art and science: the notion of representation and the role of values in theory choice and the development of scientific theories. Its aim is to address questions regarding scientific creativity and imagination, the status of scientific performances--such as thought experiments and visual aids--and the role of aesthetic considerations in the context of discovery and justification of scientific theories. Several contributions focus on the concept of beauty as employed (...) by practising scientists, the aesthetic factors at play in science and their role in decision making. Other essays address the question of scientific creativity and how aesthetic judgment resolves the problem of theory choice by employing aesthetic criteria and incorporating insights from both objectivism and subjectivism. The volume also features original perspectives on the role of the sublime in science and sheds light on the empirical work studying the experience of the sublime in science and its relation to the experience of understanding. The Aesthetics of Science tackles these topics from a variety of novel and thought-provoking angles. It will be of interest to researchers and advanced students in philosophy of science and aesthetics, as well as other subdisciplines such as epistemology and philosophy of mathematics. (shrink)

Mendelssohn's Philosophical Writings, published in 1761, bring the metaphysical tradition to bear on the topic of 'sentiments' (defined as knowledge or awareness by way of the senses). Mendelssohn offers a nuanced defence of Leibniz's theodicy and conception of freedom, an examination of the ethics of suicide, an account of the 'mixed sentiments' so central to the tragic genre, a hypothesis about weakness of will, an elaboration of the main principles and types of art, a definition of sublimity and analysis of (...) its basic forms, and, lastly, a brief tract on probability theory, aimed at rebutting Hume's scepticism. This volume also includes the essay 'On Evidence in Metaphysical Sciences', selected in 1763 by the Berlin Royal Academy of Sciences over all other submitted essays, including one by Kant, as the best answer to the question of whether metaphysical sciences are capable of the same sort and degree of evidence as mathematics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The humble origins of Russell's paradox by J. Alberto Coffa ON SEVERAL OCCASIONS Russell pointed out that the discovery of his celebrated paradox concerning the class of all classes not belonging to themselves was intimately related to Cantor's proof that there is no greatest cardinal. lOne of the earliest remarks to that effect occurs in The Principles ofMathematics where, referring to the universal class, the class of all classes (...) and the class of all propositions, he notes that when we apply the reasoning of his [Cantor's] proofto the cases in question we find ourselves met by definite contradictions, of which the one discussed in Chapter x is an example. (P. 362) And in a footnote he adds: "It was in this way that I discovered this contradiction". Throughout his writings Russell left a number ofhints concerning the sort of connection he had drawn between Cantor's proof and his own discovery. In fact, his suggestions are so specific that there would seem to be little room left for speculation concerning how the discovery took place.2 The picture that emerges almost immediately from Russell's observations is the following. For reasons which are 1 See, e.g., Bertrand Russell, The Principles of Mathematics, 2nd ed. (London: Allen & Unwin, 1937), §§100, 344-9; G. Frege, Wissenschaftlicher Briefwechsel (Hamburg: Felix Meiner Verlag, 1976), pp. 215-16; B. Russell, Essays in Analysis, ed. D. Lackey (New York: George Braziller, 1973), p. 139; B. Russell, Introducrion to Mathemarical Philosophy (New York: Simon and Schuster, 1971), p. 136; B. Russell, My Philosophical Development (New York: Simon and Schuster, 1959), pp. 75-6; The Autobiography of Bertrand Russell, I (New York: Bantam Books, 1968), 195. 2 See, e.g., Ch. Thiel's "Einleitung des Herausgebers" in Frege, Wissenschaftlicher Briefwechsel, pp. 203 and 216 (footnote), and 1. Grattan-Guinness, "How Bertrand Russell Discovered his Paradox", Historia Marhematica, 5 (1978),127-37. 31 32 Russell, nos. 33-4 (Spring-Summer 1979) never made clear, Russell decided to analyze Cantor's argument applying it to "large" classes such as the universal class V, and the class of all classes. When, for example, we consider V, its power set and the correlationf(x) = {x} if x is not a class, f(x) =. x otherwise, then Cantor's diagonal class D turns out to be the class of all classes not belonging to themselves. Moreover, since the element ofV which is taken toD byfisD itself(i.e., sincef(D) = D), Cantor's reasoning invites us to raise the question whether D belongs tof(D) (i.e., toD) or not; and it establishes that it does precisely if it doesn't.3 The purpose of this note is to present recently uncovered information that complements and corrects our present understanding of Russell's discovery of his paradox. As it turns out, far from originating from his desire to apply the ideas in Cantor's theorem, a version of Russell's paradox first occurred in an argument that Russell had devised, late in 1900, in order to establish the invalidity of that theorem. An appeal to "large" classes such as V or Class was, as we shall see, essential to Russell's attempted refutation. As he displayed the details of his counterexample Russell's paradox emerged, at first unrecognized, as the by-product of a project that the paradox itself would eventually undermine. In a paper written in 1901 and largely devoted to a popular exposition and defence of Cantor's theory of the infinite, Russell expressed what appeared to be a rpinor reservation to Cantor's treatment : There is a greatest of all infinite numbers, which is the number of things altogether, of every sort and kind. It is obvious that there cannot be a greater number than this, because, if everything has been taken, there is nothing left to add. Cantor has a proof that there is no greatest number, and if this proof were valid, the contradictions of infinity would reappear in a sublimated form. But in this one point, the master has been guilty of a very subtle fallacy, which I hope to explain in some future work.4 3 See Principles, §349. Perhaps I should remind... (shrink)

Gottfried Wilhelm Leibniz (1646–1716) was one of the great thinkers of the seventeenth and eighteenth centuries and is known as the last “universal genius”. He made deep and important contributions to the fields of metaphysics, epistemology, logic, philosophy of religion, as well as mathematics, physics, geology, jurisprudence, and history. Even the eighteenth century French atheist and materialist Denis Diderot, whose views could not have stood in greater opposition to those of Leibniz, could not help being awed by his achievement, writing (...) in his Encyclopedia, “Perhaps never has a man read as much, studied as much, meditated more, and written more than Leibniz… What he has composed on the world, God, nature, and the soul is of the most sublime eloquence. If his ideas had been expressed with the flair of Plato, the philosopher of Leipzig would cede nothing to the philosopher of Athens.” (Vol. 9, p. 379) Indeed, Diderot's mood was almost despairing in a remark from another piece, which also has a great deal of truth in it: “When one compares the talents one has with those of a Leibniz, one is tempted to throw away one's books and go die quietly in the dark of some forgotten corner.” More than a century later, Gottlob Frege, who fortunately did not cast his books away in despair, expressed similar admiration, declaring that “in his writings, Leibniz threw out such a profusion of seeds of ideas that in this respect he is virtually in a class of his own.” (“Boole's logical Calculus and the Concept script” in Posthumous Writings , p. 9) The aim of this entry is primarily to introduce Leibniz's life and summarize and explicate his views in the realms of metaphysics, epistemology, philosophical theology, and natural philosophy. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:diacritics 33.2 (2005) 71-97 [Access article in PDF] The Subject of Religion Lacan and the Ten Commandments Kenneth Reinhard Julia Reinhard Lupton Despite Freud's Nietzschean unmasking of religion as ideology, psychoanalysis has frequently been attacked as itself a religion, a cabal of analyst-priests dedicated to the worship of a dead master. Such critics "do not believe in Freud" in much the same way as atheists "do not believe in (...) God," and their rejections of psychoanalysis in the name of the secular partake in the very structure of religious thought they claim to repudiate. In Seminar XXI: Les non-dupes errent, Lacan comments on the blindness of the atheistic insight concerning religion: "I know that you're not believers, right? But that doesn't mean that you aren't all the more conned... because even if you are not believers, you still believe in that aspiration [for the love of God]. I won't say that you suppose it; rather, it supposes you" [Dec. 18, 1973; our trans.]. In Lacan's analysis, it is not that secular intellectuals suffer from unexamined religious "suppositions" or assumptions, to be swept away through a little ideology-critique or time on the couch. The case is rather, in Lacan's strong formulation, that religious discourse supposes us—supports and underwrites our very structures of being, subjectivity, and social interaction. That is, the secular subject is produced by the religious discourses that precede and continue to speak through it; the challenge for the contemporary critic is not to silence or debunk those discourses, but rather to bring the modern subject to assume responsibility for their enunciation.Throughout the decades of his seminar, Lacan addressed the monotheistic foundations of Western subjectivity as a set of discursive ruptures or cuts which continue to scar and brand the modern subject beyond their secular abrogation. Distinguishing between Freud "the individual with his atheistic profession of faith" and "the Freud who was the first to acknowledge the value and relevance of [the] myth... we call the death of God" [S VII 192–93], Lacan insists that Freud regarded monotheism as an epochal divide that irrevocably altered all that came before and after it: "On the left of this [monotheistic] message, there are some things that are henceforth outdated, obsolete; they no longer hold beyond the manifestation of the message. On the right, things are quite different" [172]. What, in Lacan's analysis, is the difference that monotheism has made, both during its periods of dominance and after? The laws, narratives, and symbols of monotheism continue to undergird key fantasies of personhood, nationhood, and neighborhood in the modernity that purports to have supplanted them. In Lacan's formulation, monotheism "supposes" the subject of these fantasies, precipitating it from out of the expanse of signifiers and in relation to a sublime object of both unbearable enjoyment and social obligation. Moreover, it is the scandal and the gift of monotheism that it not only creates moments of traumatic singularity, but also thinks the singular as trauma, rending the fabric of an animistic nature which would unite every polarity of being in the fullness of a sexual relation. Unlike the gods of Greek philosophy, the monotheistic God is not part of the nature he creates. In its decisive thinking of singularity, monotheism elicits and eludes all rapprochement with philosophical conceptions of the One, whether in the guise of Hellenized Judaism, Pauline theology, or Arab Aristotelianism. Lacan extends the monotheistic project of thinking singularity [End Page 71] by insisting that "there is something of One" [il y a de l'Un]—not the self-identical One of Greek logic, mathematics, and cosmology, but the One of a violent rupture that creates subjects and their worlds around a void, an un that un-does the primacy it speaks.If, from the Lacanian vantage, the singular invention of the God shared by the People of the Book forever separates religion from philosophy, we would also insist that religion is not simply a subset of "culture," understood as the symbolic practices that unify a people... (shrink)

In this paper I explore Žižek’s stance on ideology. I begin with an overview, move to his understanding of the ‘act’ and then move into the second part of the paper which is a discussion of the first part in relation to his encounter with Deleuze in Organs Without Body. I claim that this was a missed encounter, or rather it will always remain an impossible encounter given that Lacan, Badiou and Žižek’s philosophical embrace of negativity bumps up squarely against (...) Deleuze and Guattari’s affirmative stance. This deadlock does not offer a ‘solution’ as much as the political consequences that emerge from the two paths taken. It is further claimed that these crossroads are separated by two very different understandings of infinity as they are developed in the Kantian antinomy of the mathematical and dynamic sublime. (shrink)

This article turns one of most cited philosopher's John Dewey's title, How We Think (1933/1998) back upon itself to consider how ‘thought’ or ‘reason’ are cultural practices that historically order and generate principles for reflection and action. The discussion proceeds thusly: (1) Schooling is about changing people; (2) Changing people embodies cultural theses about modes of living, such as that of being a lifelong learner or a Learning Society. The modes of living in modern pedagogy embody changing cultural norms and (...) values about systems of reason that are to express universal cosmopolitan qualities; (3) Pedagogy fabricates the systems of reason to principles for reflection and participation that shreds provincial values in the name of greater universal cosmopolitan values; (4) This ‘making’ of cosmopolitan ‘reason’ forms through cultural practices that have overlapping sets of distinctions and differentiations about agency, the rational planning of one's biography in time, and science as a procedure for action in daily life. The educational sciences and philosophy of education are inscription devices or intellectual tools in the governing practices; (5) The inscriptions of reason, however, are more than mere qualities of thought or the mind. The narratives and images of cosmopolitan reason embody particular sublimes about collective hopes, desires and fears; (6) Further, the distinctions of cosmopolitan reason are comparative in that the very qualities of the ‘reasonable person’ create maps of its opposite: those who do not ‘fit’ the normalized qualities of the cosmopolitan thus stand outside that mode of living; The last section (7) provides three exemplars of the changing notions of the cosmopolitan and its ‘other’ in school subjects (literacy, mathematics, and music). School subjects are viewed as alchemies that transmogrify disciplinary thinking into normalizing pedagogies that fabricate who the child is and should be. The historical sketch has two layers in its educational study. One is to explore the politics of schooling with cosmopolitanism as a comparative method to consider the changing cultural practices that fabricate who child is and should be. The second raises questions about taken‐for‐granted categories and their systems of reason of education and reform. The very categories and distinctions of policy, educational research and philosophy are historicized as cultural practices to order, classify and divide what is ‘seen’ and felt as experience. (shrink)

Galileo's Paradox Contradictory or Counter-Intuitive? Imagination v. Conception Infinity as a Positive Idea Do We Experience Anything Infinite? The Sublimity of the Infinite Conclusion Bibliography Notes Appendix: A Crash Course in the Mathematics of Infinite Sets..

In lieu of an abstract, here is a brief excerpt of the content:uippraisals from the 'Past THE CLEAREST INTELLECT OF OUR AGEl H UGH MACLENNAN 19°7-199° R cently I have been rereading Bertrand Russell, and in so doing I suddenly realized that lowe to this man a good deal of such happiness as I enjoy. Over the years I had forgotten how great my debt was, but when I reread one of his books which I first read as a student, (...) I understood the extent to which he had liberated me from the psychological sadism of Calvin and Knox, to whom I had been unduly exposed when young. It is probably impossible for anyone entirely to escape once these two have got their hands around his throat, but Russell enabled me to escape a litde. 1 [This essay was recently discovered during the cataloguing for BRACERS of an obscure class of correspondence. Mr. Joseph w. Devine had sent Russell a clipping of the essay's appearance in' the Philadelphia Sunday But/etin, of 15 July 1962. I had long thought, from reading Elspeth Cameron's Hugh MacLennan: a Writers Life (1981), that he showed signs not only of having been influenced by Russell but of being the sOrt of person who is attracted to Russell's way of thinking. A promising tide in the same scholar's bibliography ofMacLennan turned out to be a fuller version of the clipping. "The Clearest Intellect of Our Age" is reprinted from The Montreal Star, 14 July 1962, "Entertainments" sec., p. 5. Russell did influence MacLennan. Neither the Russell Archives nor the inventory of the Maclennan papers at the Universiry of Calgary reveals personal contact berween the rwo. I wish I had asked MacLennan about contacts and influence seventeen years ago, when I sent him an early issue of Russell He commented: ''1 found your journal fascinating and never before had read that beautiful thing Russell wrote in his early days with Whitehead:" He is referring to the essay on the status of women in No.6, now in Papers 12.-Ed.] russell: the Journal ofthe Benrand Russell Archives McMaster Unive..ity Libraty Press noS. 11 (summer 1991): 83-5 ISSN 00,6-01631 84 HUGH MACLENNAN I suppose he really is the greatest man alive, in the sense that his teaching grows and his teaching is good, but it is pointless to argue the point between him and Churchill. It is wonderful, however, that many think he is our greatest man and that he has become an international hero to millions of the thoughtful youth. He must be the first pure logician who ever was that. Until he took his stand against nuclear war, he never appealed to the passions. He lacked the aggressions which youth admires. He never said: "Come live with me and I will be your master"; or, "Follow me and I will purge you of your sins." He had no use for self-sacrifice as such. He simply said, in effect: "Happiness is good. If you desire it, you must be reasonable." As he was intelligent enough to know that anyone who teaches that happiness is good, and teaches how to achieve it, is sute to be considered subversive to a Christian-commercial society, he bore no personal resentment when society persecuted him. The young know, of course, that Russell is now assumed by the experts to be the most important philosopher since Hume, but that is not why they love him. They love him for the sublime civilization of his courage, for his refusal to let an intensely kind nature blunt his respect for truth. They love him because he loves life even in the twentieth century; and they love him most of all because he is engage. And of course they also love the wit which refuses to be made tongue-tied by those who insist that whenever one speaks of sex or religion one must be solemn. Russell's wit is worth the study of any writer. It is based on mathematics, and Russell would agree, I think, with the remark Camillien Houde once made to me when I asked the famous mayor of Montreal how he was always able to make people laugh. Houde replied... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Kant’s Critique of the Power of Judgment: Critical EssaysTed KinnamanPaul Guyer, editor. Kant’s Critique of the Power of Judgment: Critical Essays. Lanham, MD: Rowman & Littlefield, 2003. Pp. xxiii + 253. Cloth, $75.95. Paper, $27.95.The volume under review is a collection of essays on a wide range of topics concerning Kant's Critique of the Power of Judgment. All the papers included here have been published previously, although many (...) of them in places where they might not be easily accessible to English-speaking philosophers. While some of the articles will be familiar to Kant scholars, this collection should be useful to specialists and valuable to students first delving into the third Critique.One essay in the volume, Guyer's own piece on "Kant's Principles of Reflecting Judgment," will be of particular interest to Kant scholars. Guyer's thesis here is that the account of reflecting judgment Kant offers in the Critique of the Power of Judgment is both continuous with the account of regulative principles of reason in the Critique of Pure Reason and the basis of the unity of the third Critique as a whole. He supports this by demonstrating how each of the sorts of judgment discussed in the work can be seen as an application of the broader account of reflecting judgment in general. Guyer identifies five such applications, and shows that each of them has three features central to regulative principles: they set a goal of constructing a system within a certain specific range of cognitions; they require the suitability of objects for attainment of the goal in question, and thus are transcendental [End Page 499] and not merely logical principles; and they supply heuristic advice for the investigation of nature. Thus every form of judgment can with justice be considered as an instance of the general activity of reflecting, that is, finding a universal for a given particular.Several of the essays included here concern the most prominent issues relating to the Analytic of the Beautiful. Nick Zangwill's piece deals with the disinterestedness of aesthetic judgment, while Christopher Janaway's "Kant's Aesthetics and the Empty Cognitive Stock" debunks what he sees as misguided readings of the role of concepts in judgments of taste. In "The Idealism of Purposiveness," an excerpt from his 1993 book Kantian Aesthetics Pursued (Edinburgh, 1993), Anthony Savile criticizes what he calls the "established reading" of Kant's claim that beautiful objects exhibit "purposiveness without purpose." On this reading, to say that a thing is purposive without purpose is to say that it appears to be designed, but to no particular purpose. Savile argues instead that we should take purposiveness without purpose to indicate that an object is suitable for a function, but not as a result of conscious design. Articles by Eva Schaper (from her well-known book on Kant's aesthetics) and Malcolm Budd discuss the distinction between free and dependent beauty and the account of the sublime, respectively.Some of the other selections in the volume are interesting for their focus on somewhat neglected aspects of the third Critique. One such aspect is the role of the imagination in Kant's account of aesthetic appreciation, and by extension in cognition more generally. In "Imaginative Freedom and the German Enlightenment," Jane Kneller argues that appreciation of the role of imaginative freedom in Kant's account of aesthetic judgment helps to connect Kant to the Enlightenment rationalist tradition that saw the value of art in its ability to educate and improve those who appreciate it. This education cannot, of course, be of the most straightforward nature, since Kant emphatically argues that to judge a thing beautiful is altogether different from judging it morally good. Instead, Kneller argues, our awareness of our own imaginative freedom provides us with evidence of our ability to realize the "highest good" on earth, evidence otherwise denied us in Kant's philosophy. Also addressing the theme of imagination is Donald Crawford's "Kant's Theory of Creative Imagination," in which he points out striking parallels between Kant's account of the imagination's role in mathematics and in the creation of fine art.Another aspect of Kant... (shrink)

In the sentence marked DK22 B52, Heraclitus describes a boy playing with small objects. The boy has the entire kingdom at his disposal and he himself is identified with the eon. This famous fragment has been interpreted in numerous ways both by classical philologists and philosophers. Its current interpretation is that it is a metaphor for human life. The child, not yet familiar with rules of social life, introduces elements of randomness and careless play into that life. Meanwhile, comparison of (...) Heraclitus’ sentence with the Old Indic tales, lets recognize in the sentence the mythological theme of the act of creation – God creating and governing the world. Such governing means establishing fundamental mathematical rights – the same rights that are applied in astronomical observations and scientific research as a whole. Hypothesis, that the ancient Indo-European culture affected – through India – Heraclitus, lets better understand this philosopher’s thought which harmonically combines elements of science, religion and arts. The India hypothesis also explains the aura of sublimity and holiness found in our tradition. The aura that was present in the late antiquity thinkers who acknowledged Heraclitus’ sentence and passed it to the Western literature. (shrink)

To commemorate Professor Yip Lai drunk, this article analyzes the social construction of beauty in the role. Focus on the imagination in Kant's "first critique" and "third critical" role into the comparison. In the "first critique", the imaginative scope of row rank succumb to emotional information under the force measured. In the "third critique" in the free world and the physical manifestation of the social world, you need to play an active imagination and rich creative role. Lai drunk leaf through (...) the philosophy of science and metaphysics, more step forward, from the mathematical and theoretical physics has been traced back to the aesthetics of the sublime original management of the environment. In this way, Lai In order to disclose the beauty of drunk leaves the constructive role of liaison to the beauty of creation, the beginning and end of performances In order to source of the purpose. In honor of the late Professor Jean Ladrière, this study nalyzes the role of the aesthetic in social construction. It focuses upon the contrasting role of the imagination in Kant's first and third Critiques. In the first Critique the imagination is subservient to the categories in its ordering of the sense data. In the third Critique the realization of freedom in the physical and social world requires that the imagination play an active, indeed creative role. Jean Ladrière reaches further still through the philosophy of science and metaphysics to trace the principles of the aesthetic order from mathematics and speculative physics to the role of the sublime. He thereby uncovers a constructive role for the aesthetic which joins all of creation in a celebration of its Source and End. (shrink)

Inspired by research on the Rwanda genocide and the decapitation, in July 2008, of a passenger on a Canadian Greyhound bus, this occasional paper explores the shared agitation with which we may respond to two seemingly disparate instances of evil such as these. Arguing against discontinuous claims that distinguish between pre- and post-metaphysical conceptions of evil pivoting around the figure of Kant, the article identifies three logics suggestive of continuity in Western thought on evil: negativity, functionalism and the messianic. Focusing (...) on the theme of negativity, the article argues that the essentially apophatic doctrine of the privation of evil is reconstituted in postmodern thinking as the liminal nature of evil. While acts of evil relate to what is both/either mathematically or qualitatively sublime, and while this experience may account for our agitation, we nonetheless employ figures like ‘hubris’, the ‘uncanny’ and the ‘state of exception’ to traverse the liminal in order to interpret instances of human praxis which, given their liminal nature, will always remain brute fact. The article argues that these figures, in particular the temporal structure implicit in Freud’s account of the uncanny, can usefully be explored to account for the agitation with which we respond to instances of evil as diverse as the two that inspired this article. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Matter and Spirit in the Age of Animal MagnetismEric G. WilsonDuring the Romantic period, writers on both sides of the Atlantic explored the sleepwalker as a merger of holiness and horror. Emerging when scientific thinkers for the first time were connecting spirit to electricity and magnetism, the somnambulist became to certain Romantics a disclosure of the difficulty of harmonizing unseen and seen, agency and necessity. This problem prominently arose (...) in Anton Mesmer's late eighteenth-century experiments in animal magnetism, in which the sleepwalker proved a paradox: an opaque revelation of transparent currents and an unconscious vehicle of sophisticated thought. Romantics such as Coleridge embraced the somnambulist as an embodiment of these troubles involved in relating motion and meaning. Coleridge and those who responded to him saw in the hypnotized human this sobering possibility: the invisible requires the visible to make itself manifest while the visible needs the invisible to become significant. 1 This is sublime and sinister: to elevate a material form to spiritual power is transcendence; to sink the boundless into a body is grotesque.Here I explore the philosophical implications of animal magnetism, the place of the sleepwalker in the history of ideas, and the role of the hypnotized human in Romantic writers, especially Coleridge. I also meditate on relationships between matter and spirit, machine and human, word and thing. Along the way, I place the history of ideas and the works of Romantic writers in mutually illuminating dialogues. The literary texts shed fresh light on philosophical problems while the ideas reveal hidden literary elements.The somnambulistic trance had been around long before Mesmer's magnetic sleeps. For centuries, shamans had used auto-hypnosis to sound [End Page 329] their souls and other-hypnosis to cure their tribe-members' ailments. However, somnambulism could not become a scientific phenomenon until Europeans in laboratories began to study electricity and magnetism. In the early modern period, Paracelsus argued that a vital fluid courses through the cosmos. The human being draws this flow like a magnet attracts force. When the body pulls to itself evil effluvia, it falls ill. To return patients to health, Paracelsus placed magnets on painful areas. He hoped to extract the unwanted current and return it to the cosmic swirl. 2 In "magnetizing" spirit, Paracelsus opened a door for empirical inquiry into the invisible world. In 1600, William Gilbert claimed that magnets correspond to the earth: both are animated by universal attraction and repulsion. 3 By the end of the seventeenth-century, Newton proposed that things are impelled by a force that draws and repels. Newton's theory of gravity inspired natural philosophers of the next centuries to search for a principle of which the magnet and the spark are manifestations. 4During the second half of the eighteenth century and the early part of the nineteenth, natural philosophers explored electricity and magnetism with unprecedented precision. In 1752, Benjamin Franklin revealed the mystery of lightning and perhaps the spark of life. 5 Inspired by Franklin, F. C. Oetinger, J. L. Fricker, and Prokop Divisch developed a theology of electricity, based on the belief that God is the electrical current. 6 Later in the century, Luigi Galvani and Alessandro Volta debated over whether the galvanic flow might be the origin and principle of life itself. 7 A few years before Franklin harvested lightning, John Michell argued that the magnetic force is not constrained to lodestones but is possibly pervasive. Some years later, Franz Aepinus suggested that magnetism and electricity manifest a deep energy. Soon after, C. A. de Coulomb discovered the mathematical law by which electrical and magnetic forces operate (Whittaker, pp. 50–59).These findings led to the breakthroughs of the nineteenth century. 8 In 1807, Humphry Davy hypothesized that chemical elements interact through electromagnetic affinity or repulsion. 9 In 1820, H. C. Oersted demonstrated the correspondence between electricity and magnetism. The same year, A. M. Ampere formulated the laws by which electrical and magnetic currents interact (Whittaker, pp. 81–86). Michael Faraday in 1831 revealed electromagnetic induction and thus inaugurated a second Copernican revolution: he showed that matter is not solid and discrete but a field of electromagnetic energy. 10 The dreams of [End... (shrink)

In 1764, Kant published his Observations on the Feeling of the Beautiful and the Sublime and in 1790 his influential third Critique , the Critique of the Power of Judgment . The latter contains two parts, the 'Critique of the Aesthetic Power of Judgment' and the 'Critique of the Teleological Power of Judgment'. They reveal a new principle, namely the a priori principle of purposiveness ( Zweckmäßigkeit ) of our power of judgment, and thereby offer new a priori grounds (...) for beauty and biology within the framework of Kant's transcendental philosophy. They also unite the previous two Critiques , the Critique of Pure Reason and the Critique of Practical Reason . Besides contributing to general and systematic aspects within his transcendental philosophy, Kant's aesthetics also offers new insights into old problems. It deals with feeling versus experience, subjectivity versus objectivity, disinterested pleasure, aesthetic universality, free and adherent beauty, the sensus communis , genius, aesthetic ideas, beauty as the symbol of morality, beauty of nature versus beauty of art, the sublime, and the supersensible. In this article I will limit myself to this critical aesthetics of Kant. But I will also discuss the ugly and the possibility of beauty in mathematics and see whether Kant's theory can successfully explain or deal with them. I will also compare his theory with philosophical ideas from a very different tradition, namely from Confucius, not only as a challenge to Kant's theory, but also because there is a growing interest from the Chinese side in combining ideas from Confucius and Kant, an interest that might well become influential in both East and West during the 21st century. (shrink)

Conventional wisdom holds that the murder rate has plummeted since the Middle Ages; humankind is growing more peaceful and enlightened; man is shortly to be much improved -- better genes, better neural circuits, better biochemistry; and we are approaching a technological singularity that will usher in utopia. Human Nature eviscerates these and other doctrines of a contemporary nihilism masquerading as science. In this wide-ranging work polymath David Berlinski draws upon history, mathematics, logic, and literature to retrain our gaze on an (...) old truth many are eager to forget: there is and will be about the human condition beauty, nobility, and moments of sublime insight, yes, but also ignorance and depravity. Men are not about to become like gods. (shrink)

The central question of this conference is whether the media can contribute to high quality social dialogue. The prospects for resolving that question positively in the “sound and fury” depend on recovering the idea of truth. At present the news media are lurching along from one crisis to another with an empty centre. We need to articulate a believable concept of truth as communication's master principle. As the norm of healing is to medicine, justice to politics, critical thinking to education, (...) craftsmanship to engineering, and stewardship to business, so truth-telling is the news profession's occupational norm. Truth-telling is the ethical framework that fundamentally reorders the media's professional culture and enables them to enrich social dialogue rather than undermine it.Historically the mainstream press has defined itself in terms of an objectivist worldview. Centred on human rationality and armed with the scientific method, the facts in news have been said to mirror reality. The aim has been true and incontrovertible accounts of a domain separate from human consciousness. In Bertrand Russell's formula, “truth consists in some form of correspondence between belief and fact” . In the received view, truth is defined in elementary epistemological terms as accurate representation. News corresponds to context-free neutral algorithms, and ethics is equated with impartiality.The attacks on this misguided view of human knowledge had already originated in Giambattista Vico's fantasia and Wilhelm Dilthey's verstehen in the counter-Enlightenment of the 18th century. They have continued with hermeneutics, critical theory in the Frankfurt School, American pragmatism, Wittgenstein's linguistic philosophy, Gramsci, and in their own way, Lyotard's denial of master narratives and Derrida's sliding signifiers; until the anti-foundationalism of our own day indicates a crisis in correspondence views of truth. Institutional structures remain Enlightenment-driven, but in principle the tide has turned currently toward restricting objectivism to the territory of mathematics, physics, and the natural sciences. In reporting, objectivity has become increasingly controversial as the working press' professional standard, though it will remain entrenched in our ordinary practices of news production and dissemination until an alternative mission for the press is convincingly formulated.The demise of correspondence views of truth has created a predicament for the notion of truth altogether. However, instead of appealing to coherence versions or abandoning the concept, truth needs to be relocated in the moral sphere. Truth is a problem of axiology rather than epistemology. With the dominant scheme no longer tenable, truth should become the province of ethicists who can reconstruct it as the news media's contribution to social dialogue.When truth is articulated in terms of a moral framework, we can mold its richly textured meaning around the Hebrew emeth , the Greek aletheia . In Serbo-Croatian the true is justified as with plumbline in carpentry. In the powerful wheel imagery of the Buddhist tradition, truth is the immovable axle. The Truth and Reconciliation Commission in South Africa presumes that sufferings from apartheid can be healed through truthful testimony. In Ghandhi's “satyagrapha,” the power of truth through the human spirit eventually wins over force . Dietrich Bonhoeffer's Ethics contends correctly that a truthful account lays hold of the context, motives, and presuppositions involved .Telling the truth depends on the quality of discernment so that penultimates do not gain ultimacy. Truth means, in other words, to strike gold, to get at “the core, the essence, the nub, the heart of the matter” . For Henry David Thoreau – though addressing a different issue – when we are truthful, we attempt to “drive life into a corner and¼if it proves to be mean, why then to get the genuine meanness out of it and publish its meanness to the world; or if it were sublime, to know it by personal experience and be able to give a true account of the encounter” . For the former secretary general of the United Nations, Dag Hammarskjold, “the most dangerous of all moral dilemmas is when we are obliged to conceal truth in order to help the truth be victorious” . In the Talmud, the liar's punishment is that no one believes him.Augustine , professor of rhetoric at Milan and later Bishop of Hippo, illustrates a non-correspondence view of truth. His rhetorical theory is a major contribution to the philosophy of communication, contradicting the highly secular and linear view of the ancient Greeks. As with Aristotle, rhetoric entails reasoned judgement for Augustine; however, he “break[s] away from Graeco-Roman rhetoric, moving instead toward ¼rhetoric as aletheiac act” . Rhetoric for him is not knowledge-producing or opinion-producing but truth-producing . The Epistolae Doctrina Christiana scourges the value-neutral, technical language of “word merchants” without wisdom.Truth is not fundamentally a prescriptive statement. The aletheiac act in Augustine “tends to be more relational than propositional, a dialogically interpersonal, sacramentally charitable act rather than a statement¼taking into account and being motivated by [the cardinal virtues] faith, hope, and charity” . The truth for him does not merely make things clear, but motivates us to belief and action. In truthful communication for Augustine, “it is not enough to seek to move men's minds, merely for the sake of power; instead, the power to move is to be used to lead men to truth”. (shrink)

In 1764, Kant published his Observations on the Feeling of the Beautiful and the Sublime and in 1790 his influential third Critique, the Critique of the Power of Judgment. The latter contains two parts, the ‘Critique of the Aesthetic Power of Judgment’ and the ‘Critique of the Teleological Power of Judgment’. They reveal a new principle, namely the a priori principle of purposiveness (Zweckmäßigkeit) of our power of judgment, and thereby offer new a priori grounds for beauty and biology (...) within the framework of Kant's transcendental philosophy. They also unite the previous two Critiques, the Critique of Pure Reason and the Critique of Practical Reason. Besides contributing to general and systematic aspects within his transcendental philosophy, Kant's aesthetics also offers new insights into old problems. It deals with feeling versus experience, subjectivity versus objectivity, disinterested pleasure, aesthetic universality, free and adherent beauty, the sensus communis, genius, aesthetic ideas, beauty as the symbol of morality, beauty of nature versus beauty of art, the sublime, and the supersensible. In this article I will limit myself to this critical aesthetics of Kant. But I will also discuss the ugly and the possibility of beauty in mathematics and see whether Kant's theory can successfully explain or deal with them. I will also compare his theory with philosophical ideas from a very different tradition, namely from Confucius, not only as a challenge to Kant's theory, but also because there is a growing interest from the Chinese side in combining ideas from Confucius and Kant, an interest that might well become influential in both East and West during the 21st century. (shrink)