Reality, Determination, Imagination
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Mallarmé and the Politics of Literature Sartre, Kristeva, Badiou, Rancière
Mallarmé and the Politics of Literature Sartre, Kristeva, Badiou, Rancière ROBERT BONCARDO Edinburgh University Press is one of the leading university presses in the UK. We publish academic books and journals in our selected subject areas across the humanities and social sciences, combining cutting-edge scholarship with high editorial and production values to produce academic works of lasting importance. For more information visit our website: edinburghuniversitypress.com © Robert Boncardo, 2018 Edinburgh University Press Ltd The Tun – Holyrood Road 12(2f) Jackson’s Entry Edinburgh EH8 8PJ Typeset in 10.5/13 Sabon by Servis Filmsetting Ltd, Stockport, Cheshire, and printed and bound in Great Britain by CPI Group (UK) Ltd, Croydon CR0 4YY A CIP record for this book is available from the British Library ISBN 978 1 4744 2952 8 (hardback) ISBN 978 1 4744 2954 2 (webready PDF) ISBN 978 1 4744 2955 9 (epub) The right of Robert Boncardo to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988, and the Copyright and Related Rights Regulations 2003 (SI No. 2498). Contents Acknowledgements vi Abbreviations vii Series Editor’s Preface ix Introduction: Comrade Mallarmé 1 1 Jean-Paul Sartre’s Mallarmé: Hero of an Ontological Drama, Agent of the Counter-revolution 22 2 Julia Kristeva’s Mallarmé: From Fetishism to the Theatre-Book 79 3 Alain Badiou’s Mallarmé: From the Structural Dialectic to the Poetry of the Event 122 4 Jean-Claude Milner’s Mallarmé: Nothing Has Taken Place 175 5 -
Cantor on Infinity in Nature, Number, and the Divine Mind
Cantor on Infinity in Nature, Number, and the Divine Mind Anne Newstead Abstract. The mathematician Georg Cantor strongly believed in the existence of actually infinite numbers and sets. Cantor’s “actualism” went against the Aristote- lian tradition in metaphysics and mathematics. Under the pressures to defend his theory, his metaphysics changed from Spinozistic monism to Leibnizian volunta- rist dualism. The factor motivating this change was two-fold: the desire to avoid antinomies associated with the notion of a universal collection and the desire to avoid the heresy of necessitarian pantheism. We document the changes in Can- tor’s thought with reference to his main philosophical-mathematical treatise, the Grundlagen (1883) as well as with reference to his article, “Über die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche” (“Concerning Various Perspec- tives on the Actual Infinite”) (1885). I. he Philosophical Reception of Cantor’s Ideas. Georg Cantor’s dis- covery of transfinite numbers was revolutionary. Bertrand Russell Tdescribed it thus: The mathematical theory of infinity may almost be said to begin with Cantor. The infinitesimal Calculus, though it cannot wholly dispense with infinity, has as few dealings with it as possible, and contrives to hide it away before facing the world Cantor has abandoned this cowardly policy, and has brought the skeleton out of its cupboard. He has been emboldened on this course by denying that it is a skeleton. Indeed, like many other skeletons, it was wholly dependent on its cupboard, and vanished in the light of day.1 1Bertrand Russell, The Principles of Mathematics (London: Routledge, 1992 [1903]), 304. -
I Want to Start My Story in Germany, in 1877, with a Mathematician Named Georg Cantor
LISTENING - Ron Eglash is talking about his project http://www.ted.com/talks/ 1) Do you understand these words? iteration mission scale altar mound recursion crinkle 2) Listen and answer the questions. 1. What did Georg Cantor discover? What were the consequences for him? 2. What did von Koch do? 3. What did Benoit Mandelbrot realize? 4. Why should we look at our hand? 5. What did Ron get a scholarship for? 6. In what situation did Ron use the phrase “I am a mathematician and I would like to stand on your roof.” ? 7. What is special about the royal palace? 8. What do the rings in a village in southern Zambia represent? 3)Listen for the second time and decide whether the statements are true or false. 1. Cantor realized that he had a set whose number of elements was equal to infinity. 2. When he was released from a hospital, he lost his faith in God. 3. We can use whatever seed shape we like to start with. 4. Mathematicians of the 19th century did not understand the concept of iteration and infinity. 5. Ron mentions lungs, kidney, ferns, and acacia trees to demonstrate fractals in nature. 6. The chief was very surprised when Ron wanted to see his village. 7. Termites do not create conscious fractals when building their mounds. 8. The tiny village inside the larger village is for very old people. I want to start my story in Germany, in 1877, with a mathematician named Georg Cantor. And Cantor decided he was going to take a line and erase the middle third of the line, and take those two resulting lines and bring them back into the same process, a recursive process. -
Georg Cantor English Version
GEORG CANTOR (March 3, 1845 – January 6, 1918) by HEINZ KLAUS STRICK, Germany There is hardly another mathematician whose reputation among his contemporary colleagues reflected such a wide disparity of opinion: for some, GEORG FERDINAND LUDWIG PHILIPP CANTOR was a corruptor of youth (KRONECKER), while for others, he was an exceptionally gifted mathematical researcher (DAVID HILBERT 1925: Let no one be allowed to drive us from the paradise that CANTOR created for us.) GEORG CANTOR’s father was a successful merchant and stockbroker in St. Petersburg, where he lived with his family, which included six children, in the large German colony until he was forced by ill health to move to the milder climate of Germany. In Russia, GEORG was instructed by private tutors. He then attended secondary schools in Wiesbaden and Darmstadt. After he had completed his schooling with excellent grades, particularly in mathematics, his father acceded to his son’s request to pursue mathematical studies in Zurich. GEORG CANTOR could equally well have chosen a career as a violinist, in which case he would have continued the tradition of his two grandmothers, both of whom were active as respected professional musicians in St. Petersburg. When in 1863 his father died, CANTOR transferred to Berlin, where he attended lectures by KARL WEIERSTRASS, ERNST EDUARD KUMMER, and LEOPOLD KRONECKER. On completing his doctorate in 1867 with a dissertation on a topic in number theory, CANTOR did not obtain a permanent academic position. He taught for a while at a girls’ school and at an institution for training teachers, all the while working on his habilitation thesis, which led to a teaching position at the university in Halle. -
Cantor and Continuity
Cantor and Continuity Akihiro Kanamori May 1, 2018 Georg Cantor (1845-1919), with his seminal work on sets and number, brought forth a new field of inquiry, set theory, and ushered in a way of proceeding in mathematics, one at base infinitary, topological, and combinatorial. While this was the thrust, his work at the beginning was embedded in issues and concerns of real analysis and contributed fundamentally to its 19th Century rigorization, a development turning on limits and continuity. And a continuing engagement with limits and continuity would be very much part of Cantor's mathematical journey, even as dramatically new conceptualizations emerged. Evolutionary accounts of Cantor's work mostly underscore his progressive ascent through set- theoretic constructs to transfinite number, this as the storied beginnings of set theory. In this article, we consider Cantor's work with a steady focus on con- tinuity, putting it first into the context of rigorization and then pursuing the increasingly set-theoretic constructs leading to its further elucidations. Beyond providing a narrative through the historical record about Cantor's progress, we will bring out three aspectual motifs bearing on the history and na- ture of mathematics. First, with Cantor the first mathematician to be engaged with limits and continuity through progressive activity over many years, one can see how incipiently metaphysical conceptualizations can become systemati- cally transmuted through mathematical formulations and results so that one can chart progress on the understanding of concepts. Second, with counterweight put on Cantor's early career, one can see the drive of mathematical necessity pressing through Cantor's work toward extensional mathematics, the increasing objectification of concepts compelled, and compelled only by, his mathematical investigation of aspects of continuity and culminating in the transfinite numbers and set theory. -
HISTORY and EVENT in ALAIN BADIOU Quentin Meillassoux, Translated by Thomas Nail1
PARRHESIA NUMBER 12 • 2011 • 1 - 11 HISTORY AND EVENT IN ALAIN BADIOU Quentin Meillassoux, translated by Thomas Nail1 I would like to lay out for you the main theoretical decisions in the philosophy of Alain Badiou concerning the themes of today’s seminar: history and event.2 I do not speak as a disciple of Alain Badiou, because I develop philosophical positions distinct from his: but it seems important to me, that if one seeks to enter into a conceptual contemporaneity with the Marxist and Post-Marxist demands of politics and history, that one do so with the full scope of Badiou’s system in view, a system, now built around his two principle books Being and Event (BE) and Logics of Worlds (LW). This philosophy is particularly complex, but it seems to me that one can bring it into view through the two notions of history and event. I will thus attempt to explain a nodal and seemingly paradoxical thesis of Badiou’s: that there is only a history of the eternal, because only the eternal proceeds from the event. In other words: there is only a history of truths insofar as all truth is strictly eternal and impossible to reduce to any relativism. Badiou refuses therefore two antithetical positions: on the one hand that there can be eternal truths deprived as such of their historicity—a position proper to classical metaphysics—and on the other hand conversely that there can be no eternal truth, all discursive statements being irremediably inscribed in a historico-cultural context that strictly delimits the scope of truth to the particular instance that it supports. -
Quentin Meillassoux and Florian Hecker Talk Hyperchaos
DOCUMENT UFD001 Florian Hecker Quentin Meillassoux Robin Mackay Speculative Solution: Quentin Meillassoux and Florian Hecker Talk Hyperchaos This conversation took place during the development of Florian Hecker’s piece Speculative Solution, an Urbanomic commission that explored Quentin Meillassoux’s concept URBANOMIC / DOCUMENTS of ‘Hyperchaos’ URBANOMIC.COM Chez Meillassoux, Paris, 22 July 2010 certain sounds. And rather than the idea of making a sound directly ‘out of’ chaos, I was interested in how it could be used to explore this notion of sur- prise and abrupt change: to bring this extreme dy- namic form into the piece. This object or artifact we end up with will not represent something—it wouldn’t be a recording of an instal- lation, it wouldn’t be a sonification or illustration of your concepts FLORIAN HECKER: I’m very interested in this notion of Then as I looked into the book more, this is some- surprise and sudden change in sound; so that one thing that to me seemed to have a certain feed- state of something could change into something to- back with what you’re writing, when you talk about tally different at times during the piece, and there Hume’s billiard table: that the absence of constant would be no apparent connection from the process laws would change the conditions outside the ta- that manifests one sonic structure to the next one. ble, and not only the actions happening between When Robin pointed out your book [After Finitude1] the billiard balls. And what Robin and I spoke about to me, at the time I was working on Acid in the Style this morning was how something like this possibility of David Tudor, which had this very direct, maybe of constant change could manifest itself in a piece literal, idea of a quasi-sonification of chaotic equa- that would not be merely a sonification of the idea, tions as the source of sound. -
2.5. INFINITE SETS Now That We Have Covered the Basics of Elementary
2.5. INFINITE SETS Now that we have covered the basics of elementary set theory in the previous sections, we are ready to turn to infinite sets and some more advanced concepts in this area. Shortly after Georg Cantor laid out the core principles of his new theory of sets in the late 19th century, his work led him to a trove of controversial and groundbreaking results related to the cardinalities of infinite sets. We will explore some of these extraordinary findings, including Cantor’s eponymous theorem on power sets and his famous diagonal argument, both of which imply that infinite sets come in different “sizes.” We also present one of the grandest problems in all of mathematics – the Continuum Hypothesis, which posits that the cardinality of the continuum (i.e. the set of all points on a line) is equal to that of the power set of the set of natural numbers. Lastly, we conclude this section with a foray into transfinite arithmetic, an extension of the usual arithmetic with finite numbers that includes operations with so-called aleph numbers – the cardinal numbers of infinite sets. If all of this sounds rather outlandish at the moment, don’t be surprised. The properties of infinite sets can be highly counter-intuitive and you may likely be in total disbelief after encountering some of Cantor’s theorems for the first time. Cantor himself said it best: after deducing that there are just as many points on the unit interval (0,1) as there are in n-dimensional space1, he wrote to his friend and colleague Richard Dedekind: “I see it, but I don’t believe it!” The Tricky Nature of Infinity Throughout the ages, human beings have always wondered about infinity and the notion of uncountability. -
Storozhenko, Mykyta, Ma May 2020
STOROZHENKO, MYKYTA, M.A. MAY 2020 PHILOSOPHY PHENOMENOLOGY AND METAPHYSICAL REALISM (72 pp.) Thesis Advisor: Gina Zavota The recent re-turn to metaphysical realism in Continental Philosophy, evident in the emergence of the Speculative Realism movement, has posed challenging questions to phenomenology. Most importantly, is phenomenology compatible with metaphysical realism? Meillassoux, Harman, and Sparrow charge phenomenology with being, respectively, correlationist, a philosophy of access, and metaphysically agnostic or idealist. However, their charges do not go unanswered. Zahavi responds to the challenges by pointing out how phenomenology is compatible with, and indeed inclined toward realism. He does so by looking at concrete interactions between phenomenology and realism, as well as addressing what realism is and what it entails within phenomenology. Following Zahavi, as well as my own investigation into Husserl's phenomenology, I conclude that phenomenology is compatible with metaphysical realism. PHENOMENOLOGY AND METAPHYSICAL REALISM A thesis submitted To Kent State University in partial Fulfillment of the requirements for the Degree of Master of Arts by Mykyta Storozhenko May 2020 © Copyright All rights reserved Except for previously publised materials Thesis writted by Mykyta Storozhenko B.A., Florida Atlantic University, 2018 M.A., Kent State University, 2020 Approved by Gina Zavota , Advisor Michael Byron , Chair, Department of Philosophy James L. Blank , Dean, College of Arts and Sciences TABLE OF CONTENTS------------------------------------------------------------------------------------iv -
Meillassoux, Correlationism, and the Ontological Difference G
PhænEx 12, no. 2 (winter 2018): 1-12 © 2018 G. Anthony Bruno Meillassoux, Correlationism, and the Ontological Difference G. ANTHONY BRUNO The realist credentials of post-Kantian philosophy are often disputed by those who worry that grounding ontology on the human standpoint— variously construed by Kant, German idealism, phenomenology, and existentialism—bars us from an otherwise accessible reality, impoverishing our cognitive grasp, and betraying the promise of natural science. While many such critics ally with the so-called analytic tradition, the past decade has seen the rise of thinkers versed in the so-called continental tradition who, under the loose and controversial banner of “speculative realism,” seek to overcome the alleged anthropocentrism of Kantian and post-Kantian thought by developing theories of cognitive access to human-transcendent being. Although proponents of speculative realism include Ray Brassier, Levi Bryant, Iain Hamilton Grant, and Graham Harman, my focus will be on Quentin Meillassoux, whose work has been influential both within this movement and for its sympathizers. It is Meillassoux who coins “correlationism” to name the view that we can only access the mutual dependence of thought and being and that, consequently, neither is explicable in isolation, even by the natural sciences (Meillassoux 5). And it is Meillassoux who, in his monograph After Finitude, traces correlationism to Kant’s Copernican revolution and claims its apotheosis to include Heidegger’s phenomenological claim that an understanding of being cannot dispense with an existential analysis of subjectivity. On this view, the question of being is inextricably bound to the question of the meaning of being for such beings as ourselves. -
Set Theory: Cantor
Notes prepared by Stanley Burris March 13, 2001 Set Theory: Cantor As we have seen, the naive use of classes, in particular the connection be- tween concept and extension, led to contradiction. Frege mistakenly thought he had repaired the damage in an appendix to Vol. II. Whitehead & Russell limited the possible collection of formulas one could use by typing. Another, more popular solution would be introduced by Zermelo. But ¯rst let us say a few words about the achievements of Cantor. Georg Cantor (1845{1918) 1872 - On generalizing a theorem from the theory of trigonometric series. 1874 - On a property of the concept of all real algebraic numbers. 1879{1884 - On in¯nite linear manifolds of points. (6 papers) 1890 - On an elementary problem in the study of manifolds. 1895/1897 - Contributions to the foundation to the study of trans¯nite sets. We include Cantor in our historical overview, not because of his direct contribution to logic and the formalization of mathematics, but rather be- cause he initiated the study of in¯nite sets and numbers which have provided such fascinating material, and di±culties, for logicians. After all, a natural foundation for mathematics would need to talk about sets of real numbers, etc., and any reasonably expressive system should be able to cope with one- to-one correspondences and well-orderings. Cantor started his career by working in algebraic and analytic number theory. Indeed his PhD thesis, his Habilitation, and ¯ve papers between 1867 and 1880 were devoted to this area. At Halle, where he was employed after ¯nishing his studies, Heine persuaded him to look at the subject of trigonometric series, leading to eight papers in analysis. -
Daniel Whistler
Speculations III [email protected] www.speculations-journal.org Editors Michael Austin Paul J. Ennis Fabio Gironi Thomas Gokey Robert Jackson isbn 978-0988234017 Front Cover: unanswered: witness Grace Lutheran Church Parking Lot, Linwell Road, St. Catharines, June 2003 by P. Elaine Sharpe Back Cover: unanswered: witness Flight Simulation Training Center, Opa Locka Airport, FLA, December 2002 by P. Elaine Sharpe Courtesy of P. Elaine Sharpe, used with permission. pesharpe.com The focal distance in these photograph is at the normal range of human conversational distance, 3 meters. Although the image may appear to be out of focus, it is focused on the absence of human presence. Designed by Thomas Gokey v 1.0 punctum books ✴ brooklyn, ny 2012 Editorial Introduction 5 Articles Re-asking the Question of the Gendered Subject after 7 Non-Philosophy Benjamin Norris Thing Called Love 43 That Old, Substantive, Relation Beatrice Marovich The Other Face of God 69 Lacan, Theological Structure, and the Accursed Remainder Levi R. Bryant Improper Names for God 99 Religious Language and the “Spinoza-Effect” Daniel Whistler Namelessness and the Speculative Turn 135 A Response to Whistler Daniel Colucciello Barber Diagonals 150 Truth-Procedures in Derrida and Badiou Christopher Norris Synchronicity and Correlationism 189 Carl Jung as Speculative Realist Michael Haworth Translations Über stellvertretende Verursachung 210 Graham Harman Speculative Realism 241 After finitude, and beyond? Louis Morelle Position Papers and Interview 273 Outward Bound