Badiou and Plotinus on What Comes First
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Žižek and Lacanian Henology—With a “Silent Partner”
ISSN 1751-8229 Volume Twelve, Number Two Žižek and Lacanian Henology—With a “Silent Partner” Kenji Nobutomo, Kagoshima University, Japan Abstract This article aims to clarify the meaning of henology for Lacan and Žižek. Žižek apparently rejects Neoplatonic way of thinking, but by considering Lacanian Henology through its origin, Etienne Gilson, Lacanian henology and Žižek’s Hegelian reading of the One become converged. Both of them think the movement of the One from one principle and its two aspects. The principle is that the One gives something that it does not have, and it corresponds to Lacanian definition of love. Regarding its two aspects, the first one is the logical necessity that generates necessarily the One, and the second is the logical contingency that generates contingently the surplus element. By this, we can clarify the theoretical development of each period of Lacan. In early Lacan, henology was a logic that ties his “the Symbolic” and Freudian Death drive. In middle Lacan, his main concern was the mathematical logic as the logic of the Id, and henology became the generative logic of the subject of enunciation or the subject of the jouissance. But at the same time, this movement produces as a co-product a inassimilable remainder, “object a” with the subject of signifiant. In late Lacan, by virtue of the “necessary” movement of the One and its “contingent” co-product, the universe of the discourse became indeterminate, undecidable, “not-all,” which means for Lacan “the contingent.” This characteristic became the logic of Lacanian “sexuation.” 1. Introduction: What is Henology? In a session in 1971, Jacques Lacan used the term hénologie to describe his “analytic discourse” and its relation to the classical philosophical notion of “the One.” The annoying thing, is that when you proceed, as I have just said in this writing, that it is a matter of proceeding, namely, to envisage from a discourse what plays the function of the One in it, what do I do from time to time? If you will allow me this neologism what I do is “Henology”. -
The Modal Logic of Potential Infinity, with an Application to Free Choice
The Modal Logic of Potential Infinity, With an Application to Free Choice Sequences Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Ethan Brauer, B.A. ∼6 6 Graduate Program in Philosophy The Ohio State University 2020 Dissertation Committee: Professor Stewart Shapiro, Co-adviser Professor Neil Tennant, Co-adviser Professor Chris Miller Professor Chris Pincock c Ethan Brauer, 2020 Abstract This dissertation is a study of potential infinity in mathematics and its contrast with actual infinity. Roughly, an actual infinity is a completed infinite totality. By contrast, a collection is potentially infinite when it is possible to expand it beyond any finite limit, despite not being a completed, actual infinite totality. The concept of potential infinity thus involves a notion of possibility. On this basis, recent progress has been made in giving an account of potential infinity using the resources of modal logic. Part I of this dissertation studies what the right modal logic is for reasoning about potential infinity. I begin Part I by rehearsing an argument|which is due to Linnebo and which I partially endorse|that the right modal logic is S4.2. Under this assumption, Linnebo has shown that a natural translation of non-modal first-order logic into modal first- order logic is sound and faithful. I argue that for the philosophical purposes at stake, the modal logic in question should be free and extend Linnebo's result to this setting. I then identify a limitation to the argument for S4.2 being the right modal logic for potential infinity. -
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. -
Leibniz and the Infinite
Quaderns d’Història de l’Enginyeria volum xvi 2018 LEIBNIZ AND THE INFINITE Eberhard Knobloch [email protected] 1.-Introduction. On the 5th (15th) of September, 1695 Leibniz wrote to Vincentius Placcius: “But I have so many new insights in mathematics, so many thoughts in phi- losophy, so many other literary observations that I am often irresolutely at a loss which as I wish should not perish1”. Leibniz’s extraordinary creativity especially concerned his handling of the infinite in mathematics. He was not always consistent in this respect. This paper will try to shed new light on some difficulties of this subject mainly analysing his treatise On the arithmetical quadrature of the circle, the ellipse, and the hyperbola elaborated at the end of his Parisian sojourn. 2.- Infinitely small and infinite quantities. In the Parisian treatise Leibniz introduces the notion of infinitely small rather late. First of all he uses descriptions like: ad differentiam assignata quavis minorem sibi appropinquare (to approach each other up to a difference that is smaller than any assigned difference)2, differat quantitate minore quavis data (it differs by a quantity that is smaller than any given quantity)3, differentia data quantitate minor reddi potest (the difference can be made smaller than a 1 “Habeo vero tam multa nova in Mathematicis, tot cogitationes in Philosophicis, tot alias litterarias observationes, quas vellem non perire, ut saepe inter agenda anceps haeream.” (LEIBNIZ, since 1923: II, 3, 80). 2 LEIBNIZ (2016), 18. 3 Ibid., 20. 11 Eberhard Knobloch volum xvi 2018 given quantity)4. Such a difference or such a quantity necessarily is a variable quantity. -
Metaphysics Today and Tomorrow*
1 Metaphysics Today and Tomorrow* Raphaël Millière École normale supérieure, Paris – October 2011 Translated by Mark Ohm with the assistance of Leah Orth, Jon Cogburn, and Emily Beck Cogburn “By metaphysics, I do not mean those abstract considerations of certain imaginary properties, the principal use of which is to furnish the wherewithal for endless dispute to those who want to dispute. By this science I mean the general truths which can serve as principles for the particular sciences.” Malebranche Dialogues on Metaphysics and Religion 1. The interminable agony of metaphysics Throughout the twentieth century, numerous philosophers sounded the death knell of metaphysics. Ludwig Wittgenstein, Rudolf Carnap, Martin Heidegger, Gilbert Ryle, J. L. Austin, Jacques Derrida, Jürgen Habermas, Richard Rorty, and, henceforth, Hilary Putnam: a great many tutelary figures have extolled the rejection, the exceeding, the elimination, or the deconstruction of first philosophy. All these necrological chronicles do not have the same radiance, the same seriousness, nor the same motivations, but they all agree to dismiss the discipline, which in the past was considered “the queen of the sciences”, with a violence at times comparable to the prestige it commanded at the time of its impunity. Even today, certain philosophers hastily spread the tragic news with contempt for philosophical inquiry, as if its grave solemnity bestowed upon it some obviousness. Thus, Franco Volpi writes: ‘Grand metaphysics is dead!’ is the slogan which applies to the majority of contemporary philosophers, whether continentals or of analytic profession. They all treat metaphysics as a dead dog.1 In this way, the “path of modern thought” would declare itself vociferously “anti- metaphysical and finally post-metaphysical”. -
Aquinas on Attributes
CORE Metadata, citation and similar papers at core.ac.uk Provided by MedievaleCommons@Cornell Philosophy and Theology 11 (2003), 1–41. Printed in the United States of America. Copyright C 2004 Cambridge University Press 1057-0608 DOI: 10.1017/S105706080300001X Aquinas on Attributes BRIAN LEFTOW Oriel College, Oxford Aquinas’ theory of attributes is one of the most obscure, controversial parts of his thought. There is no agreement even on so basic a matter as where he falls in the standard scheme of classifying such theories: to Copleston, he is a resemblance-nominalist1; to Armstrong, a “concept nominalist”2; to Edwards and Spade, “almost as strong a realist as Duns Scotus”3; to Gracia, Pannier, and Sullivan, neither realist nor nominalist4; to Hamlyn, the Middle Ages’ “prime exponent of realism,” although his theory adds elements of nominalism and “conceptualism”5; to Wolterstorff, just inconsistent.6 I now set out Aquinas’ view and try to answer the vexed question of how to classify it. Part of the confusion here is terminological. As emerges below, Thomas believed in “tropes” of “lowest” (infima) species of accidents and (I argue) substances.7 Many now class trope theories as a form of nominalism,8 while 1. F. C. Copleston, Aquinas (Baltimore, MD: Penguin Books, 1955), P. 94. 2. D. M. Armstrong, Nominalism and Realism (New York: Cambridge University Press, 1978), pp. 25, 83, 87. Armstrong is tentative about this. 3. Sandra Edwards, “The Realism of Aquinas,” The New Scholasticism 59 (1985): 79; Paul Vincent Spade, “Degrees of Being, Degrees of Goodness,” in Aquinas’ Moral Theory, ed. -
The Univocity of Substance and the Formal Distinction of Attributes: the Role of Duns Scotus in Deleuze's Reading of Spinoza Nathan Widder
parrhesia 33 · 2020 · 150-176 the univocity of substance and the formal distinction of attributes: the role of duns scotus in deleuze's reading of spinoza nathan widder This paper examines the role played by medieval theologian John Duns Scotus in Gilles Deleuze’s reading of Spinoza’s philosophy of expressive substance; more generally, it elaborates a crucial moment in the development of Deleuze’s philosophy of sense and difference. Deleuze contends that Spinoza adapts and extends Duns Scotus’s two most influential theses, the univocity of being and formal distinction, despite neither appearing explicitly in Spinoza’s writings. “It takes nothing away from Spinoza’s originality,” Deleuze declares, “to place him in a perspective that may already be found in Duns Scotus” (Deleuze, 1992, 49).1 Nevertheless, the historiographic evidence is clearly lacking, leaving Deleuze to admit that “it is hardly likely that” Spinoza had even read Duns Scotus (359n28). Indeed, the only support he musters for his speculation is Spinoza’s obvious in- terests in scholastic metaphysical and logical treatises, the “probable influence” of the Scotist-informed Franciscan priest Juan de Prado on his thought, and the fact that the problems Duns Scotus addresses need not be confined to Christian thought (359–360n28). The paucity of evidence supporting this “use and abuse” of history, however, does not necessarily defeat the thesis. Like other lineages Deleuze proposes, the one he traces from Duns Scotus to Spinoza, and subsequently to Nietzsche, turns not on establishing intentional references by one thinker to his predecessor, but instead on showing how the borrowings and adaptations asserted to create the connec- tion make sense of the way the second philosopher surmounts blockages he faces while responding to issues left unaddressed by the first. -
Measuring Fractals by Infinite and Infinitesimal Numbers
MEASURING FRACTALS BY INFINITE AND INFINITESIMAL NUMBERS Yaroslav D. Sergeyev DEIS, University of Calabria, Via P. Bucci, Cubo 42-C, 87036 Rende (CS), Italy, N.I. Lobachevsky State University, Nizhni Novgorod, Russia, and Institute of High Performance Computing and Networking of the National Research Council of Italy http://wwwinfo.deis.unical.it/∼yaro e-mail: [email protected] Abstract. Traditional mathematical tools used for analysis of fractals allow one to distinguish results of self-similarity processes after a finite number of iterations. For example, the result of procedure of construction of Cantor’s set after two steps is different from that obtained after three steps. However, we are not able to make such a distinction at infinity. It is shown in this paper that infinite and infinitesimal numbers proposed recently allow one to measure results of fractal processes at different iterations at infinity too. First, the new technique is used to measure at infinity sets being results of Cantor’s proce- dure. Second, it is applied to calculate the lengths of polygonal geometric spirals at different points of infinity. 1. INTRODUCTION During last decades fractals have been intensively studied and applied in various fields (see, for instance, [4, 11, 5, 7, 12, 20]). However, their mathematical analysis (except, of course, a very well developed theory of fractal dimensions) very often continues to have mainly a qualitative character and there are no many tools for a quantitative analysis of their behavior after execution of infinitely many steps of a self-similarity process of construction. Usually, we can measure fractals in a way and can give certain numerical answers to questions regarding fractals only if a finite number of steps in the procedure of their construction has been executed. -
Ois Laruelle
Frans;ois Laruelle --- and collaborators --- Dictio nary of Non-Philosophy -- translated by Taylor Adkins I Univocal -- Fran\:ois Laruelle ------ and collaborators ----- To ny Brachet. Gilbert Kieffer, Laurent Leroy, Da niel Nicolet, Anne-Fran�oise Schmid, Serge Valdinoci Dictio nary of Non-Philosophy translated by Taylor Adkins I Univocal ---- DJCT!ONNAIREDE LA NON-PHILOSOPH!Eby Fran�ois Laruelle ©Editions Kime, 1998 Translated by Taylor Adkins as Dictionary ofNon-Philosophy First Edition Minneapolis©2013, Univocal Publishing Published by Univocal 123 North 3rd Street, #202 Minneapolis, MN 55401 No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including phorocopying, recording or any other information storage or retrieval system, without prior permission in writing from the publisher. Thanks to John David Ebert and Ben Woodard Designed & Printed by Jason Wagner Distributed by the University of Minnesota Press ISBN 9781937561130 Library of Congress Control Number 2013939530 TA BLE OF CONTENTS Translator's Introduction .......................................... .....................9 Preface to the English Language Edition...................... ................. 15 Preface .........................................................................................19 Theory of the Non-Philosophical Dictionary....................... .......23 Auto-position .......................... .....................................................39 Being-in-One (Being-according-to-the-One)............................... -
Galileo and Leibniz: Different Approaches to Infinity
Arch. Hist. Exact Sci. 54 (1999) 87–99. c Springer-Verlag 1999 Galileo and Leibniz: Different Approaches to Infinity Eberhard Knobloch Communicated by J. J. Gray Introduction “God exists since mathematics is consistent, and the devil exists since we cannot prove it.” In this way Andre´ Weil, one of the leading mathematicians of this century, characterized the mathematics of our time (Meschkowski 1969, p. 112; Rosenbloom 1950, p. 72). This connection between mathematics, God and the devil is not new: I would like to recall here only the study scene in Goethe’s Faust: Faust has the devil temporarily in his hand, because the pentagram is badly drawn. What is new in Weil’s saying is the insight that even mathematics cannot provide complete foundations for itself. Metamathematics and Hilbert’s proof theory are disciplines of our century. When Hilbert set about showing how the antinomies of the set theory created by Cantor could be avoided without betraying mathematics, as described in his lecture “On the Infinite” in 1925, he emphasized the necessity of clarifying the nature of the infinite (Hilbert 1926, p. 188). The infinite plays a crucial role in analysis, this most ingenious product of mathematical science, being ramified in the most refined way. As Hilbert fittingly formulated, mathematical analysis is, so to speak, a pure symphony on the infinite (Hilbert 1926, p. 184). No wonder that three years after Hilbert’s lecture his pupil Hermann Weyl character- ized mathematics as the science of the infinite (Weyl 1925–1927, p. 1; Laugwitz 1986, p. 233). He thus defined mathematics in a completely different way than his predecessors of earlier centuries. -
Plotinus on the Soul's Omnipresence in Body
Plotinus on the Limitation of Act by Potency Gary M. Gurtler, S.J. Boston College The limitation of act by potency, central in the metaphysics of Thomas Aquinas, has its origins in Plotinus. He transforms Aristotle’s horizontal causality of change into a vertical causality of participation. Potency and infinity are not just unintelligible lack of limit, but productive power. Form determines matter but is limited by reception into matter. The experience of unity begins with sensible things, which always have parts, so what is really one is incorporeal, without division and separation. Unity is like the esse of Thomas, since it is the act that makes a thing what it is and has its fullness in God. 1. Introduction Over fifty years ago Norris Clarke, S.J., published “The Limitation of Act by Potency: Aristotelianism or Neoplatonism,” The New Scholasticism, 26 (1952) 167–194, which highlighted the role of Plotinus in formulating some of the fundamental distinctions operative in medieval philosophy. He singled out the doctrine of participation and the idea of infinity and showed how they went beyond the limits of classical Greek thought. At the same time, his work challenged some of the basic historical assumptions of Thomists about the relation of scholastic philosophy, especially St. Thomas’s, to Plato and Aristotle. I have appreciated more and more the unusual openness and self critical character of Fr. Clarke’s historical method, and am pleased to have the chance in this response to Sarah Borden’s paper to explore some of the issues raised by Fr. Clarke’s seminal article in light of my own work on Plotinus. -
John Duns Scotus's Metaphysics of Goodness
University of South Florida Scholar Commons Graduate Theses and Dissertations Graduate School 11-16-2015 John Duns Scotus’s Metaphysics of Goodness: Adventures in 13th-Century Metaethics Jeffrey W. Steele University of South Florida, [email protected] Follow this and additional works at: http://scholarcommons.usf.edu/etd Part of the Medieval History Commons, Philosophy Commons, and the Religious Thought, Theology and Philosophy of Religion Commons Scholar Commons Citation Steele, Jeffrey W., "John Duns Scotus’s Metaphysics of Goodness: Adventures in 13th-Century Metaethics" (2015). Graduate Theses and Dissertations. http://scholarcommons.usf.edu/etd/6029 This Dissertation is brought to you for free and open access by the Graduate School at Scholar Commons. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. John Duns Scotus’s Metaphysics of Goodness: Adventures in 13 th -Century Metaethics by Jeffrey Steele A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Philosophy College of Arts and Sciences University of South Florida Major Professor: Thomas Williams, Ph.D. Roger Ariew, Ph.D. Colin Heydt, Ph.D. Joanne Waugh, Ph.D Date of Approval: November 12, 2015 Keywords: Medieval Philosophy, Transcendentals, Being, Aquinas Copyright © 2015, Jeffrey Steele DEDICATION To the wife of my youth, who with patience and long-suffering endured much so that I might gain a little knowledge. And to God, fons de bonitatis . She encouraged me; he sustained me. Both have blessed me. “O taste and see that the LORD is good; How blessed is the man who takes refuge in Him!!” --Psalm 34:8 “You are the boundless good, communicating your rays of goodness so generously, and as the most lovable being of all, every single being in its own way returns to you as its ultimate end.” –John Duns Scotus, De Primo Principio Soli Deo Gloria .