DOCSLIB.ORG

Life-Writing and the Time of Action by Charity Corine Ketz a Dissertation

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Life-Writing and the Time of Action by Charity Corine Ketz a Dissertation Willing Suspense: Life-Writing and the Time of Action By Charity Corine Ketz A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in English in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Ian Duncan, chair Professor Steve Justice Professor Karen S. Feldman Summer 2017 Abstract Willing Suspense: Life-Writing and the Time of Action By Charity Corine Ketz Doctor of Philosophy in English University of California, Berkeley Professor Ian Duncan, Chair Willing Suspense: Life-Writing and the Time of Action investigates the claims of two Romantic-era poets— William Wordsworth and Samuel Taylor Coleridge—both of whom make the general form of cognition central to their autobiographies (The Prelude and Biographia Literaria respectively), both of whom contend that poetic form reveals and stylizes the temporal manner of our knowing, and both of whom connect the contemplation of poetry’s and cognition’s inner structure with psychic healing and ethical amelioration. When Wordsworth depicts the interpretive significance of an enduring perception changing at regular intervals or when Coleridge argues that our perceptions are a function of the partitions of time in which we perceive, they maintain that perceptual relativity itself indicates species being and the regular act of the mind in relating itself. As perception has propriety, as it relates itself, it also emerges as an affective response to a world that seems turned toward the perceiver or not. This value can in turn be re-described poetically, especially through poetic meter. For both poets, to contemplate temporal form, or the periodicity of thinking as it unfolds, or the symbolic nature of meter is to contemplate and become what we are. For Coleridge, we can describe human identity as a suspense: a continuous movement whose terminus both is and is not included in any description we might give; poetry is a formal means by which we become aware of our form. For Wordsworth, the pleasureable rhythms of our thought indicate the rhythms of the cosmos and our place in it. The suspense of one’s momentary personality induced by reading, and especially by meter’s simulation of cognitive regularity, may catalyze a psychic return to perceptual wholeness which, similarly, belongs to us at all times and yet may be obscured. Part of what we find in Wordsworth’s and Coleridge’s respective autobiographies and broad poetics is a manner of understanding time and its relation to personal identity that runs counter to the medieval, early modern, and postmodern understanding of this relation as expressing loss, contingency, and instability. It also runs counter to a well-established narrative linking the rise of historicism in the eighteenth century with the rise of individualizing forms and an outpouring of personal narratives. In conducting their autobiographies from the point of view of ongoingness—in which the autobiographer has not, so to speak, turned around to see what he once was—and in promoting the recurrent structure of thinking and the various, reiterating shapes in which it emerges, Wordsworth and Coleridge deliberately turn toward the general and instantiate a mode of autobiography radically unlike those autobiographies (from Rousseau’s Confessions to Mary Prince’s History) that give an account of an unique personality or of particular social relations (and abuses). 1 The outpouring of autobiographies in the eighteenth century also coincided with the rise of epistemology as a science; and the double facing of autobiography encapsulates its central question about what knowledge is and how it is known. Willing Suspense contends that there are two major modes of autobiography—retrospective and prospective—which can be distinguished by their temporal orientation, objects, and mood. Wordsworth’s and Coleridge’s autobiographies are prospective in that the parameters of thinking are continually present (for the autobiographers as for their readers) and in that The Prelude and Biographia depict the anticipatory cast of sensation. Their objects are thus common in two senses: for they involve the general finding of relational being in the world. And their mood is one of confidence—that we can understand the world and our manner of harmonizing with it. Wordsworth’s and Coleridge’s autobiographies are not, however, anomalies. They share important ground with Augustine’s Confessions and Proust’s À la recherche. They also emerge as part of a larger response to the figure of thought that dominated eighteenth- century literary culture: that of the disengaged and belated spectator. As a figure based on a rift between thinking and being, this spectator faced backward and sought something categorically different from itself and hence something unknowable. Opposing this figure, and hence, facing forward, was another figure of knowing, one that understood knowing as an action contemporaneous with itself. Locke equated knowing with the individual’s appropriative act and so with actual and relational rather than possible forms; Baumgarten newly applied the term “aesthetic” to the realm of sensate (present, temporal, anticipatory, and analogic) knowing, describing it as completing logical (or necessary) knowledge. Kierkegaard described all existential interpretation as conditioned by a prior, orienting decision to judge past actions or to hold oneself presently, continuously accountable—which is also to say, he figured interpretation as a manner of temporal orientation. Influenced indirectly by the Romantics, Bergson, like Wordsworth and Coleridge, described the anticipatory, periodic, relational nature of perception and defined the qualitative nature of time in contrast to the over-extension of the spatial law of continuity. Contemporary theorists of autobiography frequently describe this genre in terms of the creative deployment of available cultural myths, as just one form that the creation of a fictive effect (the feeling that there is an object corresponding with the text) may take, or as the (motivated) possible convergence of aesthetics and history. In so doing, autobiographical theory repeats and enlarges upon the gestures made by autobiographers like Rousseau and De Quincey without thereby grasping autobiography’s essential, equivocal form. For to argue, for example, that autobiography attempts to merge aesthetics and history is merely to repeat that it is a rhetorical construction aimed at something categorically different which cannot be an object of knowledge (and perhaps to add that, as such, it reflects upon the fact that all knowledge is similarly built on a retrojection). The Prelude and Biographia instantiate a prospective mode of autobiography, and the presence of this mode, in addition to a retrospective one, re-illuminates autobiography’s vantage and shows that it poses a far more complex question than that of the legitimacy or inevitability of our tendency to collapse aesthetic constructing and presumed historical objects. Willing Suspense argues that genre is fundamentally an epistemological rather than an aesthetic or historical category and that autobiography in particular asks us how knowledge shall be known: prospectively or retrospectively, 2 confidently or skeptically, generally or particularly, and as a matter of an individual’s act of harmonizing or as a matter of her free construction. 3 Table of Contents Acknowledgements ii Preface iii Chapter One: Autobiography as Premonition in The Prelude 1 Chapter Two: Wordsworth’s Poetics of Suspense 41 Chapter Three: Meter, Music, and the Abasement of Type 61 i Acknowledgments I am extremely grateful for the unwavering support of two incredible teachers and mentors: Ian Duncan and Steve Justice. I am likewise deeply grateful to Karen Feldman for her willingness to read scrupulously with limited time. My deepest gratitude goes to my parents—for their love, compassion, and encouragement. ii Preface Willing Suspense: Life-Writing and the Time of Action investigates the claims of two Romantic-era poets— William Wordsworth and Samuel Taylor Coleridge—both of whom make the general form of cognition central to their autobiographies, both of whom contend that poetic form reveals and stylizes the temporal manner of our knowing, and both of whom connect the contemplation of poetry’s and cognition’s inner structure with psychic healing and ethical amelioration. Wordsworth's and Coleridge's demotion of any externalized image of a past self in their autobiographical works (The Prelude and Biographia Literaria respectively) and their promotion, instead, of general structures of thinking—from the periodicity of sensation (as it arises, intensifies, and switches objects), to perception's affective inception in relation to another mind, to the figuring of cognition as a two- part movement—are central to their larger poetic projects. Their work radically reorients our understanding of autobiography and what its unique vantage may be. How does the solution of cognitive form arise in the first place, so that the question of identity—of what it means to write life—may be understood as best answered by rendering common, constant processes of mind? Wordsworth’s and Coleridge’s solution runs counter to the well-established narrative that links the proliferation of personal histories in the eighteenth and nineteenth centuries to the rise of historicism (considered as the new, acute sense of change over time and as the application of a new set of scientific
Load more

Recommended publications
  • Cauchy, Infinitesimals and Ghosts of Departed Quantifiers 3
    CAUCHY, INFINITESIMALS AND GHOSTS OF DEPARTED QUANTIFIERS JACQUES BAIR, PIOTR BLASZCZYK, ROBERT ELY, VALERIE´ HENRY, VLADIMIR KANOVEI, KARIN U. KATZ, MIKHAIL G. KATZ, TARAS KUDRYK, SEMEN S. KUTATELADZE, THOMAS MCGAFFEY, THOMAS MORMANN, DAVID M. SCHAPS, AND DAVID SHERRY Abstract. Procedures relying on infinitesimals in Leibniz, Euler and Cauchy have been interpreted in both a Weierstrassian and Robinson’s frameworks. The latter provides closer proxies for the procedures of the classical masters. Thus, Leibniz’s distinction be- tween assignable and inassignable numbers finds a proxy in the distinction between standard and nonstandard numbers in Robin- son’s framework, while Leibniz’s law of homogeneity with the im- plied notion of equality up to negligible terms finds a mathematical formalisation in terms of standard part. It is hard to provide paral- lel formalisations in a Weierstrassian framework but scholars since Ishiguro have engaged in a quest for ghosts of departed quantifiers to provide a Weierstrassian account for Leibniz’s infinitesimals. Euler similarly had notions of equality up to negligible terms, of which he distinguished two types: geometric and arithmetic. Eu- ler routinely used product decompositions into a specific infinite number of factors, and used the binomial formula with an infi- nite exponent. Such procedures have immediate hyperfinite ana- logues in Robinson’s framework, while in a Weierstrassian frame- work they can only be reinterpreted by means of paraphrases de- parting significantly from Euler’s own presentation. Cauchy gives lucid definitions of continuity in terms of infinitesimals that find ready formalisations in Robinson’s framework but scholars working in a Weierstrassian framework bend over backwards either to claim that Cauchy was vague or to engage in a quest for ghosts of de- arXiv:1712.00226v1 [math.HO] 1 Dec 2017 parted quantifiers in his work.
    [Show full text]
  • Connes on the Role of Hyperreals in Mathematics
    Found Sci DOI 10.1007/s10699-012-9316-5 Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics Vladimir Kanovei · Mikhail G. Katz · Thomas Mormann © Springer Science+Business Media Dordrecht 2012 Abstract We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in func- tional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S, all definable sets of reals are Lebesgue measurable, suggesting that Connes views a theory as being “vir- tual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnera- ble to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace − (featured on the front cover of Connes’ magnum opus) V.
    [Show full text]
  • The Legacy of Leonhard Euler: a Tricentennial Tribute (419 Pages)
    P698.TP.indd 1 9/8/09 5:23:37 PM This page intentionally left blank Lokenath Debnath The University of Texas-Pan American, USA Imperial College Press ICP P698.TP.indd 2 9/8/09 5:23:39 PM Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. THE LEGACY OF LEONHARD EULER A Tricentennial Tribute Copyright © 2010 by Imperial College Press All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-13 978-1-84816-525-0 ISBN-10 1-84816-525-0 Printed in Singapore. LaiFun - The Legacy of Leonhard.pmd 1 9/4/2009, 3:04 PM September 4, 2009 14:33 World Scientific Book - 9in x 6in LegacyLeonhard Leonhard Euler (1707–1783) ii September 4, 2009 14:33 World Scientific Book - 9in x 6in LegacyLeonhard To my wife Sadhana, grandson Kirin,and granddaughter Princess Maya, with love and affection.
    [Show full text]
  • Procedures of Leibnizian Infinitesimal Calculus: an Account in Three
    PROCEDURES OF LEIBNIZIAN INFINITESIMAL CALCULUS: AN ACCOUNT IN THREE MODERN FRAMEWORKS JACQUES BAIR, PIOTR BLASZCZYK, ROBERT ELY, MIKHAIL G. KATZ, AND KARL KUHLEMANN Abstract. Recent Leibniz scholarship has sought to gauge which foundational framework provides the most successful account of the procedures of the Leibnizian calculus (LC). While many schol- ars (e.g., Ishiguro, Levey) opt for a default Weierstrassian frame- work, Arthur compares LC to a non-Archimedean framework SIA (Smooth Infinitesimal Analysis) of Lawvere–Kock–Bell. We ana- lyze Arthur’s comparison and find it rife with equivocations and misunderstandings on issues including the non-punctiform nature of the continuum, infinite-sided polygons, and the fictionality of infinitesimals. Rabouin and Arthur claim that Leibniz considers infinities as contradictory, and that Leibniz’ definition of incompa- rables should be understood as nominal rather than as semantic. However, such claims hinge upon a conflation of Leibnizian notions of bounded infinity and unbounded infinity, a distinction empha- sized by early Knobloch. The most faithful account of LC is arguably provided by Robin- son’s framework. We exploit an axiomatic framework for infini- tesimal analysis called SPOT (conservative over ZF) to provide a formalisation of LC, including the bounded/unbounded dichotomy, the assignable/inassignable dichotomy, the generalized relation of equality up to negligible terms, and the law of continuity. arXiv:2011.12628v1 [math.HO] 25 Nov 2020 Contents 1. Introduction 3 1.1. Grafting of the Epsilontik on the calculus of Leibniz 4 1.2. From Berkeley’s ghosts to Guicciardini’s limits 5 1.3. Modern interpretations 7 1.4. Was the fictionalist interpretation a late development? 10 1.5.
    [Show full text]
  • A Historical Account of the Search for Ideal Numbers
    A HISTORICAL ACCCOUNT OF THE SEARCH FOR IDEAL NUMBERS IRFAN ALAM Abstract. Focusing on the development of nonstandard analysis, this paper attempts to better understand how knowledge is generated through new mathematical concepts. The first part of this paper deals with a history of real and complex numbers, as well as in- finitesimals and non-standard numbers. A comparison is drawn between the acceptance, among the working mathematicians, of irrationals and imaginary numbers on one hand and the acceptance of nonstandard numbers, such as the infinitesimals, on the other hand. It is argued that a geometric interpretation is not always necessary to arrive at necessarily correct results and that a notion like that of an infinitesimal could have a strong epistemic worth without having a respectable ontological status from the point of view of representing geometric objects. \Mathematics is the art of giving the same name to different things." -Henri Poincar´e 1. Introduction A lot of modern mathematics has to do with identifying equivalences between structures. We are now able to prove everything in Euclidean geometry using the algebra of ordered pairs of numbers. Indeed, we now know that all the geometric information about figures in the plane can be encoded using algebraic relations between certain quantities, after iden- tifying the two-dimensional plane with a Cartesian coordinate system. Conversely, we can get a lot of information about algebraic equations by looking at the geometric properties of relevant curves representing those equations, which is the essence of the modern area of Algebraic Geometry. This dichotomy between algebra and geometry has also helped in legitimizing formerly taboo practices of working with numbers that are so unreal that we call them imaginary.
    [Show full text]
  • The Origins of Cauchy's Rigorous Calculus
    The Origins of Cauchy's Rigorous Calculus Judith V. Grabiner Flora Sanborn Pitzer Professor of Mathematics Pitzer College Dover Publications, Inc. Mineola, New York Copyright Copyright © 1981 The Massachusetts Institute of Technology All rights reserved. Bibliographical Note This Dover edition, first published in 2005, is an unabridged republication of the edition published by The MIT Press, Cambridge, Massachusetts, 1981. Library of Congress Cataloging-in-Publication Data Grabiner, Judith V. The origins of Cauchy's rigorous calculus I Judith V. Grabiner. p.cm. Originally published: Cambridge, Mass. : MIT Press, c1981. Includes bibliographical references and index. ISBN 0-486-43815-5 (pbk.) 1. Calculus-History. 2. Cauchy, Augustin Louis, Baron, 1789-1857. I. Title. QA303.G742005 515'.09-dc22 2004059331 Manufactured in the United States of America Dover Publications, Inc., 31 East 2nd Street, Mineola, N.Y. 11501 To my parents, Alfred and Ruth Tofield Victor Contents Preface Vlll Abbreviations of Titles x Introduction Cauchy and the Nineteenth-Century Revolution in 1 Calculus 5 The Status of Foundations in Eighteenth-Century 2 Calculus 16 The Algebraic Background of Cauchy's New 3 Analysis 47 The Origins of the Basic Concepts of Cauchy's 4 Analysis: Limit, Continuity, Convergence 77 The Origins of Cauchy's Theory of the 5 Derivative 114 The Origins of Cauchy's Theory of the Definite 6 Integral 140 Conclusion 164 Appendix: Translations from Cauchy's Oeuvres 167 Notes 176 References 225 Index 241 Preface Augustin-Louis Cauchy gave the first reasonably success­ ful rigorous foundation for the calculus. Beginning with a precise definition of limit, he initiated the nineteenth­ century theories of convergence, continuity, derivative, and integral.
    [Show full text]
  • Who Gave You the Cauchy-Weierstrass Tale? The
    WHO GAVE YOU THE CAUCHY–WEIERSTRASS TALE? THE DUAL HISTORY OF RIGOROUS CALCULUS ALEXANDRE BOROVIK AND MIKHAIL G. KATZ0 Abstract. Cauchy’s contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the basis of the epsilon-delta doctrine in the context of an Archimedean con- tinuum. What does one see if one refrains from viewing Cauchy as if he had read Weierstrass already? One sees, with Felix Klein, a parallel thread for the development of analysis, in the context of an infinitesimal-enriched continuum. One sees, with Emile Borel, the seeds of the theory of rates of growth of functions as devel- oped by Paul du Bois-Reymond. One sees, with E. G. Bj¨orling, an infinitesimal definition of the criterion of uniform convergence. Cauchy’s foundational stance is hereby reconsidered. Contents 1. Introduction 2 2. A reappraisal of Cauchy’s foundational stance 4 2.1. Cauchy’s theory of orders of infinitesimals 4 2.2. How does a null sequence become a Cauchy infinitesimal? 8 2.3. An analysis of Cours d’Analyse and its infinitesimals 11 2.4. Microcontinuity and Cauchy’s sum theorem 14 2.5. Five common misconceptions in the Cauchy literature 16 arXiv:1108.2885v3 [math.HO] 16 Oct 2012 3. Comments by modern authors 18 3.1. Gilain’s limit 18 3.2. Felscher’s Bestiarium infinitesimale 19 3.3. D’Alembert or de La Chapelle? 24 3.4. Brillou¨et-Belluot: epsilon-delta, period 25 3.5.
    [Show full text]
  • Inexplicable Functions and the Euler-Maclaurin Summation Formula
    HISTORIA MATHEMATICA 25 (1998), 290±317 ARTICLE NO. HM982195 Some Aspects of Euler's Theory of Series: Inexplicable Functions and the Euler±Maclaurin Summation Formula View metadata, citation and similar papers at core.ac.uk Giovanni Ferraro brought to you by CORE provided by Elsevier - Publisher Connector Via Nazionale, 38, 80021 Afragola (Naples), Italy Wallis's method of interpolation attracted the attention of the young Euler, who obtained some important results. The problem of interpolation led Euler to formulate the problem of integration, i.e., to express the general term of a series by means of an integral. The latter problem was connected to the question of expressing the sum of a series using an integral. The outcome of this research was Euler's derivation of what would later become known as the Euler±Maclaurin formula. Euler subsequently returned to interpolation and formulated the theory of inexplicable functions including the gamma function. The methods used by Euler illustrate well the principles of 18th-century analysis. Eulerian procedures are based upon the notion of geometric quantity. A function is actually conceived as the expression of a quantity and, for this reason, it intrinsically possesses properties we can term continuity, differentiability, Taylor expansion. These correspond to the usual properties of a curve which has ``regular'' characteristics (lack of jumps, presence of tangents, curvature radius, etc.). They have a ``®gural'' clarity. Although Eulerian analysis remains rooted in geometry, it dispenses with ®gural representation: it is substantially non®gural geometry. Reasoning with ®gures (which integrates the proof in classical geometry) is replaced by reasoning with analytic symbols.
    [Show full text]
  • Introduction Gottfried Wilhelm Leibniz Was One of the Most Prolific Thinkers
    Chapter 1: Introduction “Theoria cum praxi [Theory with practice]”—Leibniz’s motto for the Berlin Society of Sciences. Gottfried Wilhelm Leibniz was one of the most prolific thinkers of all time. “Often in the morning when I am still in bed,” he wrote, “so many thoughts occur to me in a single hour that sometimes it takes me a whole day or more to write them out” (LH 338; quoted from Mates 1986, 34). These thoughts might have included designs for a new wind pump to drain the mines of the Harz mountains or for a calculating machine based on binary arithmetic, sketches for a treatise on geology or etymology, another draft of a logical calculus that was two hundred years ahead of its time, or a new derivation of Newton’s law of gravitation on strictly mechanical principles. Even before getting up, Leibniz would usually have written lengthy letters on such subjects to one or two learned correspondents, and perhaps a proposal to Peter the Great for a scientific academy, or to his employer the Duke of Hanover for a universally accessible state medical system. He might have penned a legal brief in support of the Duke’s electoral claim to certain territories, a deposition aimed at church reunification, or tried to mediate in the dispute among the Jesuits over the interpretation of Chinese religious rites. In short, Leibniz was an indefatigable one-man industry. Yet all this worldly activity seems at odds with the usual understanding of Leibniz as a philosopher. He is well known for his claim that the world is constituted by what he calls monads (or unities), which he characterizes as substances consisting in perceptions (representations of the whole of the rest of the universe) and appetitions (tendencies toward future states), governed by a law specific to each individual.
    [Show full text]
  • The Principle of Continuity and Leibniz's Theory of Consciousness
    The Principle of Continuity and Leibniz’s Theory of Consciousness LARRY M. JORGENSEN [L]es perceptions remarquables viennent par degrés de celles qui sont trop petites pour estre remar- quées.1 leibniz’s principle of continuity, in slogan form, is the principle that “nature never makes leaps,”2 or that “all natural change is produced by degrees.”3 All natural connections, whether causal, spatiotemporal, or conceptual, are governed by this principle, allowing it, according to Leibniz, to serve “not only as a test . but also as a very fruitful principle of discovery.” In this paper, I wish to use the principle of continuity as a test of a theory, much as Leibniz used it against the Cartesian physics of his day. I will begin by summarizing the principle of continuity 1A VI.vi.56; NE 56. I will use the following abbreviations for the primary texts: A Gottfried Wilhelm Leibniz, Sämtliche Schriften und Briefe, ed. Deutsche Akademie der Wissenschaften (Darmstadt, Leipzig, Berlin: Akademie Verlag, 1923–). Cited by series, volume, page. G Gottfried Wilhelm Leibniz, Die Philosophischen Schriften, ed. C. I. Gerhardt, 7 vols. (Berlin: Weidmann, 1875–1890). Cited by volume and page. GM Gottfried Wilhelm Leibniz, Leibnizens Mathematische Schriften, ed. C. I. Gerhardt, 7 vols. (Berlin: A. Asher, 1849–1863). Cited by volume and page. L Gottfried Wilhelm Leibniz, Philosophical Papers and Letters, trans. Leroy E. Loemker, 2nd ed. (Dordrecht: D. Reidel, 1970). NE Gottfried Wilhelm Leibniz, New Essays on Human Understanding, trans. Peter Remnant and Jonathan Francis Bennett (Cambridge: Cambridge University Press, 1996). PG Gottfried Wilhelm Leibniz, “Extrait d’une Lettre de M.
    [Show full text]
  • Leibniz's Analysis of Change: Vague States, Physical Continuity, and The
    Leibniz’s analysis of change: vague states, physical continuity, and the calculus Richard T. W. Arthur, (McMaster University) Mexico-Canada Early Modern Conference Western University, October 2, 2020 1 Leibniz’s analysis of change: vague states, physical continuity, and the calculus 0. Abstract One of the most puzzling features of Leibniz’s deep metaphysics is the apparent contradiction between his claims (1) that the law of continuity holds everywhere, so that in particular, change is continuous in every monad, and (2) that “changes are not really continuous”, since successive states contradict one another. In this paper I try to show in what sense these claims can be understood as compatible. My analysis depends crucially on Leibniz’s idea that enduring states are “vague”, and abstract away from further changes occurring within them at a higher resolution—consistently with his famous doctrine of petites perceptions. As Leibniz explains further in a recently transcribed unpublished manuscript, these changes are dense within any actual duration, which is conceived as actually divided by them into states that are syncategorematically infinite in number and unassignably small. The correspondence between these unassignably small intervals between changes and the differentials of his calculus allows processes to be conceived as continuous, despite the discontinuity of the changes that occur in actuality. 2 Leibniz’s analysis of change: vague states, physical continuity, and the calculus Earlier versions of this paper were presented to the Dipartimento di Filosofia, Università degli Studi di Milano, May 10, 2018; to SPHERE, Université de Paris-Diderot, Paris, November 7, 2018; at the workshop Leibniz et Leibniziennes, Centre for Theoretical Studies, Charles University, Prague, November 9, 2018; at the Society for Exact Philosophy, Annual Conference, York University, 17 May, 2019; at Harvard History of Philosophy Workshop, November 15, 2019; and at Chapman University, February 10, 2020.
    [Show full text]
  • Infinitesimals for Metaphysics: Consequences for the Ontologies Of
    Infinitesimals for Metaphysics: Consequences for the Ontologies of Space and Time Dissertation Presented in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the Graduate School of The Ohio State University By Patrick Reeder, MA Graduate Program in Philosophy The Ohio State University 2012 Dissertation Committee: Stewart Shapiro, Advisor Ben Caplan Neil Tennant Copyright by Patrick Reeder 2012 Abstract In this dissertation, I defend unorthodox conceptions of continuity: I argue that they're both conceptually viable and philosophically fruitful. After a brief introduc- tion in the first chapter, I argue in the second chapter that the standard conception of continuity|which comes to us from Georg Cantor and Richard Dedekind, and which uses the real numbers as a model|doesn't satisfy all of pretheoretic intuitions about continuity and indeed that no conception of continuity does. This opens up conceptual room for unorthodox conceptions of continuity. In the second chapter, I argue that an unorthodox conception of continuity based on infinitesimals|numbers as small as infinity is large|provides the basis for a novel account of contact: of when two material bodies touch. In the third chapter, I argue that two other unorthodox conceptions of continuity provide the basis for novel solutions to Zeno's paradox of the arrow. ii Dedication For Faye Bartlett Reeder, Ph.D. (1892-1973) iii Acknowledgments I would like to thank all those who have read and commented on significant por- tions of this dissertation: Scott Brown, Steven Brown, Wesley Cray, Justin D'Arms, Matthew Davidson, Salvatore Florio, Peter Forrest, Timothy Fuller, Alison Kerr, Teresa Kouri, Nicholaos Jones, Lindsey Mason, James McGlothlin, Michael Miller, Cathy Muller, Bradley Rettler, Tony Roy, David Sanson, Kevin Scharp, Timothy Schroeder, Lisa Shabel, Nathan Smith, Declan Smithies, William Taschek, Gabriel Uzquiano and Daniel Wilkenfeld.
    [Show full text]