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Richard T. W. Arthur
McMaster University
  1. Leibniz.Richard T. W. Arthur - 2014 - Polity.
    Few philosophers have left a legacy like that of Gottfried Wilhelm Leibniz. He has been credited not only with inventing the differential calculus, but also with anticipating the basic ideas of modern logic, information science, and fractal geometry. He made important contributions to such diverse fields as jurisprudence, geology and etymology, while sketching designs for calculating machines, wind pumps, and submarines. But the common presentation of his philosophy as a kind of unworldly idealism is at odds with all this bustling (...)
     
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  2. Space and Relativity in Newton and Leibniz.Richard Arthur - 1994 - British Journal for the Philosophy of Science 45 (1):219-240.
    In this paper I challenge the usual interpretations of Newton's and Leibniz's views on the nature of space and the relativity of motion. Newton's ‘relative space’ is not a reference frame; and Leibniz did not regard space as defined with respect to actual enduring bodies. Newton did not subscribe to the relativity of intertial motions; whereas Leibniz believed no body to be at rest, and Newton's absolute motion to be a useful fiction. A more accurate rendering of the opposition between (...)
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  3. On Thought Experiments as a Priori Science.Richard Arthur - 1999 - International Studies in the Philosophy of Science 13 (3):215 – 229.
    Against Norton's claim that all thought experiments can be reduced to explicit arguments, I defend Brown's position that certain thought experiments yield a priori knowledge. They do this, I argue, not by allowing us to perceive “Platonic universals” (Brown), even though they may contain non-propositional components that are epistemically indispensable, but by helping to identify certain tacit presuppositions or “natural interpretations” (Feyerabend's term) that lead to a contradiction when the phenomenon is described in terms of them, and by suggesting a (...)
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  4. Minkowski Spacetime and the Dimensions of the Present.Richard T. W. Arthur - unknown
    In Minkowski spacetime, because of the relativity of simultaneity to the inertial frame chosen, there is no unique world-at-an-instant. Thus the classical view that there is a unique set of events existing now in a three dimensional space cannot be sustained. The two solutions most often advanced are that the four-dimensional structure of events and processes is alone real, and that becoming present is not an objective part of reality; and that present existence is not an absolute notion, but is (...)
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  5.  24
    Mario Bunge: A Centenary Festschrift.Mario Augusto Bunge, Michael R. Matthews, Guillermo M. Denegri, Eduardo L. Ortiz, Heinz W. Droste, Alberto Cordero, Pierre Deleporte, María Manzano, Manuel Crescencio Moreno, Dominique Raynaud, Íñigo Ongay de Felipe, Nicholas Rescher, Richard T. W. Arthur, Rögnvaldur D. Ingthorsson, Evandro Agazzi, Ingvar Johansson, Joseph Agassi, Nimrod Bar-Am, Alberto Cupani, Gustavo E. Romero, Andrés Rivadulla, Art Hobson, Olival Freire Junior, Peter Slezak, Ignacio Morgado-Bernal, Marta Crivos, Leonardo Ivarola, Andreas Pickel, Russell Blackford, Michael Kary, A. Z. Obiedat, Carolina I. García Curilaf, Rafael González del Solar, Luis Marone, Javier Lopez de Casenave, Francisco Yannarella, Mauro A. E. Chaparro, José Geiser Villavicencio- Pulido, Martín Orensanz, Jean-Pierre Marquis, Reinhard Kahle, Ibrahim A. Halloun, José María Gil, Omar Ahmad, Byron Kaldis, Marc Silberstein, Carolina I. García Curilaf, Rafael González del Solar, Javier Lopez de Casenave, Íñigo Ongay de Felipe & Villavicencio-Pulid (eds.) - 2019 - Springer Verlag.
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  6.  13
    Leibniz’s Syncategorematic Infinitesimals II: Their Existence, Their Use and Their Role in the Justification of the Differential Calculus.David Rabouin & Richard T. W. Arthur - 2020 - Archive for History of Exact Sciences 74 (5):401-443.
    In this paper, we endeavour to give a historically accurate presentation of how Leibniz understood his infinitesimals, and how he justified their use. Some authors claim that when Leibniz called them “fictions” in response to the criticisms of the calculus by Rolle and others at the turn of the century, he had in mind a different meaning of “fiction” than in his earlier work, involving a commitment to their existence as non-Archimedean elements of the continuum. Against this, we show that (...)
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  7. Presupposition, Aggregation, and Leibniz’s Argument for a Plurality of Substances.Richard T. W. Arthur - 2011 - The Leibniz Review 21:91-115.
    This paper consists in a study of Leibniz’s argument for the infinite plurality of substances, versions of which recur throughout his mature corpus. It goes roughly as follows: since every body is actually divided into further bodies, it is therefore not a unity but an infinite aggregate; the reality of an aggregate, however, reduces to the reality of the unities it presupposes; the reality of body, therefore, entails an actual infinity of constituent unities everywhere in it. I argue that this (...)
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  8. Leibniz’s Theory of Space.Richard T. W. Arthur - 2013 - Foundations of Science 18 (3):499-528.
    In this paper I offer a fresh interpretation of Leibniz’s theory of space, in which I explain the connection of his relational theory to both his mathematical theory of analysis situs and his theory of substance. I argue that the elements of his mature theory are not bare bodies (as on a standard relationalist view) nor bare points (as on an absolutist view), but situations. Regarded as an accident of an individual body, a situation is the complex of its angles (...)
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  9. Time Lapse and the Degeneracy of Time: Gödel, Proper Time and Becoming in Relativity Theory.Richard T. W. Arthur - unknown
    In the transition to Einstein’s theory of Special Relativity (SR), certain concepts that had previously been thought to be univocal or absolute properties of systems turn out not to be. For instance, mass bifurcates into (i) the relativistically invariant proper mass m0, and (ii) the mass relative to an inertial frame in which it is moving at a speed v = βc, its relative mass m, whose quantity is a factor γ = (1 – β2) -1/2 times the proper mass, (...)
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  10.  81
    Leery Bedfellows: Newton and Leibniz on the Status of Infinitesimals.Richard Arthur - 2008 - In Douglas Jesseph & Ursula Goldenbaum (eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. Walter de Gruyter.
    Newton and Leibniz had profound disagreements concerning metaphysics and the relationship of mathematics to natural philosophy, as well as deeply opposed attitudes towards analysis. Nevertheless, or so I shall argue, despite these deeply held and distracting differences in their background assumptions and metaphysical views, there was a considerable consilience in their positions on the status of infinitesimals. In this paper I compare the foundation Newton provides in his Method Of First and Ultimate Ratios (sketched at some time between 1671 and (...)
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  11.  62
    Leibniz on Infinite Number, Infinite Wholes, and the Whole World: A Reply to Gregory Brown.Richard Arthur - 2001 - The Leibniz Review 11:103-116.
    Reductio arguments are notoriously inconclusive, a fact which no doubt contributes to their great fecundity. For once a contradiction has been proved, it is open to interpretation which premise should be given up. Indeed, it is often a matter of great creativity to identify what can be consistently given up. A case in point is a traditional paradox of the infinite provided by Galileo Galilei in his Two New Sciences, which has since come to be known as Galileo’s Paradox. It (...)
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  12.  61
    Infinite Number and the World Soul; in Defence of Carlin and Leibniz.Richard Arthur - 1999 - The Leibniz Review 9:105-116.
    In last year’s Review Gregory Brown took issue with Laurence Carlin’s interpretation of Leibniz’s argument as to why there could be no world soul. Carlin’s contention, in Brown’s words, is that Leibniz denies a soul to the world but not to bodies on the grounds that “while both the world and [an] aggregate of limited spatial extent are infinite in multitude, the former, but not the latter, is infinite in respect of magnitude and hence cannot be considered a whole”. Brown (...)
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  13. Newton's Fluxions and Equably Flowing Time.Richard T. W. Arthur - 1995 - Studies in History and Philosophy of Science Part A 26 (2):323-351.
  14.  33
    Continuous Creation, Continuous Time: A Refutation of the Alleged Discontinuity of Cartesian Time.Richard Arthur - 1988 - Journal of the History of Philosophy 26 (3):349-375.
  15. The Labyrinth of the Continuum: Writings on the Continuum Problem, 1672-1686.Richard T. W. Arthur (ed.) - 2001 - Yale University Press.
    This book gathers together for the first time an important body of texts written between 1672 and 1686 by the great German philosopher and polymath Gottfried Leibniz. These writings, most of them previously untranslated, represent Leibniz’s sustained attempt on a problem whose solution was crucial to the development of his thought, that of the composition of the continuum. The volume begins with excerpts from Leibniz’s Paris writings, in which he tackles such problems as whether the infinite division of matter entails (...)
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  16. Leibniz’s Actual Infinite in Relation to His Analysis of Matter.Richard T. W. Arthur - 2015 - In David Rabouin, Philip Beeley & Norma B. Goethe (eds.), G.W. Leibniz, Interrelations Between Mathematics and Philosophy. Springer Verlag.
  17. Exacting a Philosophy of Becoming From Modern Physics.Richard T. W. Arthur - 1982 - Pacific Philosophical Quarterly 63 (2):101.
  18.  91
    Leibniz and Clarke: A Study of Their Correspondence.Richard Arthur - 2001 - Mind 110 (439):874-878.
  19. The Enigma of Leibniz's Atomism.Richard Arthur - 2004 - In Daniel Garber & Steven Nadler (eds.), Oxford Studies in Early Modern Philosophy Volume 1. Oxford University Press.
  20.  46
    Infinite Aggregates and Phenomenal Wholes: Leibniz's Theory of Substance as a Solution to the Continuum Problem.Richard Arthur - 1998 - The Leibniz Review 8:25-45.
  21. Time, Inertia and the Relativity Principle.Richard T. W. Arthur - 2007
    In this paper I try to sort out a tangle of issues regarding time, inertia, proper time and the so-called “clock hypothesis” raised by Harvey Brown's discussion of them in his recent book, Physical Relativity. I attempt to clarify the connection between time and inertia, as well as the deficiencies in Newton's “derivation” of Corollary 5, by giving a group theoretic treatment original with J.-P. Provost. This shows how both the Galilei and Lorentz transformations may be derived from the relativity (...)
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  22.  61
    Leibniz and the Natural World: Activity, Passivity and Corporeal Substances in Leibniz's Philosophy? Pauline Phemister. [REVIEW]Richard Arthur - 2007 - Philosophical Quarterly 57 (226):133-137.
  23. Beeckman, Descartes and the Force of Motion.Richard Arthur - 2007 - Journal of the History of Philosophy 45 (1):1--28.
    : In this reassessment of Descartes' debt to his mentor Isaac Beeckman, I argue that they share the same basic conception of motion: the force of a body's motion—understood as the force of persisting in that motion, shorn of any connotations of internal cause—is conserved through God's direct action, is proportional to the speed and magnitude of the body, and is gained or lost only through collisions. I contend that this constitutes a fully coherent ontology of motion, original with Beeckman (...)
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  24.  68
    Leibniz’s Mechanical Principles : Commentary and Translation.Richard T. W. Arthur - 2013 - The Leibniz Review 23:101-105.
  25.  8
    Leibniz on Infinite Number, Infinite Wholes, and the Whole World: A Reply to Gregory Brown.Richard Arthur - 2001 - The Leibniz Review 11:103-116.
    Reductio arguments are notoriously inconclusive, a fact which no doubt contributes to their great fecundity. For once a contradiction has been proved, it is open to interpretation which premise should be given up. Indeed, it is often a matter of great creativity to identify what can be consistently given up. A case in point is a traditional paradox of the infinite provided by Galileo Galilei in his Two New Sciences, which has since come to be known as Galileo’s Paradox. It (...)
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  26.  17
    Infinite Aggregates and Phenomenal Wholes: Leibniz’s Theory of Substance as a Solution to the Continuum Problem.Richard Arthur - 1998 - The Leibniz Review 8:25-45.
  27.  71
    The Remarkable Fecundity of Leibniz's Work on Infinite Series.Richard Arthur - 2006 - Annals of Science 63 (2):221-225.
  28. Natural Deduction: An Introduction to Logic with Real Arguments, a Little History and Some Humour.Richard T. W. Arthur - 2011 - Broadview Press.
    Richard Arthur’s _Natural Deduction_ provides a wide-ranging introduction to logic. In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python.
     
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  29.  51
    Leibniz on Continuity.Richard T. W. Arthur - 1986 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1986:107 - 115.
    In this paper I attempt to throw new light on Leibniz's apparently conflicting remarks concerning the continuity of matter. He says that matter is "discrete" yet "actually divided to infinity" and (thus dense), and moreover that it fills (continuous) space. I defend Leibniz from the charge of inconsistency by examining the historical development of his views on continuity in their physical and mathematical context, and also by pointing up the striking similarities of his construal of continuity to the approach taken (...)
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  30. Leibniz's Syncategorematic Infinitesimals, Smooth Infinitesimal Analysis, and Newton's Proposition.Richard Arthur - manuscript
    In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s mature interpretation was fully in accord with the Archimedean Axiom: infinitesimals are fictions, whose treatment as entities incomparably smaller than finite quantities is justifiable wholly in terms of variable finite quantities that can be taken as small as desired, i.e. syncategorematically. In this paper I explain this syncategorematic interpretation, and how Leibniz used it to justify the calculus. I then compare it with the approach of Smooth Infinitesimal Analysis (...)
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  31. Leibniz and Cantor on the Actual Infinite.Richard Arthur - unknown
    I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author. Thus I believe that there is no part of matter which is not, I do not say divisible, but actually divided; and consequently the least particle ought to be considered as a world full of an infinity of different (...)
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  32.  52
    Cohesion, Division and Harmony: Physical Aspects of Leibniz's Continuum Problem (1671-1686).Richard Arthur - 1998 - Perspectives on Science 6 (1):110-135.
  33.  6
    Virtual Processes and Quantum Tunnelling as Fictions.Richard T. W. Arthur - 2012 - Science & Education 21 (10):1461-1473.
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  34.  98
    Animal Generation and Substance in Sennert and Leibniz.Richard Arthur - 2006 - In Justin E. H. Smith (ed.), The Problem of Animal Generation in Early Modern Philosophy. Cambridge University Press.
    Gottfried Leibniz is well known for his claim to have “rehabilitated” the substantial forms of scholastic philosophy, forging a reconciliation of the New Philosophy of Descartes, Mersenne and Gassendi with Aristotelian metaphysics (in his so-called Discourse on Metaphysics, 1686). Much less celebrated is the fact that fifty years earlier (in his Hypomnemata Physica, 1636) the Bratislavan physician and natural philosopher Daniel Sennert had already argued for the indispensability to atomism of (suitably re-interpreted) Aristotelian forms, in explicit opposition to the rejection (...)
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  35.  32
    Review of T Emporal Relations and Temporal Becoming. [REVIEW]Richard T. W. Arthur - 1987 - Philosophy of Science 54 (1):142-.
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  36.  5
    Infinity in Early Modern Philosophy.Igor Agostini, Richard T. W. Arthur, Geoffrey Gorham, Paul Guyer, Mogens Lærke, Yitzhak Y. Melamed, Ohad Nachtomy, Sanja Särman, Anat Schechtman, Noa Shein & Reed Winegar (eds.) - 2018 - Springer Verlag.
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  37. “A Complete Denial of the Continuous”? Leibniz's Law of Continuity.Richard Tw Arthur - unknown
  38. Actual Infinitesimals in Leibniz's Early Thought.Richard T. W. Arthur - unknown
    Before establishing his mature interpretation of infinitesimals as fictions, Gottfried Leibniz had advocated their existence as actually existing entities in the continuum. In this paper I trace the development of these early attempts, distinguishing three distinct phases in his interpretation of infinitesimals prior to his adopting a fictionalist interpretation: (i) (1669) the continuum consists of assignable points separated by unassignable gaps; (ii) (1670-71) the continuum is composed of an infinity of indivisible points, or parts smaller than any assignable, with no (...)
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  39. An Introduction to Logic: Using Natural Deduction, Real Arguments, a Little History, and Some Humour.Richard T. W. Arthur - 2016 - Broadview Press.
    In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python. A previous edition of this book appeared under the title _Natural (...)
     
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  40.  19
    Beeckman's Discrete Moments and Descartes' Disdain.Richard T. W. Arthur - 2012 - Intellectual History Review 22 (1):69-90.
    Descartes' allusions, in the Meditations and the Principles, to the individual moments of duration, has for some years stirred controversy over whether this commits him to a kind of time atomism. The origins of Descartes' way of treating moments as least intervals of duration can be traced back to his early collaboration with Isaac Beeckman. Where Beeckman (in 1618) conceived of moments as (mathematically divisible) physical indivisibles, corresponding to the durations of uniform motions between successive impacts on a body by (...)
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  41.  32
    De Summa Rerum.Richard Arthur - 1993 - The Leibniz Review 3:14-17.
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  42. From Actuals to Fictions: Four Phases in Leibniz's Early Thought on Infinitesimals.Richard Arthur - manuscript
    In this paper I attempt to trace the development of Gottfried Leibniz’s early thought on the status of the actually infinitely small in relation to the continuum. I argue that before he arrived at his mature interpretation of infinitesimals as fictions, he had advocated their existence as actually existing entities in the continuum. From among his early attempts on the continuum problem I distinguish four distinct phases in his interpretation of infinitesimals: (i) (1669) the continuum consists of assignable points separated (...)
     
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  43. Foils for Newton: Comments on Howard Stein.Richard Arthur - 1990 - In Phillip Bricker & R. I. G. Hughes (eds.), Philosophical Perspectives on Newtonian Science. MIT Press. pp. 49--56.
     
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  44.  23
    Geoffrey Hellman* and Stewart Shapiro.**Varieties of Continua—From Regions to Points and Back.Richard T. W. Arthur - 2019 - Philosophia Mathematica 27 (1):148-152.
    HellmanGeoffrey* * and ShapiroStewart.** ** Varieties of Continua—From Regions to Points and Back. Oxford University Press, 2018. ISBN: 978-0-19-871274-9. Pp. x + 208.
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  45. G.W. Leibniz, Interrelations Between Mathematics and Philosophy.Richard T. W. Arthur (ed.) - 2015 - Springer Verlag.
  46.  26
    G. W. Leibniz. The Leibniz–Arnauld Correspondence: With Selections From the Correspondence with Ernst, Landgrave of Hessen-Rheinfels. Text Established and Translated by Stephen Voss. Lix + 410 Pp., App., Notes, Bibl., Index. New Haven, Conn./London: Yale University Press, 2016. $125 . ISBN 9780300206531.G. W. Leibniz. The Leibniz–Stahl Controversy. Translated and Edited by François Duchesneau and Justin E. H. Smith. Lxxxix + 443 Pp., Notes, Index. New Haven, Conn./London: Yale University Press, 2016. $125 . ISBN 9780300161144. [REVIEW]Richard T. W. Arthur - 2019 - Isis 110 (2):408-410.
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  47.  16
    G. W. Leibniz: De Summa Rerum: Metaphysical Papers, 1675-6. [REVIEW]Richard Arthur - 1993 - The Leibniz Review 3:14-16.
    Despite his fame as a philosopher, Leibniz was a diplomat by profession, and seldom managed to engage in sustained philosophical activity for any length of time. One exception to this, though, is the period towards the end of his stay in Paris and a little afterwards, when he launched a concerted attack on most of the profoundest problems in metaphysics, tackling them with a penetration and persistence that is remarkable by any standards. The resulting series of “meditations”, to use his (...)
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  48. Kontinuität Und Mechanismus: Zur Philosophie des Jungen Leibniz in Ihrem Ideengeschichtlichen Kontext. [REVIEW]Richard Arthur, Christia Mercer, Justin Smith & Catherine Wilson - 1997 - The Leibniz Review 7:25-64.
  49.  9
    Klaas van Berkel. Isaac Beeckman on Matter and Motion. Baltimore: Johns Hopkins University Press, 2013. Pp. Viii+265. $35.96. [REVIEW]Richard T. W. Arthur - 2014 - Hopos: The Journal of the International Society for the History of Philosophy of Science 4 (1):192-196.
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  50.  10
    Leibniz’s Analysis of Change: Vague States, Physical Continuity, and the Calculus.Richard Arthur - unknown
    One of the most puzzling features of Leibniz’s deep metaphysics is the apparent contradiction between his claims that the law of continuity holds everywhere, so that in particular, change is continuous in every monad, and 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 (...)
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