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Richard T. W. Arthur
McMaster University
  1.  6
    Leibniz.Richard Arthur - 2014 - Malden, MA, USA: 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.  22
    The Reality of Time Flow: Local Becoming in Modern Physics.Richard T. W. Arthur - 2019 - Springer Verlag.
    It is commonly held that there is no place for the 'now’ in physics, and also that the passing of time is something subjective, having to do with the way reality is experienced but not with the way reality is. Indeed, the majority of modern theoretical physicists and philosophers of physics contend that the passing of time is incompatible with modern physical theory, and excluded in a fundamental description of physical reality. This book provides a forceful rebuttal of such claims. (...)
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  3.  50
    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.
    This volume has 41 chapters written to honor the 100th birthday of Mario Bunge. It celebrates the work of this influential Argentine/Canadian physicist and philosopher. Contributions show the value of Bunge’s science-informed philosophy and his systematic approach to philosophical problems. The chapters explore the exceptionally wide spectrum of Bunge’s contributions to: metaphysics, methodology and philosophy of science, philosophy of mathematics, philosophy of physics, philosophy of psychology, philosophy of social science, philosophy of biology, philosophy of technology, moral philosophy, social and political (...)
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  4. 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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  5. 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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  6. 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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  7.  34
    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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  8.  5
    The Labyrinth of the Continuum - Writings on the Continuum Problem 1672-1686.Richard T. W. Arthur (ed.) - 2013 - 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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  9. 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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  10.  86
    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.  13
    Leibniz’s Syncategorematic Actual Infinite.Richard T. W. Arthur - 2018 - In 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.), Infinity in Early Modern Philosophy. Springer Verlag. pp. 155-179.
    It is well known that Leibniz advocated the actual infinite, but that he did not admit infinite collections or infinite numbers. But his assimilation of this account to the scholastic notion of the syncategorematic infinite has given rise to controversy. A common interpretation is that in mathematics Leibniz’s syncategorematic infinite is identical with the Aristotelian potential infinite, so that it applies only to ideal entities, and is therefore distinct from the actual infinite that applies to the actual world. Against this, (...)
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  12. 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.
  13.  4
    Monads, Composition, and Force: Ariadnean Threads Through Leibniz's Labyrinth.Richard Arthur - 2018 - Oxford, United Kingdom: Oxford University Press.
    In this new work, Richard T. W. Arthur offers a fresh interpretation of Leibniz's theory of substance. He goes against a long trend of idealistic interpretations of Leibniz's thought by instead taking seriously Leibniz's claim of introducing monads to solve the problem of the composition of matter and motion.
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  14.  75
    Leibniz on Infinite Number, Infinite Wholes, and the Whole World.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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  15. 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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  16. 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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  17.  6
    Leibniz’s syncategorematic infinitesimals.Richard T. W. Arthur - 2013 - Archive for History of Exact Sciences 67 (5):553-593.
    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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  18.  68
    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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  19.  40
    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.
  20.  5
    Exacting a Philosophy of Becoming From Modern Physics.Richard T. W. Arthur - 1982 - Pacific Philosophical Quarterly 63 (2):101-110.
  21. 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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  22. 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.
  23.  17
    Russell's Leibniz Notebook.Richard T. W. Arthur & Nicholas Griffin - 2017 - Russell: The Journal of Bertrand Russell Studies 37 (1).
    In preparation for his lectures on Leibniz delivered in Cambridge in Lent Term 1899, Russell started in the summer of 1898 to keep notes on writings by and about Leibniz in a large notebook of the type he commonly used for notetaking at this time. This article prints, with annotation, all the material on Leibniz in that notebook.
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  24.  49
    Infinite Aggregates and Phenomenal Wholes.Richard Arthur - 1998 - The Leibniz Review 8:25-45.
  25.  24
    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 - Cham: Springer Verlag.
    This volume contains essays that examine infinity in early modern philosophy. The essays not only consider the ways that key figures viewed the concept. They also detail how these different beliefs about infinity influenced major philosophical systems throughout the era. These domains include mathematics, metaphysics, epistemology, ethics, science, and theology. Coverage begins with an introduction that outlines the overall importance of infinity to early modern philosophy. It then moves from a general background of infinity up through Kant. Readers will learn (...)
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  26.  29
    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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  27.  9
    Marginalia in Russell's Copy of Gerhardt's Edition of Leibniz's Philosophische Schriften.Richard T. W. Arthur, Jolen Galaugher & Nicholas Griffin - 2017 - Russell: The Journal of Bertrand Russell Studies 37 (1).
    Russell’s most important source for his book on Leibniz was C. I. Gerhardt’s seven-volume Die philosophischen Schriften von Gottfried Wilhelm Leibniz. Russell heavily annotated his copy of this important edition of Leibniz’s works. The present paper records all Russell’s marginalia, with the exception of passages marked merely by vertical lines in the margin, and provides explanatory commentary.
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  28.  12
    Leibniz on Infinite Number, Infinite Wholes, and the Whole World.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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  29.  19
    Infinite Aggregates and Phenomenal Wholes.Richard Arthur - 1998 - The Leibniz Review 8:25-45.
  30. 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 and (...)
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  31.  93
    Leibniz and Clarke: A Study of Their Correspondence.Richard Arthur - 2001 - Mind 110 (439):874-878.
  32.  12
    Leibniz and the Three Degrees of Infinity.Richard T. W. Arthur - 2022 - The Leibniz Review 32:25-46.
    In these remarks on Ohad Nachtomy’s account of Leibniz’s philosophy of the infinite in his recent book, Living Mirrors, I focus on his suggestion that living creatures be interpreted as exemplifying the second of the three degrees of infinity that Leibniz articulates in 1676, as things which are infinite in their own kind. For the infinity characterizing created substances cannot be the highest degree, which is reserved by Leibniz for the divine substance, while Nachtomy sees the lowest degree as applicable (...)
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  33. 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.
  34.  74
    The remarkable fecundity of Leibniz's work on infinite series.Richard Arthur - 2006 - Annals of Science 63 (2):221-225.
  35. 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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  36.  64
    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.
  37.  8
    Response to Vincenzo De Risi.Richard T. W. Arthur - 2022 - The Leibniz Review 32:141-145.
  38.  19
    On the significance of A. A. Robb’s philosophy of time, especially in relation to Bertrand Russell’s.Richard T. W. Arthur - 2022 - British Journal for the History of Philosophy 31 (2):251-273.
    The aim of this paper is to explain the significance of Alfred A. Robb’s philosophy of time stemming from his interpretation of relativity theory; and at the same time, to investigate the reasons for the failure of his philosophical contemporaries to appreciate its significance, with special attention to its reception on Russell’s part. The study of Russell’s reaction to Robb exposes shortcomings in Russell’s own philosophy of time, which has been extremely influential through the years. It also highlights the philosophical (...)
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  39. Kontinuität und Mechanismus. [REVIEW]Richard Arthur, Christia Mercer, Justin Smith & Catherine Wilson - 1997 - The Leibniz Review 7:25-64.
  40.  73
    Leibniz’s Mechanical Principles : Commentary and Translation.Richard T. W. Arthur - 2013 - The Leibniz Review 23:101-105.
  41.  64
    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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  42. The Enigma of Leibniz's Atomism.Richard Arthur - 2004 - Oxford Studies in Early Modern Philosophy 1:183-228.
     
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  43.  61
    Cohesion, Division and Harmony: Physical Aspects of Leibniz’s Continuum Problem.Richard Arthur - 1998 - Perspectives on Science 6 (1):110-135.
  44. 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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  45.  27
    Leibniz: Dissertation on Combinatorial Art. Translated with introduction and commentary by Massimo Mugnai, Han van Ruler, and Martin Wilson.Richard T. W. Arthur - 2020 - The Leibniz Review 30:141-145.
  46. On the flow of time.Richard Arthur - manuscript
    During the last hundred years the notion of time flow has been held in low esteem by philosophers of science. Since the metaphor depends heavily on the analogy with motion, criticisms of time flow have either attacked the analogy as poorly founded, or else argued by analogy from a “static” conception of motion. Thus (1) Bertrand Russell argued that just as motion can be conceived as existence at successive places at successive times without commitment to a state of motion at (...)
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  47.  27
    Natural Deduction: An Introduction to Logic with Real Arguments, a Little History and Some Humour.Richard T. W. Arthur - 2011 - Peterborough, Ontario, Canada: 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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  48.  39
    On the Non-Idealist Leibniz.Richard T. W. Arthur - 2018 - The Leibniz Review 28:97-101.
    This is a reply to Samuel Levey's fine review of my Monads, Composition and Force (Oxford UP, 2018) in the same issue of the Leibniz Review. In it I take up various difficulties raised by Levey that may be thought to collapse Leibniz's position into idealism after all, and attempt to provide convincing responses to them.
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  49.  12
    Leibniz's Ad schedam Hamaxariam.Osvaldo Ottaviani & Richard Arthur - 2021 - The Leibniz Review 31:61-106.
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  50.  36
    The Hegelian Roots of Russell's Critique of Leibniz.Richard T. W. Arthur - 2018 - The Leibniz Review 28:9-42.
    At the turn of the century Bertrand Russell advocated an absolutist theory of space and time, and scornfully rejected Leibniz’s relational theory in his Critical Exposition of the Philosophy of Leibniz. But by the time of the second edition, he had proposed highly influential relational theories of space and time that had much in common with Leibniz’s own views. Ironically, he never acknowledges this. In trying to get to the bottom of this enigma, I looked further at contemporary texts by (...)
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