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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. 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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  3. 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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  4. 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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  5. 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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  6.  60
    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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  7. 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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  8.  78
    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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  9.  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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  10. 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.
  11.  96
    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.
  12. 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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  13.  90
    Leibniz and Clarke: A Study of Their Correspondence.Richard Arthur - 2001 - Mind 110 (439):874-878.
  14. 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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  15.  32
    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.
  16.  59
    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.
  17.  19
    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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  18. 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.
  19.  62
    Leibniz’s Mechanical Principles : Commentary and Translation.Richard T. W. Arthur - 2013 - The Leibniz Review 23:101-105.
  20. 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.
  21.  19
    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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  22. Time, Inertia and the Relativity Principle.Richard T. W. Arthur - manuscript
    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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  23. 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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  24. Exacting a Philosophy of Becoming From Modern Physics.Richard T. W. Arthur - 1982 - Pacific Philosophical Quarterly 63 (2):101.
  25.  15
    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.
  26. 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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  27.  7
    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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  28. 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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  29.  19
    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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  30.  13
    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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  31.  6
    Virtual Processes and Quantum Tunnelling as Fictions.Richard T. W. Arthur - 2012 - Science & Education 21 (10):1461-1473.
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  32.  44
    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.
  33.  12
    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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  34.  49
    Cohesion, Division and Harmony: Physical Aspects of Leibniz's Continuum Problem (1671-1686).Richard Arthur - 1998 - Perspectives on Science 6 (1):110-135.
  35. 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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  36. 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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  37.  99
    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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  38.  31
    Leibniz’s Causal Theory of Time Revisited.Richard T. W. Arthur - 2016 - The Leibniz Review 26:151-178.
    Following the lead of Hans Reichenbach in the early twentieth century, many authors have attributed a causal theory of time to Leibniz. My exposition of Leibniz’s theory of time in a paper of 1985 has been interpreted as a version of such a causal theory, even though I was critical of the idea that Leibniz would have tried to reduce relations among monadic states to causal relations holding only among phenomena. Since that time previously unpublished texts by Leibniz have become (...)
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  39. 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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  40.  94
    Book Review:Quantum Mechanics, a Half Century Later J.L. Lopes, M. Paty. [REVIEW]Richard T. W. Arthur - 1981 - Philosophy of Science 48 (1):156-.
  41.  43
    Massimo Mugnai and the Study of Leibniz.Richard T. W. Arthur - 2013 - The Leibniz Review 23:1-5.
    This essay is an appreciation of Massimo Mugnai’s many contributions to Leibniz scholarship, as well as to the history of logic and history of philosophy more generally.
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  42.  50
    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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  43.  82
    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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  44. On Newton's Fluxional Proof of the Vector Addition of Motive Forces.Richard Arthur - manuscript
    This paper consists in an exposition of a proof Newton gave in 1666 of the parallelogram law for compounding velocities, and an examination of its implications for understanding his treatment of motion resulting from a continuously acting force in the Principia. I argue that the “moments” invoked in the fluxional proof of the vector resolution and composition of velocities are “virtual times”, a device allowing Newton to represent motions by the linear displacements produced in such a time; the ratio of (...)
     
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  45.  70
    The Remarkable Fecundity of Leibniz's Work on Infinite Series.Richard Arthur - 2006 - Annals of Science 63 (2):221-225.
  46.  24
    Niccolò Guicciardini, Isaac Newton on Mathematical Certainty and Method. Cambridge, MA and London: MIT Press, 2009. Pp. Xxiii + 422. ISBN 978-0-262-01317-8. $55.00. [REVIEW]Richard Arthur - 2011 - British Journal for the History of Science 44 (1):122-124.
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  47.  59
    Leibniz and the Zenonists: A Reply to Paolo Rossi.Richard Arthur - manuscript
    In a recent note in this review (Leibniz e gli Zenonisti, n. 3, 2001, pp. 15-22) Paolo Rossi stresses the importance of a philosophical sect that he claims has been unjustly ignored in accounts of the history of modern philosophy, the Jesuit philosophers of Louvain and Spain of the late sixteenth and early seventeenth century known as the Zenonists. The occasion for his complaint is Massimo Mugnai’s admirable new introduction to Leibniz’s thought (Introduzione alla filosofia di Leibniz, Torino, Einaudi, 2001), (...)
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  48.  53
    Leibniz: Body, Substance, Monad.Richard T. W. Arthur - 2010 - British Journal for the History of Philosophy 18 (4):721-724.
  49.  13
    Reply to Ohad Nachtomy.Richard T. W. Arthur - 2014 - The Leibniz Review 24:131-133.
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  50.  31
    De Summa Rerum.Richard Arthur - 1993 - The Leibniz Review 3:14-17.
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