42 found
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  1.  38
    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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  2. 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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  3.  15
    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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  4.  73
    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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  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.  23
    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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  7. 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.
  8.  32
    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. Cham: 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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  9. 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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  10. 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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  11.  56
    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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  12. Leibniz’s Actual Infinite in Relation to His Analysis of Matter.Richard T. W. Arthur - 2015 - In G.W. Leibniz, Interrelations Between Mathematics and Philosophy. Springer Verlag.
  13.  22
    Exacting a Philosophy of Becoming From Modern Physics.Richard T. W. Arthur - 1982 - Pacific Philosophical Quarterly 63 (2):101-110.
  14.  18
    Virtual Processes and Quantum Tunnelling as Fictions.Richard T. W. Arthur - 2012 - Science & Education 21 (10):1461-1473.
  15. 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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  16.  51
    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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  17.  42
    Leibniz’s Mechanical Principles : Commentary and Translation.Richard T. W. Arthur - 2013 - The Leibniz Review 23:101-105.
  18. 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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  19.  53
    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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  20.  37
    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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  21.  75
    (1 other version)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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  22. Russell's Conundrum: on the Relation of Leibniz's Monads to the Continuum in An Intimate Relation. Studies in the History and Philosophy of Science.Richard T. W. Arthur - 1989 - Boston Studies in the Philosophy of Science 116:171-201.
  23.  48
    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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  24.  24
    Response to Vincenzo De Risi.Richard T. W. Arthur - 2022 - The Leibniz Review 32:141-145.
  25.  42
    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.
  26. (1 other version)An Introduction to Logic: Using Natural Deduction, Real Arguments, a Little History, and Some Humour.Richard T. W. Arthur - 2016 - Peterborough, CA: 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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  27.  42
    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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  28. G.W. Leibniz, Interrelations Between Mathematics and Philosophy.Richard T. W. Arthur (ed.) - 2015 - Springer Verlag.
  29.  65
    Leibniz: Body, Substance, Monad.Richard T. W. Arthur - 2010 - British Journal for the History of Philosophy 18 (4):721-724.
  30.  12
    Mario Bunge on Causality: Some Key Insights and Their Leibnizian Precedents.Richard T. W. Arthur - 2019 - In Michael Robert Matthews (ed.), Mario Bunge: A Centenary Festschrift. Springer. pp. 185-204.
    Mario Bunge wrote his classic Causality and Modern Science more than 60 years ago, and a third revised edition was published by Dover in 1979. With its impressive scope and historical perspective it was a long way ahead of its time. But many of its insights still have not been sufficiently appreciated by physicists and philosophers alike. These include Bunge’s distinction between causation and other types of determination, his critique of the still-dominant Humean accounts of causality as leaving out the (...)
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  31.  53
    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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  32.  22
    (3 other versions)Moore's Notes on Leibniz Lectures.Richard T. W. Arthur & Nicholas Griffin - 2017 - Russell: The Journal of Bertrand Russell Studies 37 (1).
    G. E. Moore attended Russell’s lectures on Leibniz in 1899 and kept detailed notes which have been preserved among his papers. The present article prints his notes in their entirety with annotations.
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  33.  33
    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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  34. On the mathematization of free fall : Galileo, Descartes, and a history of misconstrual.Richard T. W. Arthur - 2016 - In Geoffrey Gorham (ed.), The Language of Nature: Reassessing the Mathematization of Natural Philosophy in the Seventeenth Century. Minneapolis: University of Minnesota Press.
  35.  51
    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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  36.  20
    Reply to Ohad Nachtomy.Richard T. W. Arthur - 2014 - The Leibniz Review 24:131-133.
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  37.  49
    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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  38.  40
    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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  39.  29
    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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  40.  73
    Review of Andreas blank, Leibniz: Metaphilosophy and Metaphysics 1666-1686,[REVIEW]Richard T. W. Arthur - 2006 - Notre Dame Philosophical Reviews 2006 (5).
  41. 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-.
  42.  43
    Review of T emporal Relations and Temporal Becoming. [REVIEW]Richard T. W. Arthur - 1987 - Philosophy of Science 54 (1):142-.
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