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  1. Richard T. W. Arthur, Actual Infinitesimals in Leibniz's Early Thought.
    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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  2. Richard T. W. Arthur, Minkowski Spacetime and the Dimensions of the Present.
    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 (i) that the four-dimensional structure of events and processes is alone real, and that becoming present is not an objective part of reality; and (ii) that present existence is not an absolute notion, (...)
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  3. Richard T. W. Arthur, Time Lapse and the Degeneracy of Time: Gödel, Proper Time and Becoming in Relativity Theory.
    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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  4. Richard T. W. Arthur, Time, Inertia and the Relativity Principle.
    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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  5. Richard T. W. Arthur (forthcoming). Lo zenonismo come fonte delle monadi di Leibniz: una risposta a Paolo Rossi. Rivista di Storia Della Filosofia.
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  6. Richard T. W. Arthur (2014). Klaas van Berkel . Isaac Beeckman on Matter and Motion . Baltimore: Johns Hopkins University Press, 2013. Pp. Viii+265. $35.96 (Paper). [REVIEW] Hopos: The Journal of the International Society for the History of Philosophy of Science 4 (1):192-196.
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  7. Richard T. W. Arthur (2013). Leibniz's Theory of Space. 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. Richard T. W. Arthur (2012). Presupposition, Aggregation, and Leibniz's Argument for a Plurality of Substances. The Leibniz Review 21:91-115.
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  9. Richard T. W. Arthur (2011). Beeckman's Discrete Moments and Descartes' Disdain. 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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  10. Richard T. W. Arthur (2011). Natural Deduction: An Introduction to Logic with Real Arguments, a Little History and Some Humour. 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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  11. Richard T. W. Arthur (2010). Leibniz: Body, Substance, Monad. British Journal for the History of Philosophy 18 (4):721-724.
  12. Richard T. W. Arthur (2006). Review of Andreas Blank, Leibniz: Metaphilosophy and Metaphysics 1666-1686,. [REVIEW] Notre Dame Philosophical Reviews 2006 (5).
  13. Richard T. W. Arthur (1995). Newton's Fluxions and Equably Flowing Time. Studies in History and Philosophy of Science Part A 26 (2):323-351.
  14. Richard T. W. Arthur (1989). 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. Boston Studies in the Philosophy of Science 116:171-201.
     
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  15. Richard T. W. Arthur (1987). Book Review:Temporal Relations and Temporal Becoming: A Defense of a Russellian Theory of Time L. Nathan Oaklander. [REVIEW] Philosophy of Science 54 (1):142-.
  16. Richard T. W. Arthur (1986). Leibniz on Continuity. 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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  17. Richard T. W. Arthur (1981). Book Review:Quantum Mechanics, a Half Century Later J.L. Lopes, M. Paty. [REVIEW] Philosophy of Science 48 (1):156-.