Results for 'Mathematical Universe'

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  1.  92
    The Mathematical Universe.Max Tegmark - 2007 - Foundations of Physics 38 (2):101-150.
    I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, (...)
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  2.  49
    Our Mathematical Universe?Jeremy Butterfield - unknown
    This is a discussion of some themes in Max Tegmark’s recent book, Our Mathematical Universe. It was written as a review for Plus Magazine, the online magazine of the UK’s national mathematics education and outreach project, the Mathematics Millennium Project. Since some of the discussion---about symmetry breaking, and Pythagoreanism in the philosophy of mathematics---went beyond reviewing Tegmark’s book, the material was divided into three online articles. This version combines those three articles, and adds some other material, in particular (...)
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  3.  47
    Some Comments on “The Mathematical Universe”.Gil Jannes - 2009 - Foundations of Physics 39 (4):397-406.
    I discuss some problems related to extreme mathematical realism, focusing on a recently proposed “shut-up-and-calculate” approach to physics. I offer arguments for a moderate alternative, the essence of which lies in the acceptance that mathematics is a human construction, and discuss concrete consequences of this—at first sight purely philosophical—difference in point of view.
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  4.  8
    Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. By Max Tegmark. New York: Vintage Paperbacks, 2015. 432 Pages. Paperback $17.00. [REVIEW]Paul H. Carr & Paul Arveson - 2020 - Zygon 55 (4):1131-1133.
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  5. A Mathematical Universe.F. S. Marvin - 1930 - Hibbert Journal 29:401.
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  6.  20
    Reasoning with the Infinite: From the Closed World to the Mathematical Universe.Michel Blay - 1999 - University of Chicago Press.
    "One of Michael Blay's many fine achievements in Reasoning with the Infinite is to make us realize how velocity, and later instantaneous velocity, came to play a vital part in the development of a rigorous mathematical science of motion. ...
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  7.  31
    Towards a Theory of Universes: Structure Theory and the Mathematical Universe Hypothesis.Colin Hamlin - 2017 - Synthese 194 (2):571–591.
    The maturation of the physical image has made apparent the limits of our scientific understanding of fundamental reality. These limitations serve as motivation for a new form of metaphysical inquiry that restricts itself to broadly scientific methods. Contributing towards this goal we combine the mathematical universe hypothesis as developed by Max Tegmark with the axioms of Stewart Shapiro’s structure theory. The result is a theory we call the Theory of the Structural Multiverse (TSM). The focus is on informal (...)
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  8.  11
    Universes in Explicit Mathematics.Gerhard Jäger, Reinhard Kahle & Thomas Studer - 2001 - Annals of Pure and Applied Logic 109 (3):141-162.
    This paper deals with universes in explicit mathematics. After introducing some basic definitions, the limit axiom and possible ordering principles for universes are discussed. Later, we turn to least universes, strictness and name induction. Special emphasis is put on theories for explicit mathematics with universes which are proof-theoretically equivalent to Feferman's.
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  9.  2
    Reasoning with the Infinite: From the Closed World to the Mathematical Universe.M. B. DeBevoise (ed.) - 1998 - University of Chicago Press.
    Until the Scientific Revolution, the nature and motions of heavenly objects were mysterious and unpredictable. The Scientific Revolution was revolutionary in part because it saw the advent of many mathematical tools—chief among them the calculus—that natural philosophers could use to explain and predict these cosmic motions. Michel Blay traces the origins of this mathematization of the world, from Galileo to Newton and Laplace, and considers the profound philosophical consequences of submitting the infinite to rational analysis. "One of Michael Blay's (...)
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  10. Reasoning with the Infinite: From the Closed World to the Mathematical Universe.M. B. DeBevoise (ed.) - 1998 - University of Chicago Press.
    Until the Scientific Revolution, the nature and motions of heavenly objects were mysterious and unpredictable. The Scientific Revolution was revolutionary in part because it saw the advent of many mathematical tools—chief among them the calculus—that natural philosophers could use to explain and predict these cosmic motions. Michel Blay traces the origins of this mathematization of the world, from Galileo to Newton and Laplace, and considers the profound philosophical consequences of submitting the infinite to rational analysis. "One of Michael Blay's (...)
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  11.  8
    The [Mathematical Formula] Quantification Operator in Explicit Mathematics with Universes and Iterated Fixed Point Theories with Ordinals.Markus Marzetta & Thomas Strahm - 1997 - Archive for Mathematical Logic 36 (6):391-413.
    This paper is about two topics: 1. systems of explicit mathematics with universes and a non-constructive quantification operator $\mu$; 2. iterated fixed point theories with ordinals. We give a proof-theoretic treatment of both families of theories; in particular, ordinal theories are used to get upper bounds for explicit theories with finitely many universes.
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  12.  50
    Mathematical and Philosophical Newton: Niccoló Guicciardini: Isaac Newton on Mathematical Certainty and Method. Cambridge, MA: The MIT Press, 2009, 448pp, US$55.00, £40.95 HB Andrew Janiak: Newton as Philosopher. Cambridge: Cambridge University Press, 2008, 208pp, £47 HB.Steffen Ducheyne - 2011 - Metascience 20 (3):467-476.
    Mathematical and philosophical Newton Content Type Journal Article Pages 1-10 DOI 10.1007/s11016-010-9520-2 Authors Steffen Ducheyne, Centre for Logic and Philosophy of Science, Ghent University, Blandijnberg 2, 9000 Ghent, Belgium Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.
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  13.  1
    Taylor Walter. Equational Logic. Houston Journal of Mathematics, Survey 1979. Department of Mathematics, University of Houston, Houston 1979, Iii + 83 Pp. [REVIEW]Heinrich Werner - 1982 - Journal of Symbolic Logic 47 (2):450-450.
  14.  18
    The Usefulness of Mathematical Learning Explained and Demonstrated: Being Mathematical Lectures Read in the Publick Schools at the University of Cambridge.Isaac Barrow - 1734 - London: Cass.
    (I) MATHEMATICAL LECTURES. LECTURE I. Of the Name and general Division of the Mathematical Sciences. BEING about to treat upon the Mathematical Sciences, ...
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  15.  9
    Nidditch P. H.. Introductory Formal Logic of Mathematics. University Tutorial Press Ltd., London 1957, Vii + 188 Pp. [REVIEW]Gert Heinz Müller - 1960 - Journal of Symbolic Logic 25 (1):77-78.
  16.  7
    Goodstein R. L.. Constructive Formalism. Essays on the Foundations of Mathematics. University College, Leicester, England, 1951, 91 Pp.Goodstein R. L.. The Foundations of Mathematics. An Inaugural Lecture Delivered at the University College of Leicester 13th November 1951. University College, Leicester, England, Pub. 1952, 27 Pp. [REVIEW]John Myhill - 1953 - Journal of Symbolic Logic 18 (3):258-260.
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  17. An Euclidean Measure of Size for Mathematical Universes.Vieri Benci, Mauro Nasso & Marco Forti - 2007 - Logique Et Analyse 50.
  18.  4
    Reasoning with the Infinite: From the Closed World to the Mathematical Universe. Michel Blay, M. B. DeBevoise.Antoni Malet - 2000 - Isis 91 (4):778-779.
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  19.  10
    Michel Blay, Reasoning with the Infinite. From the Closed World to the Mathematical Universe (Chicago: University of Chicago Press, 1998) 216 Pp. $ 30.00 (Cloth) ISBN 0 226 05834 4; $ 15.00 (Paper) 0 226 05835 2. [REVIEW]Paolo Mancosu - 1999 - Early Science and Medicine 4 (4):365-366.
  20.  8
    Reasoning with the Infinite. From the Closed World to the Mathematical Universe[REVIEW]Paolo Mancosu - 1999 - Early Science and Medicine 4 (4):365-366.
  21.  35
    Models, Mathematics, and Measurement: A Review of Reconstructing Reality by Margaret MorrisonMargaret Morrison, Reconstructing Reality: Models, Mathematics, and Simulations. Oxford: Oxford University Press , Viii+334 Pp., $65.00. [REVIEW]Paul Humphreys - 2016 - Philosophy of Science 83 (4):627-633.
  22.  6
    Mathematical Intuition and Natural Numbers: A Critical Discussion: Charles Parsons, Mathematical Thought and Its Objects, Cambridge University Press, New York, 2008, Xx+ 378 Pp. [REVIEW]Felix Mühlhölzer - 2010 - Erkenntnis 73 (2):265-292.
    Charles Parsons’ book “Mathematical Thought and Its Objects” of 2008 is critically discussed by concentrating on one of Parsons’ main themes: the role of intuition in our understanding of arithmetic. Parsons argues for a version of structuralism which is restricted by the condition that some paradigmatic structure should be presented that makes clear the actual existence of structures of the necessary sort. Parsons’ paradigmatic structure is the so-called ‘intuitive model’ of arithmetic realized by Hilbert’s strings of strokes. This paper (...)
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  23.  9
    Mathematics and Mathematicians at Sapienza University in Rome.Federica Favino - 2006 - Science & Education 15 (2-4):357-392.
    This article introduces some data regarding the teaching of mathematics in La Sapienza in the 17th century, with particular reference to the discipline’s role in the statutes, the lecturers, the courses’ programmes, the interest that Popes took in it. Specifically, it will focus on the changes that occured at the end of the 17th century, with regards to the development of the discipline and the improvement of a ‘‘scientific culture’’ in the city of the Pope.
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  24. Address at the Princeton University Bicentennial Conference on Problems of Mathematics (December 17-19, 1946).Alfred Tarski & Hourya Sinaceur - 2000 - Bulletin of Symbolic Logic 6 (1):1-44.
    This article presents Tarski's Address at the Princeton Bicentennial Conference on Problems of Mathematics, together with a separate summary. Two accounts of the discussion which followed are also included. The central topic of the Address and of the discussion is decision problems. The introductory note gives information about the Conference, about the background of the subjects discussed in the Address, and about subsequent developments to these subjects.
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  25.  3
    University Mathematics at the Turn of the Century Unpublished Recollections of W. H. Young.I. Grattan-Guinness - 1972 - Annals of Science 28 (4):369-384.
  26.  6
    The Mathematical Aspect of the Universe.James Jeans - 1932 - Philosophy 7 (25):3 - 14.
    In Plutarch’s Quæstiones Conviviales there is a discussion on the topic—π.
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  27. Science and Mathematics: The Scope and Limits of Mathematical Fictionalism: Mary Leng: Mathematics and Reality. Oxford: Oxford University Press, 2010, X+278pp, £39.00 HB. [REVIEW]Christopher Pincock, Alan Baker, Alexander Paseau & Mary Leng - 2012 - Metascience 21 (2):269-294.
    Science and mathematics: the scope and limits of mathematical fictionalism Content Type Journal Article Category Book Symposium Pages 1-26 DOI 10.1007/s11016-011-9640-3 Authors Christopher Pincock, University of Missouri, 438 Strickland Hall, Columbia, MO 65211-4160, USA Alan Baker, Department of Philosophy, Swarthmore College, Swarthmore, PA 19081, USA Alexander Paseau, Wadham College, Oxford, OX1 3PN UK Mary Leng, Department of Philosophy, University of York, Heslington, York, YO10 5DD UK Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.
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  28.  37
    From Universal Mathematics to Universal Method: Descartes's "Turn" in Rule IV of The.Pamela Kraus - 1983 - Journal of the History of Philosophy 21 (2):159-174.
  29.  5
    From Universal Mathematics to Universal Method: Descartes's "Turn" in Rule IV of the "Regulae".Pamela A. Kraus - 1983 - Journal of the History of Philosophy 21 (2):159.
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  30.  19
    Address At The Princeton University Bicentennial Conference On Problems Of Mathematics , By, Pages 1 -- 44.Alfred Tarski & Hourya Sinaceur - 2000 - Bulletin of Symbolic Logic 6 (1):1-44.
    This article presents Tarski's Address at the Princeton Bicentennial Conference on Problems of Mathematics, together with a separate summary. Two accounts of the discussion which followed are also included. The central topic of the Address and of the discussion is decision problems. The introductory note gives information about the Conference, about the background of the subjects discussed in the Address, and about subsequent developments to these subjects.
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  31.  73
    A Pluralist Account of Non-Causal Explanation in Science and Mathematics: Marc Lange: Because Without Cause: Non-Causal Explanation in Science and Mathematics. Oxford: Oxford University Press, 2017, Xxii+489pp, $74.00 HB.Juha Saatsi - 2018 - Metascience 27 (1):3-9.
    Contribution to a review symposium on Marc Lange's Because without cause: Non-causal explanation in science and mathematics. Oxford: Oxford University Press, 2017.
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  32.  11
    Degrees Bounding Principles and Universal Instances in Reverse Mathematics.Ludovic Patey - 2015 - Annals of Pure and Applied Logic 166 (11):1165-1185.
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  33. Mathematical Intuition and Natural Numbers: A Critical Discussion: Charles Parsons, Mathematical Thought and Its Objects, Cambridge University Press, New York, 2008, Xx + 378 Pp.Felix Mühlhölzer - 2010 - Erkenntnis 73 (2):265-292.
    Charles Parsons’ book “Mathematical Thought and Its Objects” of 2008 (Cambridge University Press, New York) is critically discussed by concentrating on one of Parsons’ main themes: the role of intuition in our understanding of arithmetic (“intuition” in the specific sense of Kant and Hilbert). Parsons argues for a version of structuralism which is restricted by the condition that some paradigmatic structure should be presented that makes clear the actual existence of structures of the necessary sort. Parsons’ paradigmatic structure is (...)
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  34.  43
    The Concept of a Universal Learning System as a Basis for Creating a General Mathematical Theory of Learning.Yury P. Shimansky - 2004 - Minds and Machines 14 (4):453-484.
    The number of studies related to natural and artificial mechanisms of learning rapidly increases. However, there is no general theory of learning that could provide a unifying basis for exploring different directions in this growing field. For a long time the development of such a theory has been hindered by nativists' belief that the development of a biological organism during ontogeny should be viewed as parameterization of an innate, encoded in the genome structure by an innate algorithm, and nothing essentially (...)
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  35. Mathematics and Reality.Stewart Shapiro - 1983 - Philosophy of Science 50 (4):523-548.
    The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for engaging in philosophy at all make an account of the relationship between mathematics and reality a priority, not only in philosophy of mathematics and philosophy of science, but also in general epistemology/metaphysics. This is followed by a (rather brief) survey of the major, traditional (...)
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  36.  39
    The Foundations of Mathematics and Other Logical Essays. By Frank Plumpton Ramsey M.A., Fellow and Director of Studies in Mathematics of King's College, Lecturer in Mathematics in the University of Cambridge. Edited by R. B. Braithwaite M.A., Fellow of King's College, Cambridge. With a Preface by G. E. Moore Litt.D., Hon. LL.D., (St. Andrews), F.B.A., Fellow of Trinity College, and Professor of Mental Philosophy and Logic in the University of Cambridge. (London: Kegan Paul, Trench, Trübner & Co. 1931. Pp. Xviii + 292. Price 15s.). [REVIEW]Bertrand Russell - 1932 - Philosophy 7 (25):84-.
  37. Constructive Mathematics: Proceedings of the New Mexico State University Conference Held at Las Cruces, New Mexico, August 11-15, 1980. [REVIEW]Fred Richman (ed.) - 1981 - Springer Verlag.
  38.  21
    Penelope Maddy. Naturalism in Mathematics. Clarendon Press, Oxford University Press, Oxford and New York1998 , Ix + 254 Pp. [REVIEW]Bob Hale - 1999 - Journal of Symbolic Logic 64 (1):394-396.
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  39. Mathematical Platonism and the Nature of Infinity.Gilbert B. Côté - 2013 - Open Journal of Philosophy 3 (3):372-375.
    An analysis of the counter-intuitive properties of infinity as understood differently in mathematics, classical physics and quantum physics allows the consideration of various paradoxes under a new light (e.g. Zeno’s dichotomy, Torricelli’s trumpet, and the weirdness of quantum physics). It provides strong support for the reality of abstractness and mathematical Platonism, and a plausible reason why there is something rather than nothing in the concrete universe. The conclusions are far reaching for science and philosophy.
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  40.  25
    Mathematics, Technology, and Art in Later Renaissance Italy: Alexander Marr: Between Raphael and Galileo: Mutio Oddi and the Mathematical Culture of Late Renaissance Italy. Chicago and London: The University of Chicago Press, 2011, Xiii+359pp, $45.00 HB.Ann E. Moyer - 2014 - Metascience 23 (2):281-284.
    Andrew Marr has built this masterful study of Mutio Oddi on a set of ironies. He begins with a bitter blow of fortune: Oddi, in the middle of an apparently promising life as mathematician and architect in his native Urbino, had fallen afoul of his lord the Duke, accused of participating in a plot to depose him. After years of apparently unjust imprisonment, he was released in 1610, but into exile. Yet Oddi managed to recast his career in Milan and (...)
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  41. Mathematical Shortcomings in a Simulated Universe.Samuel Alexander - 2018 - The Reasoner 12 (9):71-72.
    I present an argument that for any computer-simulated civilization we design, the mathematical knowledge recorded by that civilization has one of two limitations. It is untrustworthy, or it is weaker than our own mathematical knowledge. This is paradoxical because it seems that nothing prevents us from building in all sorts of advantages for the inhabitants of said simulation.
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  42.  22
    Geometry: The First Universal Language of Mathematics.I. G. Bashmakova & G. S. Smirnova - 2000 - In Emily Grosholz & Herbert Breger (eds.), The Growth of Mathematical Knowledge. Kluwer Academic Publishers. pp. 331--340.
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  43.  20
    Realization of Constructive Set Theory Into Explicit Mathematics: A Lower Bound for Impredicative Mahlo Universe.Sergei Tupailo - 2003 - Annals of Pure and Applied Logic 120 (1-3):165-196.
    We define a realizability interpretation of Aczel's Constructive Set Theory CZF into Explicit Mathematics. The final results are that CZF extended by Mahlo principles is realizable in corresponding extensions of T 0 , thus providing relative lower bounds for the proof-theoretic strength of the latter.
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  44.  52
    David Hilbert. Mathematical Problems. Lecture Delivered Before the International Congress of Mathematicians at Paris in 1900. A Reprint of 1084 . Mathematical Developments Arising From Hilbert Problems, Proceedings of the Symposium in Pure Mathematics of the American Mathematical Society, Held at Northern Illinois University, De Kalb, Illinois, May 1974, Edited by Felix E. Browder, Proceedings of Symposia in Pure Mathematics, Vol. 28, American Mathematical Society, Providence1976, Pp. 1–34. - Donald A. Martin. Hilbert's First Problem: The Continuum Hypothesis. A Reprint of 1084 . Mathematical Developments Arising From Hilbert Problems, Proceedings of the Symposium in Pure Mathematics of the American Mathematical Society, Held at Northern Illinois University, De Kalb, Illinois, May 1974, Edited by Felix E. Browder, Proceedings of Symposia in Pure Mathematics, Vol. 28, American Mathematical Society, Providence1976, Pp. 81–92. - G. Kreisel. What Have We Learnt From Hilbert's Second Proble. [REVIEW]C. Smoryński - 1979 - Journal of Symbolic Logic 44 (1):116-119.
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  45.  25
    Greek Mathematics Salomon Bochner: The Role of Mathematics in the Rise of Science. Pp. X+386. Princeton: University Press, 1966. Cloth, 72s. [REVIEW]D. R. Dicks - 1968 - The Classical Review 18 (03):345-348.
  46.  18
    Mathematics The Usefulness of Mathematical Learning Explained and Demonstrated: Being Mathematical Lectures Read in the Publick Schools at the University.… Translated by… John Kirkby . By Isaac Barrow. Reprint. London: Frank Cass, 1970. Pp. Xxxii + 456. £7.35. [REVIEW]D. T. Whiteside - 1972 - British Journal for the History of Science 6 (1):86-88.
  47.  9
    Mesopotamian Mathematics: Eleanor Robson: Mathematics in Ancient Iraq. A Social History, Princeton University Press, Princeton, New Jersey, 2008, Xxiii + 441 Pp, US $49.50 HB.Piedad Yuste - 2010 - Metascience 19 (2):225-227.
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  48.  12
    The Mathematical Association Library at the University of Leicester.R. L. Goodstein - 1974 - British Journal for the History of Science 7 (1):100-103.
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  49.  15
    The Mathematical Practitioners of Hanoverian England 1714–1840. By E. G. R. Taylor. Cambridge University Press for the Institute of Navigation. Pp. Xv + 502. Diagrams. 1966. 84s. [REVIEW]J. F. Scott - 1967 - British Journal for the History of Science 3 (3):300-300.
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  50.  9
    The Mathematical Principles Underlying Newton's 'Principia Mathematica,' Being the Ninth Gibson Lecture in the History of Mathematics Delivered Within the University of GlasgowD. T. Whiteside.Christoph J. Scriba - 1974 - Isis 65 (1):121-121.
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