Results for 'mathematical universe'

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  1. 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.  50
    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.  20
    Reasoning with the Infinite: From the Closed World to the Mathematical Universe.Michel Blay - 1998 - 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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  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.  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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  7.  33
    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. An Euclidean Measure of Size for Mathematical Universes.Vieri Benci, Mauro Nasso & Marco Forti - 2007 - Logique Et Analyse 50.
  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.  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.
  12.  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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  13.  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.
  14.  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.
  15.  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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    Mathematical Sciences J. L. Heilbron & Bruce R. Wheaton, Literature on the History of Physics in the Twentieth Century. Berkeley: University of California Office for History of Science and Technology, 1981. Pp. Xi + 485. No Price Stated. ISBN 0-918102-012-2. David De Vorkin, The History of Modern Astronomy and Astrophysics. A Selected, Annotated, Bibliography. New York: Garland Publishing, 1982. Pp. Xxvii + 434. $65.00. ISBN 0-8240-9283-X. [REVIEW]John Hendry - 1983 - British Journal for the History of Science 16 (3):292-293.
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  17.  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.
  18.  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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  19.  7
    Mathematics and Plausible Reasoning. G. Polya Princeton: Princeton University Press, 1954. Vol. I, Induction and Analogy in Mathematics, Pp. Xii, 280, $5.50. Vol. II, Patterns of Plausible Inference, Pp. X, 190, $4.50. The Set $9.00.Tibor Rado - 1956 - Philosophy of Science 23 (2):167-167.
  20. 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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  21.  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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  22.  7
    Richard J.Oosterhoff. Making Mathematical Culture: University and Print in the Circle of Lefèvre D’Étaples. Oxford, United Kingdom: Oxford University Press, 2018, Xiv + 276 Pp. ISBN: 9780198823520. [REVIEW]Angela Axworthy - 2020 - Centaurus 62 (1):211-213.
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  23.  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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  24. 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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  25.  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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  26.  18
    Exotic Worlds: Victorian Mathematics: Raymond Flood, Adrian Rice, Robin Wilson : Mathematics in Victorian Britain. Oxford: Oxford University Press, 2011, Ix+466pp, £29.99, $55.00 HB. [REVIEW]David E. Rowe - 2013 - Metascience 22 (2):447-450.
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  27.  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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  28.  47
    Models, Mathematics, and Measurement: A Review of Reconstructing Reality by Margaret Morrison - Margaret Morrison, Reconstructing Reality: Models, Mathematics, and Simulations. Oxford: Oxford University Press (2015), Viii+334 Pp., $65.00 (Cloth). [REVIEW]Paul Humphreys - 2016 - Philosophy of Science 83 (4):627-633.
  29.  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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  30. Universal Algorithmic Intelligence: A Mathematical Top-Down Approach.Marcus Hutter - 2007 - In Ben Goertzel & Cassio Pennachin (eds.), Artificial General Intelligence. Springer Verlag. pp. 227-290.
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  31.  24
    Mathematics and Poetry in Hellenistic Alexandria - R. Netz Ludic Proof. Greek Mathematics and the Alexandrian Aesthetic. Pp. XVI + 255, Figs. Cambridge: Cambridge University Press, 2009. Cased, £62, Us$107. Isbn: 978-0-521-89894-2. [REVIEW]Markus Asper - 2013 - The Classical Review 63 (1):75-77.
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  32. 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.
  33.  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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  34.  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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  35.  8
    Mathematics in Philosophy, Selected Essays, by Charles Parsons, Cornell University Press, Ithaca, N.Y., 1983, 365 Pp. [REVIEW]Stewart Shapiro - 1988 - Journal of Symbolic Logic 53 (1):320-329.
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  36.  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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  37.  7
    Mathematics in Kant's Critical Philosophy.Emily Carson & Lisa Shabel (eds.) - 2015 - Routledge.
    There is a long tradition, in the history and philosophy of science, of studying Kant’s philosophy of mathematics, but recently philosophers have begun to examine the way in which Kant’s reflections on mathematics play a role in his philosophy more generally, and in its development. For example, in the Critique of Pure Reason , Kant outlines the method of philosophy in general by contrasting it with the method of mathematics; in the Critique of Practical Reason , Kant compares the Formula (...)
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  38.  10
    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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  39.  58
    Advances in Contemporary Logic and Computer Science: Proceedings of the Eleventh Brazilian Conference on Mathematical Logic, May 6-10, 1996, Salvador, Bahia, Brazil. [REVIEW]Walter A. Carnielli, Itala M. L. D'ottaviano & Brazilian Conference on Mathematical Logic - 1999
    This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society (co-sponsored by the Centre for Logic, Epistemology and the History of Science, State University of Campinas, Sao Paulo) in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and (...)
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  40.  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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  41.  26
    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.
  42. Reviews: Mathematics and Logic-Symbols, Impossible Numbers, and Geometric Entanglements: British Algebra Through the Commentaries on Newton's Universal Arithmetick. [REVIEW]Helena M. Pycior & M. Seltman - 1998 - Annals of Science 55 (4):438-439.
     
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  43.  20
    Mathematics La Logique de Charles Sanders Peirce. De l'Algèbre aux Graphes. By Pierre Thibaud. Aix En Provence: Université de Provence, 1975. Pp. 184. 50 Francs. Men and Institutions in American Mathematics. Edited by J. Dalton Tarwater, John T. White and John D. Miller. Lubbock, Texas: Texas Tech. University, 1976. Pp. 136. $5.00. [REVIEW]I. Grattan-Guinness - 1977 - British Journal for the History of Science 10 (3):255-256.
  44.  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.
  45.  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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  46. 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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  47.  18
    Mathematics - The Mathematical Papers of Isaac Newton, Volume III, 1670–1673. Ed. By D. T. Whiteside, with the Assistance in Publication of M. A. Hoskin and A. Prag. London: Cambridge University Press. 1969. Pp. Xxxvii + 576. £10 10s. [REVIEW]J. D. North - 1970 - British Journal for the History of Science 5 (2):188-189.
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  48.  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.
  49.  18
    Economics - Mathematical Politics or Science of Diminishing Returns? Rosenberg Alexander. University of Chicago Press, 1992, Xvii + 266 Pages. [REVIEW]A. W. Coats - 1995 - Economics and Philosophy 11 (2):386.
  50.  20
    The Universe in Zero Words: The Story of Mathematics as Told Through Equations. [REVIEW]Marcel Boumans - 2015 - The European Legacy 20 (5):558-559.
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