ثَبْت المراجع

كتب

  • Niels H. Abel, Oeuvres complètes, v. 2, Johnson Reprint Corp., 1964.
  • Alexander Abian, The Theory of Sets and Transfinite Arithmetic, W.B. Saunders Co., 1965.
  • Howard Anton, Calculus with Analytic Geometry, John Wiley & Sons, 1980.
  • John D. Barrow, Pi in the Sky: Counting, Thinking, and Being, Clarendon/Oxford University Press, 1992.
  • Paul Benacerraf and Hilary Putnam, Eds., Philosophy of Mathematics: Selected Readings, Prentice-Hall, 1964.
  • J. A. Benardate, Infinity: An Essay in Metaphysics, Clarendon/Oxford University Press, 1964.
  • Eric T. Bell, Men of Mathematics, Simon & Schuster, 1937.
  • David Berlinski, A Tour of the Calculus, Pantheon Books, 1995.
  • Max Black, Problems of Analysis, Cornell University Press, 1954.
  • Carl Boyer, A History of Mathematics, 2nd ed. w/Uta Merzbach, John Wiley & Sons, 1991.
  • T. J. I. Bromwich and T. MacRobert, An Introduction to the Theory of Infinite Series, 3rd ed., Chelsea Books, 1991.
  • Bryan H. Bunch, Mathematical Fallacies and Paradoxes, Van Nostrand Reinhold Co., 1982.
  • Georg Cantor, Contributions to the Founding of the Theory of Transfinite Numbers, trans. P. E. B. Jourdain, Open Court Publishers, 1915; Reprint = Dover Books, 1960.
  • Georg Cantor, Transfinite Numbers: Three Papers on Transfinite Numbers from the Mathematische Annalen, G. A. Bingley Publishers, 1941.
  • Georg Cantor, Gesammelte Abhandlungen mathematischen und philosophischen Inhalts (= Collected Papers). Eds. E. Zermelo and A. Fraenkel. 2nd ed., G. Olms Verlagsbuchhandlung, Hildesheim FRG, 1966.
  • Augustin-Louis Cauchy, Cours d’analyse algébrique, = v. 3 of Cauchy, Oeuvres complètes, 2nd ed., Gauthier-Villars, Paris FR, 1899.
  • Jean Cavaillès, Philosophie mathématique, Hermann, Paris FR, 1962 (has French versions of all the important Cantor-Dedekind correspondence on pp. 179–251).
  • Nathalie Charraud, Infini et Inconscient: Essai stir Georg Cantor, Anthropos, Paris FR, 1994.
  • Christopher Clapham, Ed., The Concise Oxford Dictionary of Mathematics, 2nd ed., Oxford University Press, 1996.
  • Paul J. Cohen, Set Theory and the Continuum Hypothesis, W. A. Benjamin, Inc., 1966.
  • Frederick Copleston, A History of Philosophy, v. I pt. II, Image Books, 1962.
  • Richard Courant and Herbert Robbins (Revised by Ian Stewart), What is Mathematics? An Elementary Approach to Ideas and Methods, Oxford Press, 1996.
  • Joseph W. Dauben, Georg Cantor: His Mathematics and Philosophy of the Infinite, Princeton University Press, 1979.
  • Richard Dedekind, Essays on the Theory of Numbers, trans. W. W. Beman, Open Court Publishing Co., 1901; Reprint = Dover Books, 1963.
  • Paul Edwards, Ed., The Encyclopedia of Philosophy, 1st ed., v. 1–8, Collier MacMillan Publishers, 1967.
  • P. E. Erlich, Ed., Real Numbers, Generalizations of the Reals, and Theories of Continua, Kluwer Academic Publishers, 1994.
  • J.-B. Joseph Fourier, Analytic Theory of Heat, Dover Books, 1955.
  • Abraham Fraenkel, Set Theory and Logic, Addison-Wesley Publishing Co., 1966.
  • Galileo Galilei, Dialogues Concerning Two New Sciences, Dover Books, 1952.
  • Alan Gleason, Who Is Fourier? Transnational College of LEX/Language Research Foundation, 1995.
  • Kurt Gödel, The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory, Princeton University Press, 1940.
  • Ivor Grattan-Guinness, Ed., From the Calculus to Set Theory, Gerald Duckworth & Co., London UK, 1980.
  • Leland R. Halberg and Howard Zink, Mathematics for Technicians, with an Introduction to Calculus, Wadsworth Publishing Co., 1972.
  • Michael Hallett, Cantorian Set Theory and Limitation of Size, Oxford University Press, 1984.
  • G. H. Hardy, Divergent Series, Oxford University/Clarendon Press, 1949.
  • G. H. Hardy, A Mathematician’s Apology, Cambridge University Press, 1967/1992.
  • T. L. Heath, The Thirteen Books of Euclid’s Elements, v. 1–3, Dover Books 1954.
  • Hugh Honour and John Fleming, The Visual Arts: A History, Prentice-Hall, 1982.
  • Geoffrey Hunter, Metalogic: An Introduction to the Metatheory of Standard First Order Logic, University of California Press, 1971.
  • E. V. Huntington, The Continuum and Other Types of Serial Order, with an Introduction to Cantor’s Transfinite Numbers, Harvard University Press, 1929.
  • Stephen C. Kleene, Introduction to Metamathematics, Van Nostrand, 1952.
  • Morris Kline, Mathematical Thought from Ancient to Modern Times, v. 1–3, Oxford University Press, 1972.
  • George J. Klir and Bo Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice-Hall, 1995.
  • Shaughan Lavine, Understanding the Infinite, Harvard University Press, 1994.
  • Paolo Mancuso, Ed., From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s, Oxford University Press, 1998.
  • W. G. McCallum, D. Hughes-Hallett, and A. M. Gleason, Multivariable Calculus (Draft Version), John Wiley & Sons, 1994.
  • Richard McKeon, Ed., Basic Works of Aristotle, Random House, 1941.
  • Elliott Mendelson, Introduction to Mathematical Logic, 2nd ed., D. Van Nostrand Co., 1979.
  • Robert Miller, Bob Miller’s Calc I Helper, McGraw-Hill, 1991.
  • David Nelson, Ed., The Penguin Dictionary of Mathematics, 2nd ed., Penguin Books, 1989.
  • Theoni Pappas, Mathematical Scandals, Wide World Publishing, 1997.
  • Henri Poincaré, Mathematics and Science: Last Essays, trans. J. W. Boldue, Dover Books, 1963.
  • W. V. O. Quine, Set Theory and Its Logic, Belknap/Harvard University Press, 1963.
  • Georg F. B. Riemann, Collected Mathematical Works, Dover Books, 1953.
  • Rudy Rucker, Infinity and the Mind, Birkhäuser Boston, Inc., 1982.
  • Bertrand Russell, Introduction to Mathematical Philosophy, Allen and Unwin, London UK, 1919.
  • Bertrand Russell, Mysticism and Logic, Doubleday Anchor Books, 1957.
  • Bertrand Russell, Principles of Mathematics, 2nd ed., W. W. Norton & Co., 1938.
  • Gilbert Ryle, Dilemmas: The Tarner Lectures 1953, Cambridge University Press, 1960.
  • R. M. Sainsbury, Paradoxes, Cambridge University Press, 1987.
  • Ferdinand de la Saussure, Cours de linguistique générale (R. Engler, Ed.), Harrasowitz, Wiesbaden FRG, 1974.
  • Charles Seife, Zero: The Biography of a Dangerous Idea, Viking Press, 2000.
  • Waclaw Sierpinski, Hypothèse du Continu, Monografie Matematyczne, Warsaw PL, 1934.
  • Patrick Suppes, Axiomatic Set Theory, D. Van Nostrand Co., 1965.
  • University of St. Andrews, MacTutor History of Mathematics Web Site:www.groups.dcs.st-and.ac.uk/~history’.
  • I. M. Vinogradov, Ed., Soviet Mathematical Encyclopedia, v. 9, Kluwer Academic Publishers, 1993.
  • Eric W. Weisstein, CRC Concise Encyclopedia of Mathematics, CRC Press, 1999.
  • Hermann Weyl, Philosophy of Mathematics and Natural Science, Princeton University Press, 1949.

مقالات وأبحاث

  • George Berkeley, “The Analyst, Or a Discourse Addressed to an Infidel Mathematician Wherein It is Examined Whether the Object, Principles, and Inferences of the Modern Analysis are More Distinctly Conceived, or More Evidently Deduced, than Religious Mysteries and Points of Faith. ‘First Cast the Beam Out of Thine Own Eye; and Then Shalt Thou See Clearly to Cast Out the Mote Out [sic] of Thy Brother’s Eye,”’ in A. A. Luce, Ed., The Works of George Berkeley, Bishop of Cloyne, Thomas Nelson & Sons, 1951.
  • Jorge L. Borges, “Avatars of the Tortoise,” in D. Yates and J. Irby, Eds., Labyrinths, New Directions, 1962, pp. 202–208.
  • Luitzen E. J. Brouwer, “Intuitionism and Formalism,” trans. A. Dresden, Bulletin of the American Mathematical Society v. 30, 1913, pp. 81–96.
  • Georg Cantor, “Foundations of the Theory of Manifolds,” trans. U. R. Parpart, The Campaigner No. 9, 1976, pp. 69–97.
  • Georg Cantor, “Principien einer Theorie der Ordnungstypen” (= “Principles of a Theory of Order-Types”), mss. 1885, in I. Grattan-Guinness, “An Unpublished Paper by Georg Cantor,” Acta Mathematica v. 124, 1970, pp. 65–106.
  • Joseph W. Dauben, “Denumerability and Dimension: The Origins of Georg Cantor’s Theory of Sets,” Rete v. 2, 1974, pp. 105–135.
  • Joseph W. Dauben, “Georg Cantor and Pope Leo XIII: Mathematics, Theology, and the Infinite,” Journal of the History of Ideas v. 38, 1977, pp. 85–108.
  • Joseph W. Dauben, “The Trigonometric Background to Georg Cantor’s Theory of Sets,” Archive for the History of the Exact Sciences v. 7, 1971, pp. 181–216.
  • H. N. Freudenthal, “Did Cauchy Plagiarize Bolzano?” Archive for the History of the Exact Sciences v. 7, 1971, pp. 375–392.
  • Kurt Gödel, “Russell’s Mathematical Logic,” in P. A. Schlipp, Ed., The Philosophy of Bertrand Russell, Northwestern University Press, 1944.
  • Kurt Gödel, “What is Cantor’s Continuum Problem?” in Benacerraf and Putnam’s Philosophy of Mathematics, pp. 258–273.
  • Ivor Grattan-Guinness, “Towards a Biography of Georg Cantor,” Annals of Science v. 27 No. 4, 1971, pp. 345–392.
  • G. H. Hardy, “Mathematical Proof,” Mind v. 30, 1929, pp. 1–26.
  • David Hilbert, “Über das Unendliche,Acta Mathematica v. 48, 1926, pp. 91–122.
  • Leonard Hill, “Fraenkel’s Biography of Georg Cantor,” Scripta Mathematica No. 2, 1933, pp. 41–47.
  • Abraham Robinson, “The Metaphysics of the Calculus,” in J. Hintikka, Ed., The Philosophy of Mathematics, Oxford University Press, 1969, pp. 153–163.
  • Rudolf V. B. Rucker, “One of Georg Cantor’s Speculations on Physical Infinities,” Speculations in Science and Technology, 1978, pp. 419–421. Rudolf v. B. Rucker, “The Actual Infinite,” Speculations in Science and Technology, 1980, pp. 63–76.
  • Bertrand Russell, “Mathematical Logic as Based on the Theory of Types,” American Journal of Mathematics v. 30, 1908-1909, pp. 222–262.
  • Waclaw Sierpinski, “L’Hypothèse généralisée du continu et l’axiome du choix,” Fundamenta Mathematicae v. 34, 1947, pp. 1–6.
  • H. Wang, “The Axiomatization of Arithmetic,” Journal of Symbolic Logic v. 22, 1957, pp. 145–158.
  • R. L. Wilder, “The Role of the Axiomatic Method,” American Mathematical Monthly v. 74, 1967, pp. 115–127.
  • Frederick Will, “Will the Future Be Like the Past?” in A. Flew, Ed., Logic and Language, 2nd Series, Basil Blackwell, Oxford UK, 1959, pp. 32–50

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