Ad Infinitum

Reading Schedule -- updated 4/30

E-Reserves

Links

• Parthenon 1 2 3 and Chartres 1 2 3 4
• Large Numbers
• Who Can Name the Bigger Number? -- Scott Aaronson
• Busy Beavers and Knuth up-arrows-- Wikipedia
• Constructivism is Difficult -- Eric Schechter
• Was Pythagoras Chinese? -- also see Wikipedia and Stanford Encyclopedia articles on Pythagoras.
• Simplicius, "Five arguments for the existence of the unlimited” from Commentary on Aristotle's Physics III, pp. 85-91.
• Thomas Heath, “Aristotle on the Continuous and the Infinite” --from History of Greek Mathematics, pp. 342-344.
• Bertrand Russell, "The Philosophy of the Continuum" --from Principles of Mathematics, pp. 346-354.
• Harold Cherniss on Aristotle's discussion of Zeno --from from Aristotle’s Criticism of Presocratic Philosophy, pp. 155-161.
• Archimedes Palimpsest -- see Wikipedia article here.
• Nova site on Archimedes -- includes Approximating PI (an interactive Flash applet).
• Archimedes, Quadrature of the Parabola -- also see the Wikipedia entry. A nice visualization of the mechanical proof is given at Matematicas Visuales and there is an excellent discussion of the geometrical proof here.
• Saint Augustine on Time -- from Book XI of the Confessions
• William of Ockham, "Is a line composed of points? -- Quodlibet I, q 9.
• William of Ockham, On the Infinite Power of God -- Quodlibets II, q. 2; III, q 1; VII, q. 18. on e-reserve.
• Philip E. B. Jourdain,"The Rise of Modern Mathematics -- The Infinitesimal Calculus", from The Nature of Mathematics, pp. 94-108
• The Analyst: or, A Discourse Addressed to an Infidel Mathematician --Bishop Berkeley's famous polemic on the infinitesimal calculus (complete text). Related documents here.
• Bertrand Russell, The Infinitesimal Calculus -- from Principles of Mathematics
• Stanford Encyclopedia of Philosophy article on Bernard Bolzano (1781-1848)
• Peter Suber, A Crash Course in the Mathematics of Infinite Sets
• Hans Hahn, "Infinity"
• Joseph Dauben, Georg Cantor and the Battle for Transfinite Set Theory (.pdf)
• Wikipedia article on Georg Cantor
• Kurt Gödel, What is Cantor's Continuum Problem?
• Jerome H. Keisler Elementary Calculus: an Approach Using Infinitesimals (1976) -- a text based upon Abraham Robinson, Non-standard Analysis (1966)
• Ladislav Kvasz, The Invisible Link Between Mathematics and Theology
• Alvin Plantinga and Patrick Grim, Truth, Omniscience, and Cantorian Arguments
• Fred Richman, Confessions of a formalist, Platonist intuitionist
• The Axiom of Choice Home Page -- Eric Schechter
• Articles from the Stanford Encyclopedia of Philosophy
  • Continuity and Infinitesmals
  • Supertasks
  • Intuitionistic Logic
  • Hilbert's Program
  • Wittgenstein's Philosophy of Mathematics
  • Set Theory: Constructive and Intuitionistic ZF

• Kurt Gödel
  • On Formally Undecidable Propositions of Principia Mathematica and Related Systems --the text of Gödel's 1931 paper in a translation which uses modern notation.
  • The modern development of the foundations of mathematics in the light of philosophy --Gödel (1961)
  • Gödel's Theorem and Around --K. Podnieks
  • Gödel's Proof --Peter Suber
  • Gödel's Philosophy of Mathematics --Harold Ravitch
  • Minds, Machines and Gödel and The Implications of Gödel's Theorem --J. R. Lucas
  • Links to Articles on Gödel and AI (with responses to J.R. Lucas and Roger Penrose) --David Chalmers and David Bourget
  • Portraits of Kurt Gödel

• Constructive Mathematics -- Fred Richman
• A Constructivist Perspective on Physics -- Peter Fletcher
• The Unreasonable Effectiveness of Mathematics in the Natural Sciences --Eugene Wigner
• Notes on Intuitionism
• Collective Nouns -- also see here
• Uselessness of set theory? -- from Richard Borcherds' blog, Mathematics and Physics
• Nik Weaver, Is Set Theory Indispensable?
• Splitting Time from Space -- on Hořava Gravity (Scientific American, November, 2009)
• Einstein, Poincare, and Modernity -- Peter Galison and D. Graham Burnett
• Peirce's Clarifications of Continuity by Jérôme Havenel
• Dedekind-infinite sets -- Wikipedia
• On the Number of Russell's socks or 2 + 2 + 2 +. . . = ? -- Herrlich and Tachtsis
• A Note from Brian Wynne
• The Infinite -- Thomas Jech
• Infinite Reflections -- Peter Suber