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Carnegie Mellon University, Department of Philosophy,
Summer 2000

The Nature of Mathematical Reasoning

Dirk Schlimm

Required Texts

Here is the literature, that is relevant for this course.
  • Jon Barwise and John Etchemendy. The Language of First-Order Logic. CSLI Lecture Notes. CSLI Publications, Stanford, 1993.

  • Selected essays (will be handed out in class).

  • Related Reading

    General Overviews and Historical Material:

  • John Barrow. Pi in the Sky: Counting Thinking and Being. Clarendon Press, 1992.

  • Eric T. Bell. The Magic of Numbers. Dover, 1974.

  • Stanislas Dehaene. The Number Sense. Oxford University Press, 1997.

  • J. Dubbey. Development of Modern Mathematics. Crane, Russek & Co, 1970.

  • H. Eves. An Introduction to the History of Mathematics. Saunders College Publishing, 1983.

  • Clark Glymour. Thinking Things Through. MIT Press, Cambridge, MA, 1992.

  • Morris Kline. Mathematics in Western Culture. Oxford University Press, 1974.

  • A. N. Kolmogorov and A. Yushkevich, editors. Mathematics of the 19th Century: Mathematical Logic, Algebra, Number Theory, Probability Theory. Birkhauser Verlag, Basel, 1992.

  • Robert Osserman. Poetry of the Universe. Anchor Books, 1996.

  • John Paulos. Innumeracy: Mathematical Illiteracy and its Consequences. Hill and Wang, New York, 1988.

  • Ivars Peterson. The Mathematical Tourist: Snapshots of Modern Mathematics. W. H. Freeman and Co., 1988.

  • Logic and Set Theory

  • Jon Barwise and John Etchemendy. Turing's World 3.0. CSLI Lecture Notes #35. CSLI Publications, Stanford, 1993.

  • R. Exner and M. Rosskopf. Logic in Elementary Mathematics. McGraw-Hill, New York, 1959.

  • A. Fraenkel. Abstract Set Theory. North-Holland, Amsterdam, 1961.

  • Gottlob Frege. The Foundations of Arithmetic: A logico-mathematical enquiry into the concept of number. Philosophical Library, 1950. Original: 1884.

  • K. Hrbacek and T. Jech. Introduction to Set Theory. Marcel Dekker, New York, 1984.

  • G. Hunter. Metalogic. Univ. of California Press, Berkeley, CA, 1973.

  • Stephen Kleene. troduction to Metamathematics. Wolters-Noordhoff, Groningen, 1954.

  • D. Kalish, R. Montague, and G. Mar. Logic: Techniques of Formal Reasoning. arcourt Brace Javanonich, 1984.

  • Rudy Rucker. Infinity and the Mind. Princeton University Press, Princeton N.J., 1995.

  • P. Suppes. Introduction to Logic. D. Van Nostrand, New York, 1957.

  • On Gödel's theorems

  • Ernest Nagel and James R. Newman. Gödel's proof. New York University Press, 1958.

  • Douglas R. Hofstadter. Gödel, Escher, Bach : an eternal golden braid. Basic Books, New York, 1979.

  • Logic and Mathematical Problem Solving

  • M. Gardner. The Scientific American Book of Mathematical Puzzles & Diversions. Simon and Schuster, New York, 1959.

  • G. Polya. How to Solve It : A New Aspect of Mathematical Method. Princeton University Press, Princeton, N.J, 1973.

  • R. Smullyan. What is the Name of this Book?. Simon and Schuster, New York, 1978.

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    © Dirk Schlimm, Last modified: August 4, 2000