Proof and Other Dilemmas

Book cover

In 2008, POM SIGMAA founders Bonnie Gold and Roger A. Simons edited a volume, "Proof and Other Dilemmas: Mathematics and Philosophy", and published it in the MAA Spectrum series. This volume has articles on a wide range of questions related to Philosophy of Mathematics, ranging from proof, the nature of mathematical objects, mathematics as it is practiced, and so on. Contributors include many members of POM SIGMAA.

Table of Contents
  1. Proof and How it is Changing
    1. Proof: Its Nature and Significance, Michael Detlefsen
    2. Implications of Experimental Mathematics for the Philosophy of Mathematics, Jonathan Borwein
    3. On the Roles of Proof in Mathematics, Joseph Auslander
  2. Social Constructivist Views of Mathematics
    1. When Is a Problem Solved?, Philip J. Davis
    2. Mathematical Practice as a Scientific Problem, Reuben Hersh
    3. Mathematics Domains: Social Constructs?, Julian Cole
  3. The Nature of Mathematical Objects and Mathematical Knowledge
    1. The Existence of Mathematical Objects, Charles Chihara
    2. Mathematical Objects, Stewart Shapiro
    3. Mathematical Platonism, Mark Balaguer
    4. The Nature of Mathematical Objects, Øystein Linnebo
    5. When is One Thing Equal to Some Other Thing?, Barry Mazur
  4. The Nature of Mathematics and its Applications
    1. Extreme Science: Mathematics as the Science of Relations as Such, R. S. D. Thomas
    2. What is Mathematics? A Pedagogical Answer to a Philosophical Question, Guershon Harel
    3. What Will Count as Mathematics in 2100?, Keith Devlin
    4. Mathematics Applied: The Case of Addition, Mark Steiner
    5. Probability--A Philosophical Overview, Alan Hajek

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