24.801: Philosophy of Mathematics

Fall 2000


This seminar takes up four or five related topics. First, the relations if any between realism (the view that mathematics is "objective") and platonism (which postulates the existence of mathematical objects).   Second, a recently influential version of platonism whose authors mean their approach to be consistent with antirealism. This is "Fregean Platonism" as proposed originally by Crispin Wright.   Third, the relations if any between fictionalism as maintained by Hartry Field and figuralism as maintained by yours truly.  Fourth, the alleged necessity of mathematical objects and mathematical truth.  Fifth,  if there's time,  the bearing of all this on mathematical practice.
Stephen Yablo, Philosophy
Office: E39-314
Phone: 258-0740
Office Hours: by appointment
E-mail: yablo@mit.edu
Thursdays 2:00-5:00 in 39-335
Papers will be available for copying in the rack by the graduate student mailboxes. See below for a list of likely readings. There may be the odd classroom handout as well.
Requirements Notes TENTATIVE SCHEDULE:

September 7   Platonism & Realism: Actualist Strategies

September 14  Platonism & Realism: Modal Strategies September 21  Fregean Platonism: Bad Company September 28 Fregean Platonism: Julius Caesar October 5  Fregean Platonism: Logical Issues October 12 Fictionalism October 19  Figuralism October 26  Are Numbers Necessary?

November 2  Or Do They Just Seem That Way?

November 9 Mathematical Practice: Explanation November 16 Mathematical Practice: New Objects

November 23 Thanksgiving Holiday

November 30 Mathematical Practice: New Axioms

December 7 Mathematical Practice: New Concepts


  1. Shapiro & Weir, "New V, ZF, and Abstraction"
  2. Shapiro & Weir, "Neo-Logicist Logic"
  3. Rosen, "A Study in Modal Deviance"
  4. Rosen, "Refutation of Nominalism(?)"
  5. Detlefsen, "Fregean Hierarchies and Mathematical Explanation"
  6. Field, "The Conceptual Contingency of Abstract Objects"
  7. Hale/Wright, "Nominalism and the Contingency of Abstract Objects"
  8. Hale, "Is Platonism Epistemologically Bankrupt?"
  9. Goodman, "Mathematics as a Natural Science"
  10. Kessler, "Mathematics and Modality"
  11. Putnam, "Mathematics Without Foundations"
  12. Gemes, "Explanation, Unification, and Content"
  13. Manders, "Domain Extension and the Philosophy of Mathematics"
  14. Manders, "Logical and Conceptual Relations in Mathematics"
  15. Kitcher, "Innovation and Understanding in Mathematics"
  16. Detlefsen, "Fregean Hierarchies and Mathematical Explanation"
  17. Maddy, "The Roots of Contemporary Platonism"
  18. Burgess, "Why I Am Not A Nominalist"
  19. Linsky & Zalta, "Naturalized Platonism versus Platonized Naturalism"
  20. Linsky & Zalta, review of Balaguer, Platonism and Anti-Platonism in Mathematics
  21. Kitcher, "Frege's Epistemology"
  22. Steiner, "Mathematics, Explanation, and Scientific Knowledge"
  23. McCarthy, "Platonism and Possibility"
  24. Friedman, "Explanation and Scientific Understanding"
  25. Chihara, "Mathematical Discovery and Concept Formation"
  26. Wright, "On the Philosophical Significance of Frege's Theorem"
  27. Wright, "On the Harmless Impredicativity of N= (Hume's Principle)"
  28. Boolos, "Is Hume's Principle Analytic?"
  29. Parsons, "Wright on Abstraction and Set Theory"
  30. Heck, "The Julius Caesar Objection"
  31. Sandborg, "Mathematical Explanation and the Theory of Why-Questions"
  32. Detlefsen, "Fregean Hierarchies & Math. Explanation"
  33. Steiner, "Mathematical Explanation"
  34. Kitcher, "Explanatory Unification"
  35. Manders, "Logic and Conceptual Relns in Math"
  36. Beall, "From Full-Blooded Plat to Really..."
  37. Tappenden, "Extending Knowledge and Fruitful Concepts"
  38. Cheyne, "Problems with Profligate Platonism"
  39. Tennant, "On the Necessity of Mathematical Objects"