I. Logicism and Its Demise
Apr. 5: Frege, Foundations of Arithmetic, §§1-17 (pp. 1-24) and §§45-61 (pp. 58-72). Recommended: Shapiro, Thinking about Mathematics, ch. 1 (pp. 3-20).
Apr. 12: Frege, Foundations of Arithmetic, §§62-91 (pp. 73-104); Shapiro, Thinking about Mathematics, beginning of ch. 5 (pp. 107-24).
Apr. 17: Carnap, ``Empiricism, Semantics and Ontology'' (Benacerraf and Putnam, pp. 241-71); Ayer, ``The a priori'' (Benacerraf and Putnam, pp. 315-28); Shapiro, Thinking about Mathematics, end of ch. 5 (pp. 124-39).
Apr. 24: Quine, ``Truth by Convention'' and ``Carnap and Logical Truth'' (Benacerraf and Putnam, pp. 329-76). Recommended: Shapiro, Thinking about Mathematics, ch. 6 (pp. 140-71).
May 1: Benacerraf, ``What Numbers Could Not Be'' (Benacerraf and Putnam, pp. 272-94); Putnam, ``The Analytic and the Synthetic'' (on e-res). Recommended: Shapiro, Thinking about Mathematics, ch. 7 (pp. 172-97). By this date, decide which midterm assignment you are doing.
II. New Problems
May 8: Quine, ``On What There Is'' (on e-res); Benacerraf, ``Mathematical Truth'' (Benacerraf and Putnam, pp. 403-20); Putnam, ``What is Mathematical Truth?'' (on e-res). Recommended: Shapiro, Thinking about Mathematics, ch. 2 (pp. 21-45).
May 15: Chihara, Ontology and the Vicious Circle Principle, ch. 3, §§1-5 (pp. 84-120); ch. 4, §§1-4 (pp. 173-191) and §§7-8 (pp. 200-211). (on e-res) (and midterm paper due).
May 22: Field, Science without Numbers, ``Preliminary Remarks'' and ch. 1-5, except appendix to ch. 1 (pp. 1-16, 20-46) (on e-res); Shapiro, Thinking about Mathematics, ch. 9 (pp. 226-256).
May 29: Maddy, Realism in Mathematics, ch. 2, §§2-3 (pp. 50-75), and ``Physicalistic Platonism'' (on e-res); Shapiro, Thinking about Mathematics, ch. 8 (pp. 201-25).
June 5: Resnik, ``Mathematics as a Science of Patterns: Ontology and Reference'' and ``Mathematics as a Science of Patterns: Epistemology''; D. Lewis, ``Mathematics is Megethology'' (all three on e-res); Shapiro, Thinking about Mathematics, ch. 10.
June 12: final paper due.