Philosophy of Mathematics 2004/2005; 2nd Semester Institute for Logic, Language & Computation Universiteit van Amsterdam

Objectives. This course is both a course for philosophers (with sufficient formal skills) to learn something about a particular and peculiar branch of philosophy of science dealing with abstract entities, and a course for logicians to see connections between the history and mathematical investigation of logic and their applications in philosophy.

Contents. We cover the basic questions of Philosophy of Mathematics: Ontology - Truth - Knowledge. We discuss the standard approaches towards these questions by the different schools: Platonists, Formalists, Naturalists, Structuralists and others. We also discuss historically important schools of philosophy of mathematics like the logicists and the intuitionists.

Format. Lectures, student presentations, plenary discussions.
Syllabus: PDF-File.
Read the GRE Scoring Guidelines and the GRE Samples for essay writing with grades. (As a rough guideline, benchmark 6 would be 'excellent', benchmark 5 between 'excellent' and 'good', benchmark 4 between 'good' and 'OK', benchmark 3 'OK', and benchmark 2 and benchmark 1 'not OK'.)

Study materials. Stewart Shapiro, Thinking about Mathematics, Oxford University Press 2000 (amazon.de).

Classes:

• February 9. Lecture. Technicalities. The fundamental questions of philosophy of science and mathematics (p.3-20).
• February 16. Lecture. Some basic positions of ontology and epistemology (p.21-45).
• February 23. Presentations & Discussion. Plato (p.49-63).
  Presenters: H. van den Berg, C. Foster, S. van Otterloo
  Homework Assignment #1 (Deadline: March 9th, 2005). PDF-File
• March 2. CANCELLED.
• March 9. Presentations & Discussion. Aristotle (p.63-72).
  Presenters: R. Carota, I. Dimitriou . Aristotle, Metaphysics. Book M. Book N.
• March 16. Presentations & Discussion. Kant and Mill (p.73-103).
  Presenters: H. van den Berg, T. Daniëls, W. Koolen-Wijkstra, G. de Vries . Slides: PDF-File.
  Homework Assignment #2 (Deadline: April 6th, 2005). PDF-File.
  Crispin Wright, Is Hume's Principle Analytic?, Notre Dame Journal of Formal Logic 40 (1999), p. 6-30; PDF-File.
• March 23. Presentations & Discussion. Logicism (p.107-139).
  Presenters: E. Andrade, C. Foster, (S. Holland). Slides: Frege. Russell. Neologicism. Carnap.
• March 30. EXAM WEEK. There will be no midterm for this course but no class either.
• April 6. Presentations & Discussion. Formalism I: Frege and the early Hilbert (p.140-157).
  Presenters: E. Andrade, T. Daniëls. Slides: Basic Formalism, Hilbert.
• April 13. Presentations & Discussion. Formalism II: Hilbert's Programme and its collapse (p.158-171).
  Presenters: J. Cassee, G. Lacerda, M. Pennings. Slides: PDF-File.
• April 20. Presentations & Discussion. Intuitionism (p.172-197).
  Presenters: W. Koolen-Wijkstra, M. Pennings. Slides: PDF-File.
• April 27. Presentations & Discussion. Platonism: Gödel and Quine (p.201-220).
  Presenters: R. Carota, S. Holland, G. de Vries
  Homework Assignment #3 (Deadline: May 11th, 2005). PDF-File.
  Gideon Rosen, Review of Naturalism in mathematics by P. Maddy, British Journal of Philosophy of Science 50 (1999), p.467-474: PDF-File
• May 4. Presentations & Discussion. Maddy: Set-theoretic realism and set-theoretic naturalism. (p.220-225 and Penelope Maddy, Three forms of naturalism, in: Stewart Shapiro (ed.), The Oxford Handbook of Philosophy of Mathematics and Logic, Oxford University Press 2005, p.437-459: PDF-File).
  Further Reading:
  Penelope Maddy, Some Naturalistic Reflections on Set Theoretic Method, Topoi 20 (2001), p.17-27: PDF-File.
  Penelope Maddy, Set-theoretic naturalism, Journal of Symbolic Logic 61 (1996), p. 490-514. Accessible from UvA computers via JSTOR.
  Presenters: I. Dimitriou, H. Nordmark, J. Vosmaer
• May 11. Presentations & Discussion. Nominalism (p.226-243).
  Presenters: J. Cassee, G. Lacerda
• May 18. Presentations & Discussion. Structuralism (p.257-289).
  Presenters: H. Nordmark, J. Vosmaer
• May 25. EXAM WEEK. Written final three-hour exam with six questions in P.018; 16:15 - 19:00.