Instructor: Dr Benedikt Löwe
Time: Wednesday, 17-19
ECTS credit points: 6
Course language: English
Intended Audience: M.Sc. students of Logic and Mathematics,
M.A. students of Philosophy
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.
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.
Lectures, student presentations, plenary discussions.
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'.)
Stewart Shapiro, Thinking about Mathematics, Oxford University Press 2000
- 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
- February 23. Presentations & Discussion. Plato
Presenters: H. van den Berg, C. Foster, S. van
Homework Assignment #1 (Deadline: March 9th, 2005). PDF-File
- March 2. CANCELLED.
- March 9. Presentations & Discussion. Aristotle
Presenters: R. Carota, I. Dimitriou
- March 16. Presentations & Discussion. Kant and Mill
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.
Principle Analytic?, Notre Dame Journal of Formal Logic 40
(1999), p. 6-30; PDF-File.
- March 23. Presentations & Discussion. Logicism
Presenters: E. Andrade, C. Foster, (S.
- 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.
- April 13. Presentations & Discussion. Formalism II:
Hilbert's Programme and its collapse
Presenters: J. Cassee, G. Lacerda, M.
- April 20. Presentations & Discussion. Intuitionism
Presenters: W. Koolen-Wijkstra, M.
- 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).
Gideon Rosen, Review of Naturalism in mathematics
by P. Maddy, British Journal of Philosophy of Science 50 (1999), p.467-474:
- 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,
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.
- May 11. Presentations & Discussion. Nominalism
Presenters: J. Cassee, G. Lacerda
- May 18. Presentations & Discussion. Structuralism
Presenters: H. Nordmark, J.
- May 25. EXAM WEEK. Written final three-hour exam with six
questions in P.018; 16:15 - 19:00.
Last update : May 25th, 2005