Instructor: Dr Benedikt Löwe
Vakcode: MolPM6
Time: Wednesday, 17-19
Place: P.018
ECTS credit points: 6
Course language: English
Intended Audience: M.Sc. students of Logic and Mathematics,
M.A. students of Philosophy
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.
Last update : May 25th, 2005