Title: Syllabus-Minta:
Author: Janos Hardi
Last saved by: András Máté
Company: Philolaos Publishing

Code(s):
Title: A historical introduction into the philosophy of mathematics
Lecturer(s): András Máté assoc. prof. (retired)
Location and time: P 10:00-11:30, i/129
Consultation (e-mail): mate.andras53@gmail.com

General aim of the course:
Intruduction to the problems of the philosophy of mathematics and its classical schools, with an outlook to the contemporary debates.

Content of the course:
Developments and problems in 19th century mathematics
Bolzano, Cantor and the infinite
Frege’s logicism and his construction of natural numbers
Dedekind’s construction of natural numbers
New paradoxes of infinity – the first fall of logicism
The logicism of Russell and Ramsey
Hilbert’s program and the arithmetisation
Brouwer’s intuitionism
Gödel’s theorems and the second fall of logicism
The paradox of the liar and the indefinability of truth
Decision problem, Church-thesis, Church(-Turing)-theorem

Examination and evaluation system:
For the grade, the student  should produce a presentation about some subject connected with the topic of the course. It will be discussed at a "house conference" in the exam period.  (S)he should participate in the discussion of the presentations of the other students, too.

Bibliography:
Benacerraf, P. – H. Putnam (eds.): Philosophy of mathematics, Cambridge U.P., 1983
van Heijenooort, J. (ed.): From Frege To Gödel: A Source Book in Mathematical Logic, 1879-1931. Harvard U. P.; reprinted with corrections, 1977.
Mancosu, P. (ed.): From Brouwer to Hilbert. The Debate on the Foundations of Mathematics in the 1920s, Oxford University Press,  1998.