Philosophy of Mathematics

Pre-requisites: The first-year course in Logic, and the second-year course in Mathematics

Course objectives: Students should become familiar with some fundamental mathematical concepts (which is not quite a philosophical but rather a mathematical matter) in order to be able to understand the disagreement between different philosophies of mathematics.

Course description: Some fundamental mathematical concepts as they are understood within set theory, and some concepts of category theory, incompleteness phenomena, the basic directions in the philosophy of mathematics (platonism, constructivism, formalism, logicism). It is also possible that the whole course will be devoted to one classical author (Goedel, Brouwer, Hilbert, Frege, Wittgenstein), and some of his fundamental texts. The more technical aspects would be covered as practical work.

Learning Outcomes: Students familiarized with fundamental mathematical concepts have become able to understand the disagreement between different philosophies of mathematics.

Literature/Reading:

• Ž. Mijajlović, Z. Marković i K. Došen, Hilbertovi problemi i logika, Zavod za udžbenike i nastavna sredstva, Beograd, 1986

• G.S. Boolos, J.P. Burgess and R.C. Jeffrey, Computability and Logic, Cambridge University Press, 2007

• Z. Šikić (prir.), Novija filozofija matematike, Nolit, 1987

• P. Benacerraf and H. Putnam (eds), Philosophy of Mathematics: Selected Readings (second edition), Cambridge University Press, 1983

• jedno ili više klasičnih dela iz filozofije matematike od Fregea, ili Hilberta, ili Brauvera, ili Gedela, ili Vitgenštajna -- već šta se te godine izučava