AK2021 Foundational Issues in Mathematics 7.5 credits

The subject matter of mathematics is – or, at any rate, appears to be – a universe of abstract objects such as numbers, functions, and sets. Such objects can hardly be located in space and time; nevertheless we can study them and get to know their properties. How is this possible, and how reliable is such knowledge? Do numbers even exist independently of us, or are they rather some kind of mental construction? Is mathematical truth the same thing as provability, or may there be mathematical facts beyond the scope of rational inquiry? And can we ever be confident that our mathematical theories are free of contradiction?

In the course, we will study how three schools of thought in the philosophy of mathematics – logicism, intutionism, and finitism – have approached these issues, from a conceptual/philosophical point of view as well as from a technical/mathematical one. We will also find reason to acquaint ourselves with the traditional set-theoretical construction of mathematical number systems.

On completion of the course, the student should be able to

- account for, and with critical reflection discuss, concepts and problems from the philosophy of mathematics;

- recount and contrast the positions of central figures and schools of thought in the philosophy of mathematics; and

- handle technical concepts and methods relevant to foundational issues in mathematics.

Higher education equivalent to 120 credits (two whole years) or more.

- A. George & D. J. Velleman: Philosophies of Mathematics. Oxford: Blackwell, 2002.

- Further reading material may be added.

If the course is discontinued, students may request to be examined during the following two academic years.

• TEN1 - Exam 1, 4.0 credits, grading scale: A, B, C, D, E, FX, F
• TEN2 - Exam 2, 3.5 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

- Examination 1 (TEN1; 4.0 credits), grading scale A-F

- Examination 2 (TEN2; 3.5 credits), grading scale A-F

Tor Sandqvist

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.