AK2001 Mathematics and Reality 7.5 credits

This course is about the relation between mathematics and reality from two perspectives. First, there are questions within mathematics: What does it mean to say that mathematical propositions are true? What does it mean to say that they are provable? Are there mathematical objects? Is a mathematical theory nothing but its axioms? Has mathematics a secure foundation? Secondly, there are questions about the relation between mathematics and the physical reality. How come we are able to use mathematics in order to increase our knowledge of physical reality and to manipulate it? Has the world a structure that can be described mathematically? What is the relation between mathematical entities and operations such as numbers, lines, sets, addition, differentiation and physical quantities and practices for counting, measuring, etc.?

Upon completion of the course, the student should be able
-- to account for central concepts and questions in the philosophy of mathematics;
-- to recount and contrast the standpoints of historically important thinkers and schools in the philosophy of mathematics;
-- to describe in outline the content and philosophical significance of technical notions and results such as decidability, formal deduction, Russell's antinomy, and Gödel's incompleteness theorems; and
-- to engage in critical written reflection on such primary texts in philosophy of mathematics as are included in the course literature.

University studies corresponding to at least 120 credits (two full years).

30 credits (half a year) of university studies in mathematics or philosophy is recommended.

Course literature will be posted on the course home page no later than four weeks before the course starts.

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

• INL1 - Assignment, 3.0 credits, grading scale: A, B, C, D, E, FX, F
• TEN1 - Examination, 4.5 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.

John Cantwell

• 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.

Old course code: 1H1601