AK2001 Mathematics and Reality 7.5 credits

Matematiken och verkligheten

This is an introduction to the philosophy of mathematics, especially the relationship between mathematics and reality.

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.?

Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

Course information

Content and learning outcomes

Course contents *

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.?

Intended learning outcomes *

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.

Course Disposition

Lectures 20 h

Tutorials 10 h

Literature and preparations

Specific prerequisites *

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

Recommended prerequisites

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

Equipment

No information inserted

Literature

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

Examination and completion

Grading scale *

A, B, C, D, E, FX, F

Examination *

  • 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.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

John Cantwell

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web AK2001

Offered by

ABE/Philosophy

Main field of study *

Built Environment

Education cycle *

Second cycle

Add-on studies

No information inserted

Contact

Tor Sandqvist, tosa@kth.se, 08-790 9529

Ethical approach *

  • 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.

Supplementary information

Old course code: 1H1601