.The official course outline is available in the e-classroom during the course.
University of Alberta
Faculty of Arts
Department of Philosophy
Phil 367: Introduction to the philosophy of
mathematics
Winter term (2012/13)
Mathematics is often grouped together with the sciences. However, the subject of study in mathematics seems to be strikingly different from the bits and pieces of “nature,” that are the topics of investigation in the empirical sciences. Philosophical questions arise immediately: Do numbers, triangles, etc. exist? What sort of existence do they have? How can we acquire beliefs and knowledge about these objects? What does make mathematics “unreasonably effective” in its applications?
The history of philosophy and mathematics has plenty of thinkers who provided various answers to such questions. In this course, we will touch upon the three main approaches from the early part of the 20th century that aimed at explaining the status of mathematical objects and mathematical knowledge: logicism, intuitionism and formalism. Further ways to tackle some of the same issues go under the labels platonism, realism, constructivism, nominalism, structuralism and fictionalism — and these approaches will also be mentioned briefly or more extensively.
Reasoning, often involving symbols, plays a central role in mathematics, especially, since the late 19th century, when mathematics lost most of its immediacy, which necessitated the introduction of more rigorous methods of proof. This course will explore not only some of the well-known connections between mathematics and logic, but it will also investigate the place and function of diagrams, computer-generated proofs, pictures and computerized experiments in mathematics — viewed as a discipline developed and practiced by mathematicians.
The course — inevitably — will include mathematical examples. They will be either rather simple (i.e., high-school level illustrations), or they will be explained in the textbook or in the lectures. There is no formal prerequisite for the course, and it is not required that you have taken a course in mathematics at the university level. Nevertheless, interest in and knowledge of mathematics will surely be advantageous.
Time: M, W, F
13:00 pm – 13:50 pm
Textbook: Brown, J. R., Philosophy of
Mathematics: A Contemporary Introduction to the World of Proofs and
Pictures, (2nd ed.)
Routledge Contemporary Introductions to
Philosophy, Routledge, New York, NY, 2008. (required)
For further information, please contact the instructor at
.
The official course outline is available in the e-classroom
during the course.
[Last updated on March 9th, 2012.]