University
of Alberta

Faculty
of Arts

Department of Philosophy

Phil 367: Introduction to the philosophy of mathematics
— Winter term (2018)

*Mathematics* is often grouped together with the *sciences*.
However, mathematics seems to study something strikingly different
from the bits and pieces of “nature,” that are the objects of
investigation in the empirical sciences. Philosophical questions arise
immediately: Do numbers, triangles, manifolds and functions 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 of mathematics lists plenty of thinkers who
gave various answers to such questions. In this course, we will
touch upon 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*. These latter approaches
will also be mentioned — some of them at greater length than others.

*Reasoning* with symbols, often in a completely abstract setting,
plays a central role in mathematics, especially, since the late 19th
century. The loss of immediacy that was provided by geometric and
physical insights necessitated the introduction of more rigorous methods of
proof. This course will explore some of the well-known (as well as some
less well-known) connections between mathematics and various systems of
logic. We will also glance at other questions such as the role of
notation, of pictures, of computers and of experiments in mathematical
practice.

The course — inevitably — will include some examples from mathematics. They will be either quite 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 university-level course in mathematics. Nevertheless, interest in or knowledge of mathematics will surely be helpful or even advantageous.)

**Time:**
M, W, F 13:00 pm – 13:50 pm

**Texts:**
Colyvan, M., *An Introduction to the Philosophy of Mathematics*,
Cambridge University Press, Cambridge (UK),
2012. (required)

Shapiro, S., *Thinking about Mathematics: The Philosophy of
Mathematics*, Oxford University Press, Oxford, (UK), 2000. (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 3rd, 2017.]