Simon Fraser University
Engaging the World

Course Outlines

Summer 2025 - PHIL 435 E100

Selected Topics (4)

Foundations of Mathematics

Class Number: 3342

Delivery Method: In Person

Overview

  • Course Times + Location:

    May 12 – Aug 8, 2025: Tue, 4:30–8:20 p.m.
    Burnaby

  • Prerequisites:

    Two 300-level PHIL courses.

Description

CALENDAR DESCRIPTION:

A specific topic, philosopher or philosophical work to be dealt with as occasion and demand warrant. May be repeated for credit.

COURSE DETAILS:

Selected Topics: Foundations of mathematics
[Note: this course is to be taught concurrently with PHIL 814.]

This course aims to examine the standard set-theoretic foundations of mathematics and their philosophical underpinnings. Focus will be put on infinitary constructions such as number systems (natural, rational, real, perhaps hyperreal) and on the use of set-theoretic principles such as the axiom of choice. Although philosophical examination of the principles in question will be on the agenda, the primary objective is to familiarize students with the technical apparatus used in the standard foundations and with the details of the key proofs. Students are expected to not only have an extensive background in logic, but also to have had exposure to axiomatic set theory; ideally, students will have taken PHIL 310 or something equivalent.

COURSE-LEVEL EDUCATIONAL GOALS:


The learning objectives for this course are:

- Developing a knowledge of infinitary principles used in set theory to provide foundations for branches of mathematics such as arithmetic, calculus, and geometry.

- Developing a technical knowledge of the proof methods used to acquire knowledge of infinite objects.

- Critically reflect on the assumptions underlying the standard mathematical account of foundations.

- Examine and critically reflect alternative accounts of foundations.

Grading

  • In-class participation 10%
  • Ten (10) homework assignments 50%
  • Either a term paper or a final exam 40%

Materials

REQUIRED READING:


Course material will be distributed in PDF.

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Department Undergraduate Notes:

Thinking of a Philosophy Major or Minor? The Concentration in Law and Philosophy? The Certificate in Ethics? The Philosophy and Methodology of Science Certificate?
Contact the PHIL Advisor at philcomm@sfu.ca   More details on our website: SFU Philosophy

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

At SFU, you are expected to act honestly and responsibly in all your academic work. Cheating, plagiarism, or any other form of academic dishonesty harms your own learning, undermines the efforts of your classmates who pursue their studies honestly, and goes against the core values of the university.

To learn more about the academic disciplinary process and relevant academic supports, visit: 


RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.