## Course outline

Mathematics has exerted a particular attraction to philosophers
throughout history. For example, tradition has it that the phrase "Let
no one ignorant of geometry enter" marked the entrance to Plato's
Academy, Kant famously argued that "5+7=12" is a synthetic
proposition that is knowable a priori, and Frege worried how we can
determine whether Julius Caesar is a number
or not. However, even after more than 2000 years of philosophical
reflections on the nature of mathematical truths, the status of
mathematical objects, the sources of mathematical knowledge, the
applicability of mathematics in science, and the methodology of
mathematical practice, these topics *still* continue to puzzle
philosophers.

This course provides an historically informed introduction to
philosophy of mathematics. It is intended to present an overview of
prominent issues and arguments, to motivate the students to
appreciate this fascinating subject matter, and enable them to
discuss contemporary research in philosophy of mathematics.
To this end, philosophical reflections on mathematics and particular
episodes in the history of mathematics will be presented and discussed
side by side. Simple examples from mathematical practice (mainly
geometry, arithmetic, and algebra) serve as illustrations for the
subject matter the philosophical reflections are about, and, at the
same time, they serve as proving ground for the adequateness of the
philosophical claims about mathematics.

## Topics

The course is divided into seven parts (of about 2 weeks each):- Introduction
- From things to numbers (Arithmetic)
- Historical positions (Geometry)
- Developments in 19th century geometry and some philosophical reactions
- Foundational positions in the 20th century (Logicism, Formalism, Intuitionism)
- Current positions: Realism (Fictionalism & Empiricism) and Structuralism (Set theory & Category theory)
- Mathematical practice and methodology

## Requirements

Introduction to Deductive Logic (Phil 210, or equivalent) or permission by the instructor.

No particular background in mathematics above high-school level is required.

## Grading

Students are expected to attend and participate in class, do the
assigned readings, complete weekly homework assignments, take three in-class quizzes, write a critical summary of a recent research article, and write a final
paper.
Assignments and papers are due at the beginning of class on the date
mentioned on the assignment and have to be turned in on paper.
Grading will be based on correctness *and* clarity.

The *final grade* depends on homework
assignments (5%), three quizzes (5%, 10%, and 10%: 25% in total), a critical summary of a contemporary research
article (25%), and a final paper (45%).

Every student can take up to two "late days" for handing in the homework assignments or papers during the semester. Otherwise, late homework will not be accepted (except in cases of documented emergencies).

This is a new course that can be used to fulfill a degree requirement in philosophy: Minor: Group B, Major: Group A.

## The fine print

McGill University values academic integrity. Therefore all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see www.mcgill.ca/students/srr/honest for more information).

Instructor generated course materials (e.g., handouts, notes, summaries, exam questions, etc.) are protected by law and may not be copied or distributed in any form or in any medium without explicit permission of the instructor. Note that infringements of copyright can be subject to follow up by the University under the Code of Student Conduct and Disciplinary Procedures.

In accord with McGill University's Charter of Students' Rights, students in this course have the right to submit in English or in French any written work that is to be graded.

In the event of extraordinary circumstances beyond the University’s control, the content and/or evaluation scheme in this course is subject to change.