Phil 411: Topics in Philosophy of Logic and Mathematics, Fall 2008


Aim of the course: 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 motivate the student to appreciate this fascinating subject matter, to give her an overview of prominent issues and arguments, and enable her 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. The 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.

In sum, in this course the student learns about

  1. The history of mathematics
  2. Major developments in philosophy of mathematics
  3. Current research in philosophy of mathematics

Prerequisites: Introduction to Deductive Logic (Phil 210, or equivalent), and one intermediate course in philosophy. It is recommended that students are familiar with the material taught in Intermediate Logic (Phil 310, or equivalent).
Textbooks: The following two books are required for this course. For the philosophical discussions the lectures will follow closely:
  • Stewart Shapiro: Thinking about Mathematics, Oxford Univ. Press, 2000.
For the mathematical content of the course, we will make use of:
  • Howard Eves: Foundations and Fundamental Concepts of Mathematics, third edition, Dover, 1997.
Both books are available at The Word Bookstore, 469 Milton Street (5 mins. from the University Street Gates). These texts are essential.

Additional reading materials will be on course reserve, available online or handed out in class.
Requirements & grading: Students are expected to attend and participate in class, do the assigned readings, complete weekly homework assignments, write two critical summaries of recent research articles, and write a final paper.
The final grade depends on homework assignments (30%), two critical summaries of contemporary research articles (20% each), and the final paper (30%). 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).
Academic integrity: 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 for more information).

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