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
- The history of mathematics
- Major developments in philosophy of mathematics
- 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 www.mcgill.ca/integrity for
more information).
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Phil 411: Topics in Philosophy of Logic and
Mathematics, Fall 2008