PHIL 3342 Philosophy of Mathematics

Through the ages, philosophers have thought that mathematics embodies the highest standards for knowledge. Even our best science might get things entirely wrong, but we will never have to worry that 2+2 isn't 4. However, events such as the invention of non-Euclidean geometry, the discovery of paradoxes related to infinity, and Godel's demonstration that arithmetic is incomplete have raised deep worries about the foundations of mathematics. This course will present these and other challenges to confidence in mathematics, and then discuss a number of philosophical theories about how our confidence can be restored. A main concern will be to understand what accounts for the truth of the claims of mathematics.

Teacher: Jim Garson MWF 2:00-3:00 502 AH x3205 jgarson@uh.edu

Books: TM = Thinking about Mathematics S. Shapiro

B&P = Philosophy of Mathematics: Readings Benaceraff & Putnam

ML = Mathematical Logic S. Kleene

0. Introduction: What is Philosophy of Mathematics?

Jan. 20 TM Ch. 1

1. History of the Philosophy of Mathematics

Jan. 22 – Feb. 1 TM Ch. 3 - 4

2. Non-Euclidean Geometry

Feb. 3 - Feb 5 "The Straight Line," M. Kline, SA 1956 (April)

3. Infinity

Feb. 8 - 12 ML, 32-33; TM, Ch. 2,

4. Paradoxes

Feb 15 - 17 ML, 35

Feb. 19 REVIEW

Feb. 22 QUIZ 1 (1 HOUR)

5. Logicism

Feb. 24 - Mar 12 TM Ch. 5; B&P pp. 366-381

SPRING BREAK

6. Formalism

Mar. 22 - 31 ML, 36; TM Ch. 6; B&P pp. 134-151

Apr. 2 REVIEW

Apr. 5 QUIZ 2 (1 HOUR)

7. Intuitionism

Apr. 7 - 21 TM Ch. 7; B&P pp. 55-64

8. To Be Announced

Apr. 23 - 28

Apr. 30, May 3 REVIEW OF THE WHOLE COURSE

May 10 2 HOUR FINAL

Regular class attendance is essential and will be checked. You will be dropped after 2 unexcused absences in a row, or a total of 3 unexcused absences. There will be occasional homework assignments handed out in class. Late work will not be accepted unless it is accompanied by a good excuse in writing.

How your grade is calculated:

Homework: 25% QUIZ 1: 20% QUIZ 2: 20% FINAL: 35%