Return to PL 3074 Spring 2003 homepage

PL 3074 -  Philosophy of Mathematics - Spring 2003

 
Prof:  Jonathan Bain Fall 2002
Office:  RH 201D Tues/Thurs 3:00-4:50
Off. hr:  Weds 11:00 - 12:00 or by appt.  LC 102
phone:  260-3688

I.  Description
Mathematics is sometimes referred to as the science of the infinite.  How can we make sense of this description?  In particular, are the objects of mathematics real?  What does it mean to say that a mathematical claim is true?  What is the nature of mathematical knowledge?  What is the relation between mathematics and the physical world?  In the first part of this course we will look at how contemporary philosophers have attempted to answer these and related questions.  In the second part of the course, we will consider the notion of infinity from historical and philosophical points of view.

II.  Required Texts
  • Brown, J. R. (1999) Philosophy of Mathematics, Routledge.
  • Hart, W. D. (ed.) (1996) The Philosophy of Mathematics, Oxford.
  • Moore, A. W. (2001) The Infinite, 2nd Ed., Routledge.

    • III.  Assessment
    1.  You will be required to contribute to an online discussion group.  Each week, 2 or 3 questions on the next week’s reading assignment will be posted to the group.  You will then have to contribute a minimum of two posts.  These posts can either be in the form of answers to one or more of the assigned questions, or responses to prior posts for that week.

    2.  You will be required to write three papers of about 5 pages each (typed, 10- or 12-point, double-spaced, spell-checked!).  Suggested topics for papers will be provided at least 2 weeks before their due dates.  These papers should conform to the guidelines for writing philosophy papers that will be handed out in class.

    3.  One midterm and one final will be given.  They will consist of short essay questions.

    IV.  Grade Distribution
    Papers:  25% total
    Midterm:  30%
    Final:  30%
    Participation (email list and in-class):  15% 
    V.  Modified Class Schedule: The following modified schedule may (still) be subject to revision over the course of the semester.  Reading assignments must be completed by the date on which they appear.
     

    Week 1 Tues 1/21
    Introduction:  The Mathematical Image 
    Brown Chap 1    		 Thurs 1/23
    Benacerraf:  "Mathematical Truth"
    Hart, pp. 14-30
    Week 2 Tues 1/28
    Platonism
    Brown Chaps 2, 3    		 Thurs 1/30
    Platonism
    Brown Chaps 2, 3
    Week 3 Tues 2/4
    Platonism
    Brown Chaps 2, 3    		 Thurs 2/6
    Tait:  "Truth and Proof:  The Platonism of Mathematics"
    Hart, pp. 142-167
    Week 4 Tues 2/11
    Applied Mathematics
    Brown Chap 4    		 Thurs 2/13
    NO CLASS
    Week 5 Tues 2/18
    NO CLASS (Pres. Day Makeup)    		 Thurs 2/20
    Formalism:  Hilbert & Godel
    Brown Chap 5
    Week 6 Tues 2/25
    Formalism:  Hilbert & Godel
    Brown Chap 5
    Paper #1 due    		 Thurs 2/27
    Putnam:  "Mathematics Without Foundations"
    Hart, pp. 235-271
    Week 7 Tues 3/4
    Knots & Definitions
    Brown Chaps 6, 7    		 Thurs 3/6
    Maddy:  "Perception and Mathematics"
    Hart, pp. 114-141
    Week 8 Tues 3/11
    Constructivism & Intuitionism
    Brown Chap 8    		 Thurs 3/13
    MIDTERM
    Week 9 Tues 3/18
    SPRING BREAK    		 Thurs 3/20
    SPRING BREAK
    Week 10 Tues 3/25
    Wittgenstein on Mathematics
    Brown Chap 9    		 Thurs 3/27
    Mathematics and Computation
    Brown Chap 10
    Paper #2 due
    Week 11 Tues 4/1
    Paradoxes of the Infinite and Early Greek History
    Moore Intro and Chaps 1, 2    		 Thurs 4/4
    Parsons:  "The Structuralist View of Mathematical Objects"
    Hart, pp. 272-309
    Week 12 Tues 4/8
    Pre-Cantor from the Calculus to Kant
    Moore Chaps 4-6    		 Thurs 4/10
    Pre-Cantor from the Calculus to Kant
    Moore Chaps 4-6
    Week 13 Tues 4/15
    Cantor and Transfinite Numbers
    Moore Chaps 8, 9    		 Thurs 4/17
    Cantor and Transfinite Numbers
    Moore Chaps 8, 9
    Week 14 Tues 4/22
    Sets, Lowenheim-Skolem, and Godel
    Moore Chaps 10-12    		 Thurs 4/24
    Parsons:  "Mathematical Intuition"
    Hart, pp. 95-113
    Week 15 Tues 4/29
    Wittgenstein on the Infinite
    Moore Chaps 13-15 
    Paper #3 due
    Week 16 Final (Date to be announced by Registrar in its Infinite Wisdom)

    Important Dates Spring 2003:

    School Closed--Martin Luther King Jr. holiday Mon, Jan 20
    Classes Begin Tues, Jan 21
    No Classes -- Spring Break Mon-Fri, Mar 17-21
    Classes End Tues, Apr 29
    Reading days Weds, Apr 30 - Fri, May 2
    Final exams Mon-Wed, May 5-16