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d |
Day |
Date |
Content |
Readings |
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Historical positions |
|
| 1 |
1 |
Tue |
Sep 2 |
Introduction to the course |
|
| |
2 |
Thu |
Sep 4 |
Questions and positions in philosophy of mathematics |
Shapiro, Ch.1-2 |
| 2 |
3 |
Tue |
Sep 9 |
Euclid's Elements |
Eves, Ch.1-2 |
| |
4 |
Thu |
Sep 11 |
Plato |
Shapiro, Ch.3 |
| 3 |
5 |
Tue |
Sep 16 |
Aristotle |
Shapiro, Ch.3 |
| |
6 |
Thu |
Sep 18 |
Locke and Berkeley |
Handout (WebCT) |
| 4 |
7 |
Tue |
Sep 23 |
Kant |
Shapiro, Ch.5 |
| |
|
|
|
Modern mathematics and traditional positions |
|
| |
8 |
Thu |
Sep 25 |
Non-Euclidean geometry |
Eves, Ch.3 |
| 5 |
9 |
Tue |
Sep 30 |
Analytic and projective geometry |
Eves, Ch.4.4-5 |
| |
10 |
Thu |
Oct 2 |
Frege |
Shapiro,
Ch.5.1; Handout |
| 6 |
11 |
Tue |
Oct 7 |
Russell |
Shapiro, Ch.5.2, 5.4 |
| |
12 |
Thu |
Oct 9 |
Hilbert's
Grundlagen der Geometrie; Formalism
(First critical research article summary due) |
Eves, Ch.4 and 6; Shapiro, Ch.6.1-2 |
| 7 |
13 |
Tue |
Oct 14 |
Frege-Hilbert debate; Hilbert's
programme |
Shapiro, Ch.6.3-6 |
| |
14 |
Thu |
Oct 16 |
Gödel's Incompleteness Theorems |
Eves, App. A.9; Shapiro Ch.6.4 |
| 8 |
15 |
Tue |
Oct 21 |
Intuitionism |
Shapiro, Ch.7 |
| |
|
Thu |
Oct 23 |
(No class) |
|
| 9 |
16 |
Tue |
Oct 28 |
Logical Positivism and Quine |
Shapiro, Ch.5.4 and 8.2 |
| |
17 |
Thu |
Oct 30 |
Set
Theory; Gödel's realism
(Second critical summary due) |
Eves,
Ch.8; Shapiro, Ch.8.1 and 8.3 |
| 10 |
18 |
Tue |
Nov 4 |
Algebraic Structures |
Eves, Ch.5 |
| |
19 |
Thu |
Nov 6 |
Structuralism |
Shapiro Ch.10 |
| |
|
|
|
New directions |
|
| 11 |
20 |
Tue |
Nov 11 |
Traditional philosophy of mathematics;
Foundationalism; Philosophy of science |
|
| |
21 |
Thu |
Nov 13 |
Challenging foundationalism; Lakatos |
(online) |
| 12 |
22 |
Tue |
Nov 18 |
Lakatos: Proofs and Refutations |
(online) |
| |
23 |
Thu |
Nov 20 |
The cognitive basis of mathematics |
(online) |
| 13 |
24 |
Tue |
Nov 25 |
Lakoff and Núñez: Embodied philosophy of mathematics |
(online) |
| |
25 |
Thu |
Nov 27 |
Philosophical replies to Lakoff and Núñez
(Final paper due) |
(online) |
Phil 411: Topics in Philosophy of Logic and
Mathematics, Fall 2008