PHI 314 PHILOSOPHY OF MATHEMATICS J.BURGESS & H. HALVORSON SPRING 2014 MW 11:00-12:30
TEXTS R&S J. Burgess, Rigor & Structure available for downloading at www.princeton.edu/~jburgess/anecdota.htm
B&P P. Benacerraf & H. Putnam,
eds., Philosophy
of Mathematics: Selected Readings readings
from this source required
WoM J. R. Newman, ed., The World of Mathematics (4 volumes) on
reserve in Firestone readings
from this source recommended
jstor # item available on University network at URL
www.jstor.org/stable/# readings
from this source recommended
SEP Stanford Encyclopedia on-line source best found by Googling on SEP and title readings from this source recommended
01 |
03 FEB Introduction & Organizational |
05 FEB Mathematical vs Physical Geometry (HH) WoM3 Hempel "Geometry & Empirical Science" |
02 |
10 FEB Pre-Rigorous Mathematics (JB) R&S, chapter 1 WoM1 Berkeley "Analyst" WoM3 Hahn "Crisis in Intuition" |
12 FEB Rigorization of Mathematics (JB) R&S, chapter 2 WoM1 Dedekind "Irrational Numbers" |
03 |
17 FEB Frege on Number (JB) B&P Frege "Concept of Number" WoM White "Locus of Mathematical Reality" |
19 FEB RussellÕs Paradox & Theory of Types (JB) B&P Russell "Intro. to Mathematical Philosophy" B&P Poincar "Nature of Mathematical Reasoning" 1st 800-1200 word
paper due |
04 |
24 FEB Anti- Post-, & Neo-Logicism (JB) B&P Carnap ŅLogicist FoundationsÓ B&P Ayer "The A Priori" B&P Hempel "Nature of Mathematical Truth" |
26 FEB Intuitionist Critique (HH) B&P Heyting "Intuitionist Foundations" B&P Heyting "Disputation" |
05 |
03 MAR Intuitionist Program (HH) B&P Brouwer "Intuitionism & Formalism" B&P Brouwe "Consciousness, Philosophy, Mathematics" |
05 MAR Neo-Intuitionism (HH) B&P Dummett "Philosophical Foundations" (first half of paper) 2nd 800-1200 word paper due |
06 |
10 MAR Ultra-Intuitionism (JB) WoM4 Lewis Carroll "What the Tortoise Said to Achilles" |
12 MAR FormalismÕs Gambit (JB) B&P Hilbert "On the Infinite" B&P Von Neumann "Formalist Foundations" B&P (optional!) Kreisel "Hilbert's Program" |
07 |
24 MAR FormalismÕs Failure: GdelÕs Theorem (JB) WoM3 Newman & Nagel "Goedel's Proof" jstor 3749270 Lucas "Minds, Machines, & Gdel" |
26 MAR Anti-formalism (JB) B&P Gdel "What Is Cantor's Continuum Problem?" B&P Boolos "Iterative Concept of Set" 3rd 800-1200 word paper due |
08 |
31 MAR Foundations of
Mathematics Post-Gdel guest speaker: Harvey Friedman |
02 APR Nominalist Critique (JB) B&P Benacerraf "Mathematical Truth" B&P Bernays "Platonism in Mathematics" |
09 |
07 APR Nominalist Program (JB&HH) B&P Putnam "Mathematics without Foundations" jstor 2026384 Malament review of Field "Science w/o Numbers" |
09 APR Anti-Nominalism (JB) B&P Carnap ŅEmpiricism, Semantics, OntologyÓ B&P Quine "Carnap & Logical Truth" 4th 800-1200 paper due |
10 |
14 APR Indispensability Argument (JB) SEP Colyvan "Indispensability Arguments" |
16 APR Structuralism (HH) Benacerraf "What Numbers Could Not Be" |
11 |
21 APR Defense of a Version of Structuralism guest speaker: Geoffrey Hellman |
23 APR Varieties of Structuralism (HH) R&S, chapter 3 WoM3 Eddington "Theory of Groups" 5th 800-1200 word paper due |
12 |
28 APR Category Theory & Structuralism (HH) R&S, chapter 4 |
30 APR Conclusion final 4000-6000 word paper due DEANÕS DATE 13
MAY |
Each 80-minute session will consist of a 45-50 minute lecture by one of JB or HH, followed by a 5-10 commentary by the other,
followed by 15-20 of general discussion (beginning with questions from students to the speaker or commentator, but becoming free-form), and a final summary of at most 5 minutes (emphasizing issues for futher study) by the speaker.