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

             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               readings from this source recommended

            SEP     Stanford Encyclopedia on-line source best found by Googling on SEP and title        readings from this source recommended


03 FEB

Introduction & Organizational




05 FEB

Mathematical vs Physical Geometry (HH)

WoM3 Hempel "Geometry & Empirical Science"



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"



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 PoincarŽ "Nature of Mathematical Reasoning"

1st 800-1200 word paper due


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"



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


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"



24 MAR

FormalismÕs Failure: GšdelÕs Theorem (JB)

WoM3 Newman & Nagel "Goedel's Proof"

jstor 3749270 Lucas "Minds, Machines, & Gšdel"


26 MAR

Anti-formalism (JB)

B&P Gšdel "What Is Cantor's Continuum Problem?"

B&P Boolos "Iterative Concept of Set"

3rd 800-1200 word  paper due


31 MAR

Foundations of Mathematics Post-Gšdel

guest speaker: Harvey Friedman


02 APR

Nominalist Critique (JB)

B&P Benacerraf "Mathematical Truth"

B&P Bernays "Platonism in Mathematics"



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


14 APR

Indispensability Argument (JB)

SEP Colyvan "Indispensability Arguments"



16 APR

Structuralism (HH)

Benacerraf "What Numbers Could Not Be"




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


28 APR

Category Theory & Structuralism (HH)

R&S, chapter 4

30 APR




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.