PHI 314: PHILOSOPHY OF MATHEMATICS Syllabus Spring 2018 Communications: John P. Burgess, the instructor, can be reached by v-mail at 8-4310, by e-mail jburgess@princeton.edu. Time & Place: Two classes. MW 11:00-12:20. Room 62 McCosh. Each 80-minute course meeting will be divided into roughly 55 minutes of lecture and 25 minutes of discussion, but the group will be small enough that student with questions should feel free to interrupt the lecture and not wait for the discussion afterwards. Office Hours: Tue 1-3, or by appointment. Location, room 224, 1879 Hall. Office hours will be held also during reading period. Readings: Required readings are listed in boldface on the week-by-week list below. Students should at least have skimmed them before the week the are listed under below, and may need to reread them after the lectures of that week. They will be made available in electronic form to registered students, but it is strongly recommended that students obtain from Amazon or elsewhere a hard copy of Benacerraf & Putnam Philosophy of Mathematics: Selected Readings SECOND EDITION. All required readings will be from this source. Used paperbacks can often be found advertised on-line for a very low price. There will be many recommended readings, but it is not expected that any one student will read them all. However, a student writing on a particular question should do those recommended readings most closely related to it. Recommended for general background is Burgess, Rigor & Structure, to be skimmed through the term. It can be downloaded using the URL «www.princeton.edu/~jburgess/X.pdf» (Insert in place of the X the code given on the week-by=week list below. Similarly for other downloads.) Papers: Two 1000-word papers will be required during the term. They will be due at the second session of the 5th and the 11th weeks of the term. Each is to be written on one of a list of topic questions that will be circulated at least a week before the due date of the paper. A 2000-word paper is due on dean’s date. It is to be written on a topic proposed by the student and submitted to the instructor for approval before the end of classes. Students with little experience writing philosophy papers are advised to consult «http://www.jimpryor.net/teaching/guidelines/writing.html» and invited to submit at the second session of the 3rd week a draft of the first paper for comment. Submission: Hard copies are preferred but electronic submission will be acceptable PROVIDED it is in pdf forma and NOT in docx format. If submitting a hard copy, keep an electronic file or scan. Course boxes are in the atrium connecting 1879 & Marx Halls. The IN box is on the SOUTH (nearer to Lake Carnegie) side. It is for submitting papers only. Do not remove anything from this box. The OUT box is on the NORTH (nearer to Nassau Street) side. It is for returned papers only. Do not leave anything in this box. Acknowledgments: Each undergraduate paper should bear the words “This paper represents my own work in accordance with University regulations,” followed by the student’s signature. (Note the exact wording: There is no mention of “honor”, since the honor system applies only to in-class examinations.) The relevant regulations are to be found in the University publication Rights, Rules, and Responsibilities, with which students should be familiar. Lateness: There is a grade penalty of 1 point (on a scale of 100) per weekday to a maximum of 10 (or one full letter, e.g. from A- to B-) for unexcused lateness. By University policy, when extensions are sought on medical grounds, verification from University Health Services must be presented. Extensions for foreseeable reasons (such as scheduled extra-curricular activities requiring the student to be off-campus) should be sought in advance. Note that “Dean’s Date” is so called because only deans can grant extensions past that date; individual faculty may not do so on their own authority; please don’t even ask until you have spoken with your academic dean.

1st WEEK MON 05 FEB / WED 07 FEB Introductory 01JB Burgess Rigor & Structure 01CH Hempel Geometry & Empirical Science 01HH Hahn Crisis in Intuition 2nd WEEK MON 12 FEB / WED 14 FEB Before Logicism 02GB Berkeley Analyst (selections) 02RD Dedekind Irrational Numbers 02HP Poincaré The Nature of Mathematical Reasoning 3rd WEEK MON 19 FEB / WED 21 FEB Logicism: Frege & Russell 03GF Frege Foundations of Arithmetic (selections) 03BR Russell Introduction to Mathematical Philosophy (selections) 03RC Carnap Logicist Foundations 4th WEEK MON 26 FEB / WED 28 FEB After Logicism 04CH Hempel The Nature of Mathematical Truth 04AA Ayer The A Priori 04LC Carroll What the Tortoise Said to Achilles 5th WEEK MON 05 MAR / WED 07 MAR Intuitionism 005AH Heyting Disputation 05LB1 Brouwer Consciousness, Philosophy, Mathematics (selections) 05LB2 Brouwer Intuitionism & Formalism 6th WEEK MON 12 MAR / WED 14 MAR Formalism 06AH Heyting Intuitionist Foundations 06JN Neumann Formaist Foundations 06DH Hilbert On the Infinite SPRING BREAK

7th WEEK MON 26 MAR Guest Speaker Silvia de Toffoli “Diagrammatic Reasoning in Mathematics” WED 28 MAR Gödel 07MD Dummett Philosophical Basis of Intuitionistic Logic 07NN Newman Gödel’s Proof 07JL Lucas Minds, Machines, & Gödel 8th WEEK MON 02 APR / WED 04 APR Platonism 08PB Bernays Platonism in Mathematics 08KG Gödel Cantor’s Continuum Problem 08GB Boolos Iterative Conception of Set 9th WEEK MON 09 APR / WED 11 APR Nominalism 09PB Benacerraf Mathematical Truth 09HP Putnam Mathematics without Foundations 09DM Malament Review of Field 10th WEEK MON 16 APR / WED 18 APR Anti-Nominalism 10RC Carnap Empiricism, Semantics, Ontology 10WQ Quine Carnap & Logical Truth 10MC Colyvan Indispensability Arguments 11th WEEK MON 23 APR / WED 25 APR Structuralism 11PB Benacerraf What Numbers Could Not Be 11GH Hellman Three Varieties of Mathematical Structuralism 11AE Eddington Theory of Groups 12th WEEK MON 30 APR Guest Speaker Hans Halvorson “The Role of Mathematics in Physics" WED 02 MAY Conclusion 12TB Bays Review of Mancosu 12EW Wigner Unreasonable Effectiveness 12LW White Locus of Mathematical Reality