Monday, Wednesday, and Friday
10:00 A.M.-10:50 A.M.
314 Modern Languages
The following is the official course description:
Philosophy of Mathematics (3) Problems at the foundations of geometry and set theory. Logicism, formalism, and intuitionism. Nominalism vs. realism. Epistemology of mathematics.
We shall study problems at the foundations of arithmetic, geometry, analysis, and set theory. Most of the problems we look at are in fact more general, and concern all abstract objects, from melodies to meanings to plots to properties. Epistemology of mathematics: logicism, formalism, finitism, intuitionism, predicativism, and antifoundationalism. Metaphysics of mathematics: nominalism, fictionalism, and realism, especially structuralism. Effect of theorems of Löwenheim, Skolem, and Gödel on the philosophy of mathematics. Readings may include works by Corcoran, Gödel, Putnam, Quine, Benacerraf, Field, von Neumann, Brouwer, Poincaré, Weyl, and others. Though some of the texts are unfortunately rather technical, no knowledge of mathematics is assumed: almost every Friday (see the detailed calendar below) will be devoted to discussion, largely to help you get the point of some of the texts without (or with, depending on class interest) all the technical details.
The text should be available in the ASUA bookstore.
Paul Benacerraf and Hilary Putnam, eds., Philosophy of Mathematics: Selected Readings, 2nd edition (Cambridge University Press, New York, 1983).
Suggested text: Jean van Heijenoort, From Frege to Gödel 1879-1931: A Source Book in Mathematical Logic (iUniverse, 1999).
The base web page for this course is Philosophy of Mathematics. It is my present intention to post all of my class notes (that is, what I would otherwise have written on the blackboard) here on the wiki. You should post comments, questions, corrections, and discussions here.
Attend class. Be prompt. Participate. Ask questions. Make use of office hours and of the Wiki.
Students with physical, psychological, or learning disabilities are encouraged to contact the Disability Resource Center. If you have a documented disability and anticipate needing accommodations in this course, please make arrangements with me immediately.
The final examination will be Wednesday, 11 May, 11 A.M.-1 P.M. The final examination is a mandatory part of the course. If you will be unable to take it for any reason, do not take this course. Of course, with documentation, serious medical excuses and the like will be accepted. Airplane tickets, weddings, and so forth, will not be.
For the undergraduate course, numbered 416: There will be two required typed, double-spaced papers, one of 5 pages (that is, approximately 1,250 words, or 6,250 characters in length) and one of twice that length, a midterm examination, and a final examination. In addition, you will be required to make some contribution to the wiki for a specified class date. Keep a copy of each paper when you hand it in!
For the graduate course, numbered 516: There will be two required 10-12-page typed, double-spaced papers (that is, papers of approximately 2,500-3,000 words, or 12,500-15,000 characters in length), a midterm examination, and a final examination. In addition, you will be required to make some contribution to the wiki for a specified class date. Keep a copy of each paper when you hand it in!
Your papers should each concern one of the assigned topics (see the next paragraph), presenting the relevant positions clearly and assessing their strengths and weaknesses. Note that if you get a position wrong, you are unlikely to assess it well. There is rarely only one correct interpretation of anything, but--whatever your interpretation--you must document it by giving page or line references to the passages on which the interpretation is based. Do not use quotations unless the precise wording of a passage is crucial. Explain the views in your own words.
The papers for the course are not primarily research papers, though I shall expect, especially for the graduate portion of the course, evidence that you have done relevant research. You must show that you have read the relevant texts carefully, thought about them, and made some sense of them. Do not report the views of others. Struggle with the texts on your own. The papers will be on topics of your choice concerning the reading we have done to that point. Pick a specific argument or group of arguments to present and evaluate.
If you do consult works other than the assigned texts, list them in a bibliography with additional acknowledgment given to any writer who influenced your thinking. If you quote from any work, or paraphrase it, you must note explicitly that you have done so--in the case of direct quotation, the use of quotation marks will suffice. Failure to acknowledge sources or to note quotation or paraphrase constitutes plagiarism, which is the ultimate academic crime--see the section in the Guide for Students. 1 Plagiarism may result in a failing grade for the course, at my discretion.
Page references to the assigned texts should be given in parentheses in the body of a paper. Secondary literature should usually be mentioned in footnotes. The Chicago Manual of Style is a useful reference for other matters of style.
All questions on the examination will be essay questions. The examination will cover all material presented in class and in the assigned readings. You will be allowed to consult your notes but not your books. (Please draw the obvious moral: take good notes on your reading.)
Each of the two papers will count for 40% of your course grade. Your examination grade will be the remaining 20%. Your attendance and participation in the class and the wiki will determine what happens to your grade in borderline or questionable cases.
If you wish to complete an assignment late, you must get approval from Professor Lavine at least one week before the assignment is due. Otherwise, short of serious medical excuses with written documentation, late work may result in grading penalties.
If you believe that a mistake has been made in the grading of one of your papers or the examination, you must put your reasons for thinking so in writing and then submit them to Professor Lavine within one week from the time the paper or examination was returned. All grades that have not been appealed will be considered final after one week. No oral appeals of grades will be considered. If there is still a problem after receiving a response to your appeal, you may then make an appointment to discuss the matter with Professor Lavine.
Office hours are for your benefit. I encourage you to come, whether to talk about the readings, the class discussions, or the papers--or even just to chat. You are particularly strongly encouraged to discuss the paper topics and comments on your finished papers. Individual discussions usually result in more learning than classes alone. Use the opportunity.
My office hours are Mondays, Wednesdays, and Fridays 11:00 A.M.-11:50 A.M. in room 208 Social Sciences or by appointment. My telephone number is 621-7109, or I may be reached outside of office hours by leaving a message at the department office, 621-3120 or by e-mail, shaughan@arizona.edu .
The second half of the course will be devoted to reading selected papers, which will be available for copying in the Philosophy Department Office (213 Social Sciences) and on the internet when possible. The topic or topics we focus on will be decided in class during the planning meeting. Be sure to think about what you will want to cover.