Professor: Abe Stone
`abestone@ucsc.edu`

Office: Cowell Annex A-106

Phone (office): 459-5723

AIM: abestone3

Office hours: Mon. 2-3pm, Tues. 1pm-2pm, or by appointment.

The basic purpose of the course will be to explain how contemporary Analytic philosophy of mathematics came to its current set of problems, and explore some of the main approaches which have been taken in addressing those problems. We will begin with a consideration of the view known as ``logicism'' (roughly speaking: that all mathematics is part of logic), which dominated Analytic philosophy in the middle decades of the 20th century, and look at some of the reasons why that view was largely abandoned. In the second part of the course, we will see how, with the widespread rejection of logicism, a new set of problems--particularly, questions about whether mathematical entities exist and, if so, what they are--came to seem pressing. We will then look briefly at three popular answers to those questions: realism, nominalism (and/or ``fictionalism''), and structuralism.

Readings will be from primary text and, in parallel,
from Shapiro's textbook, *Thinking about Mathematics*. No
familiarity with any particular area of mathematics (other than
introductory-level logic) will be assumed, but students will be
expected to pick up some technical knowledge as we go along, and some
of the readings will include a fair amount of mathematical symbolism
(hence the math prerequisite).

Class participation; midterm paper (4-5 pages) or class presentation; final paper (approximately 8-10 pages). By May 1, you should decide which midterm assignment you are doing (and talk to me about topics). Midterm papers, for those who choose that option, are due May 15. The final paper is due June 12.

Gottlob Frege, *The Foundations of Arithmetic*, tr. J.L. Austin,
2nd revised ed. (ISBN: 0810106051).

Stewart Shapiro, *Thinking about Mathematics: The Philosophy of
Mathematics* (ISBN: 0192893068).

Paul Benacerraf and Hilary Putnam, eds., *Philosophy of
Mathematics: Selected Readings*, 2nd ed. (ISBN: 052129648X).

The above texts should be available at the Literary Guillotine. Readings not on the above list will be available on e-reserve.