Philosophy of Mathematics examines some of the philosophical presumptions behind mathematics. Here are some very basic examples.
Are numbers real—that is, do they exist either as objects (the Number One), or as properties of other objects (one piece of paper)? If they don’t exist in any way, then how can mathematical statements (1 + 1 = 2) manage to be true? How, then, can mathematics actually work when we apply it to the world (bank accounts, building bridges, etc.)? If, on the other hand, they do exist, where are they, and how do we know?
One goal of the course is to further develop (past 101 and the student’s 2xx PL course) the student's sense both of what makes an argument a good argument, and of what sorts of conclusions are worth arguing for, in the first place. (It is the special feature of PL 3xx courses to apply various philosophical theories and methods to a quite particular subject outside of philosophy, e.g., mathematics, science, language, art, and so forth). Another goal of this course is to hone the reading and writing skills needed to personally benefit from some of the greatest intellectual documents world civilizations have to offer. Primarily, though, the aim of this course is to transmit the benefits of having one’s contemporary world-view fundamentally challenged by extraordinary, but carefully argued for, alternatives.