The course deals with fundamental philosophical questions concerning mathematical knowledge: what is the nature of this knowledge? How is it possible? What is different and what is common to mathematical knowledge and scientific knowledge in general? Is mathematical knowledge certain and, if so, what is the source of this certainty? What is the subject of mathematical research and what are its objects? What is the role of mathematical proof as a way of justification and of explanation.

The course examines questions that focus primarily on two main areas of mathematical knowledge: geometry and arithmetic. During the course we will review a number of traditional approaches that attempt to address these problems, and analyze the weaknesses and strengths of each of these approaches.

The course does not assume any specific, previous knowledge in mathematics or philosophy. The required concepts will be introduced as necessary during the course itself. However, students with a background in mathematics or philosophy will be able to significantly connect the ideas learned in classed to questions related to their previous knowledge. At the same time, the course is not suitable for those who are set aback if they come across—within a philosophical text, or in class—a logical or mathematical formula (properly explained in class) such as the following:

∀x ∀y {(Px & Py) → ∃ f [f(q(x), q(y), d(x,y), k) = F]} where F =

Course Requirements

Students will receive their grade by way of a home test. The test is based on two texts dealing with subjects related to the material studied in the course, but which raise additional ideas that were not directly studied in class. Students will be asked questions of "philosophical reading comprehension" about these texts, based on insights and concepts learned throughout the course, as well as on three articles that the students should read throughout the course.