# 34I0156

What is the nature of mathematical knowledge, as compared to knowledge of the natural world? What, if any, is the connection between the two? What role does mathematics play in empirical sciences such as physics? What role does philosophy play in clarifying the foundations of mathematics? Do abstract objects, such as numbers, exist? Is mathematics somehow true of our world, or is it merely an ingenious language devised by humans to address all sorts of problems?

In this class, we will address these questions and study how leading philosophers and mathematicians have attempted to answer them, giving special attention to the influential schools of logicism, formalism, and intuitionism.

No prior university-level mathematics or philosophy is presupposed, although both will be helpful. Since it offers a focal point for many issues raised in the class, I will give a self-contained introduction to set theory. I will presuppose the notation of first-order logic with quantifiers. If you ever took a logic class, you've seen this; if you haven't, don't worry: you'll quickly pick it up.

This course will be conducted entirely in English. I plan to be giving lectures throughout, even though there will be the possibility of giving presentations in case someone needs them to obtain credit.