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 college 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.

Accessibility and Prerequisites. I presuppose the notation of first-order logic with quantifiers. As we will skip some parts of set theory you have already seen in the logic class, I also presuppose the logic course you have taken in the fall semester. As for the mathematics, I hope you can count. Nothing more will be presupposed, and even the counting will be carefully introduced.

This course will be taught in English.

Recommended Texts

  • Stewart Shapiro. Thinking about Mathematics: The Philosophy of Mathematics. Oxford University Press (2000).
  • Most reading materials are available through icorsi.

Course Requirements and Evaluation

The grade for this course will be determined by the points obtained from a single type of evaluation: there will be three sets of homework assignments each worth 10 points.

Homework assignments are listed here:

Course Materials

Course materials such as lecture notes, handouts, etc will be made available as they will be used in class.