Logistics:

Credits:	2
Meetings:	Fridays, 2:00pm to 3:00pm
Classsroom:	TBD

Course Description: This study module explores fundamental questions about the nature of mathematical knowledge, truth, and practice. Through engagement with classical and contemporary perspectives, we will investigate the the epistemological foundations of mathematical knowledge, ontological status of mathematical objects, and the relationship between mathematics, computer science, and human cognition.

We will discuss the following topics:

1. Classical Approaches: Including Platonist conceptions of abstract objects, the logicist reduction programs of Frege, Russell, Whitehead, Dedekind, and Peano, and finally Hilbert's Program for formalization of all of mathematics in axiomatic form.
2. Alternative Perspectives: Analysis of critical responses to classical positions, including Brouwer's Intuitionism with its constructivist emphasis, the Quasi-empiricist approaches of Hamming, Quine, Putnam, and Lakatos, and some of the Social Constructivist accounts of mathematical knowledge.
3. Structuralism: : Including Benacerraf's fundamental dilemmas, and approaches developed to address them by considering mathematical objects as positions within relational structures.
4. Mathematical Aesthetics: The epistemological significance of beauty in proof selection, theoretical development, and mathematical discovery and the cognitive foundations of mathematical creativity.
5. Philosophy of Computer Science: Some foundational questions at the intersection of philosophy, mathematics, and computation, such as the ontological status of computation (algorithms), the nature of computational (automated) proofs, and the relationship between abstract mathematical objects and their concrete representation in computer science.

This course does not deal with the questions of ethics in mathematics and computer science. Some of these questions are discussed in AI and Philosophy [PHI-2188], Philosophy of Science [PHI-2240], Ethics and Technology [PHI-2665], and Introduction to Ethics [PHI-2730].

Evaluation: Active participation (including completing the required readings) is critical to the learning experience. There are no assignments beyond the required readings. Our objective is to write an original paper. This may be completed individually or in a small group. The final paper will contribute to the majority of your grade.

Attendance Policy: Attendance is mandatory and only two unexcused absences will be permitted. Excessive absences will impact your grade.