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Philosophy of Mathematics (PH342)

This module will be a survey of philosophy of mathematics. We will begin by focusing on classical, (Plato and Aristotle), and modern, (Descartes, Kant, and Mill), sources. We will then turn to the major foundational schools of the early 20th century: logicism, (Frege and Russell), intuitionism, (Brouwer and Heyting) and formalism, (Hilbert). We’ll next consider the early development of set theory and the major limitative results of the 1930s, (e.g. Gödel’s Incompleteness Theorems), and inquire into their significance with respect to mathematical knowledge, provability, truth, and ontology. Finally, we will survey several recent philosophical proposals about the nature of mathematics, (structuralism, nominalism, fictionalism).

Learning Outcomes or Aims

By the end of the module the student should be able to: 1) demonstrate knowledge of some of the central topics in the philosophy of mathematics, and of the history; 2) understand the significance questions in the philosophy of mathematics have to wider issues in philosophy and the foundations of mathematics; 3) articulate their own view of the relative merits of different theories and engage critically with the arguments put forward in support of them.

PH342

Module Director:

Walter Dean