This module is not running 2015-16.
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).
The following is a list of topics for this module in the 2014/15 academic year; precise seminar content may change from year to year.
- Introduction, philosophical background
- Classical perspectives
- Rationalism and empiricism
- Interlude on set theory, second-order logic, and arithmetic
- Logicism and neo-logicism
- Formalism and the Hilbert Programme
- Paradoxes, Godel’s Theorems, and set theoretic independence
Timing and CATS
This module runs in the Spring Term and is worth 15 CATS.