## Philosophy of mathematics, logic and computation

Cambridge
has long been a major centre for philosophy of mathematics, logic and
computation. Alfred North Whitehead and Bertrand Russell developed their
theory of types here. Their three-volume *Principia Mathematica*
provides a foundation for mathematics that is free from Russell's paradox. Ludwig Wittgenstein initially
studied with Russell, developing his philosophical ideas on logic. Eight years
after its publication, Wittgenstein returned to Cambridge, submitting his *Tractatus
Logico-Philosophicus* as his PhD thesis; he later became a Fellow of Trinity, and then Professor of Philosophy.
Wittgenstein's nominal PhD supervisor was Frank
Plumpton Ramsey, who
produced profound technical and philosophical works before his tragically early
death. Alan Turing, too, is perhaps best
known for his technical work (and his tragic death); however, his paper ‘On
Computable Numbers’ is perhaps the landmark document in the philosophy of
computation.

Cambridge
remains exceptionally strong in these areas today. Rarely for an undergraduate
course in philosophy, logic is compulsory in Cambridge for both first and
second years. Several recent PhD students have written doctoral dissertations
on philosophy of mathematics or logic. And we have a thriving research
environment. Our philosophical logic seminar meets every Thursday during term
time. Every January, we hold a graduate conference in philosophy of logic and
mathematics. We have recently held international conferences on the foundations
of mathematics and on logical form. Current research by faculty and affiliated
members includes the philosophy of set theory, philosophy and model theory,
plural logic, Frege's concept *horse* paradox, and
Wittgenstein's pre-Tractarian writings.

Tim Button

November 2012