CamPoS: Cambridge Philosophy of Science

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