What Are Foundations of Mathematics and What Are They For?

The conference aims to bring together philosophers, logicians and mathematicans to reflect on the following core questions: What are foundations of mathematics? Does mathematics need a foundation? If so, why and in what form?

'What are foundations?' It is often said that mathematics should be founded on set theory, and in particular the theory ZFC. The central role of ZFC as a foundation of mathematics has been criticized from various standpoints. Some have suggested that mathematics should be founded on set theories which extend, or are incompatible with, ZFC; others have argued that the foundation should be sought in a different framework such as category theory, structuralism, (neo-)logicism or higher-order logic; other still have suggested that mathematics neither has nor needs a foundation at all.

'What are they for?' Looking at the philosophical and mathematical literature, when people talk about foundations they have different things in mind: sometimes they understand foundations in an epistemic, sometimes in an ontological, sense; or perhaps a foundation should provide us with an arena within which all mathematical objects can be studied and compared and all questions of existence and proof in mathematics settled.

One might ask whether any one of the putative foundational frameworks (e.g. set theory, category theory) can yield mathematical foundations in all three senses. If not, does this require that we give up on mathematical foundations altogether? Or could we adopt a pluralism about mathematical foundations, perhaps accepting different foundations for different purposes? Where would either of these approaches leave us?

Registration

Registration is now open. To register, please go to the conference website and follow instructions.

Poster

To download a poster of the conference, please go to:

http://www.phil.cam.ac.uk/foundations/FoundationsOfMathematics.pdf

For questions, please contact the conference organisers, Tim Button, Luca
Incurvati and Michael Potter, at [email protected]