**10-12 July 2012
Cambridge, U.K.**

What Are Foundations of Mathematics and What Are They For? Fitzwilliam College, Cambridge, 10th - 12th July 2012 Invited Speakers: Steve Awodey (Carnegie Mellon) Patricia Blanchette (Notre Dame) Michael Detlefsen (Notre Dame) Tim Gowers (Cambridge) Peter Koellner (Harvard) Brendan Larvor (Hertfordshire) Hannes Leitgeb (Munich) Mary Leng (Liverpool) Donald Martin (UCLA) Alex Paseau (Oxford) Jouko Väänänen (Helsinki) Alan Weir (Glasgow) Philip Welch (Bristol) 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? We invite papers suitable for a 40 minute presentation. Papers should be accompanied by an abstract of no more than 150 words, and should be suitable for blind refereeing. Please include a separate detachable cover sheet including name, title, institution, and contact details. Please note that we cannot accept more than one submission per person. The deadline for receipt of submissions is: 16th March 2012 We will aim to notify authors of the decision regarding their papers soon after the deadline. Submissions should be in .doc, .rtf or .pdf format and should be e-mailed to cam.phil.conf@gmail.com. Receipt of submission will be confirmed by e-mail. Further information (including information about registration) will be available soon on the conference website: http://www.phil.cam.ac.uk/foundations/ For questions, please contact the conference organisers, Tim Button, Luca Incurvati and Michael Potter, at cam.phil.conf@gmail.com The organisers gratefully acknowledge funding from the Aristostelian Society, the British Academy, the Mind Association and the British Logic Colloquium.