terça-feira, 13 de março de 2012

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 and Amsterdam)

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?

CALL FOR PAPERS

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.

REGISTRATION

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

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

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 cam.phil.conf@gmail.com

The organisers gratefully acknowledge funding from the Analysis Trust,
the Aristostelian Society, the British Academy, the Mind Association
and the British Logic Colloquium.

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