segunda-feira, 5 de dezembro de 2011

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.

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