[FOM] Workshop in Berlin "Towards a New Epistemology of Mathematics"

Benedikt Loewe bloewe at science.uva.nl
Sat Mar 25 17:52:09 EST 2006


     Towards a New Epistemology of Mathematics
      Workshop at GAP.6 (http://www.gap6.de/)
      Freie Universitaet Berlin
      September 14 & 15, 2006

deadline: 1 April 2006

organized by Bernd Buldt (Konstanz), Benedikt Löwe (Amsterdam), Thomas
Müller (Bonn).

Invited Speakers include:
Leo Corry (Tel Aviv)
Keith Devlin (Stanford)
Katja Lengnink (Darmstadt)
Bart Van Kerkhove (Brussels)

The organizers cordially invite contributed
papers from all relevant areas  of research,
including historical, didactical, and empirical
approaches to  the philosophy of mathematics.
(Please use the online submission form on
the workshop webpage.)

The deadline for submission is April 1st, 2006.

Aims and scope

Traditionally, there has been a deep divide between philosophy of
mathematics dealing with foundational issues (questions about mathematical
ontology, connections between logic and mathematics, and the proper
axiomatic framework) and sociological and didactical approaches to
mathematics deadling with a description of mathematical practice
(including mathematics education and related matters).  Currently, we
witness this picture undergoing considerable changes.

In the tradition of the "Grundlagenkrise," philosophy of mathematics was
focussed on the battles between the schools of Platonism, intuitionism,
and formalism - approaches that have entirely lost their lustre.  In the
past ten to fifteen years, however, new viewpoints entered the
philosophical debate, viz., naturalism (e.g., Maddy), structuralism (e.g.,
Shapiro), and social constructivism (e.g., Lakatos, Tymocko, Hersh).
All of these approaches to mathematical thinking have in common that they
focus on mathematical practice, take seriously linguistic usage in the
community of professionals, and emphasize (naturalism in a weak sense,
social constructivism in a very strong sense) the social embedding of
mathematical practice and therefore of the epistemic prerequisites of
mathematical research.  Accordingly, Corfield in his 2003
monograph "Towards a Philosophy of Real Mathematics" demands more
attention to the areas of mainstream mathematics and criticizes the fact
that philosophers of mathematics disregard everything since Godel's
theorem as a kind of footnote to mathematics, irrelevant to their
loftier concerns.  But not only the philosophical community has started to
discuss mathematical practice. A (now famous) joint paper by Princeton
mathematicians Arthur Jaffe and Frank Quinn on rigour in mathematics
incited the so-called "Jaffe-Quinn debate" in mathematics (published in
the "Bulletin of the American Mathematical Society" in 1993).  In its wake
many working mathematicians have discussed the practical consequences of
the social conventions in the mathematical community, most famously Bill
Thurston in a reply published in the same journal in 1994, who describes a
view of mathematical practice that focusses much more on the social
acceptance mechanisms of the community than on formal proof.

All these developments question the special character of philosophy of
mathematics as traditionally conceived.  Our workshop is devoted
to developing this line of development further, putting special emphasis
on the epistemological issues involved.

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