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"Towards a New Epistemology of Mathematics", Workshop at GAP.6, FU Berlin, September 2006

Towards a New Epistemology of Mathematics

    Workshop at GAP.6 (http://www.gap6.de/)
          Freie Universitaet Berlin
           September 14 & 15, 2006

     http://www.phimsamp.uni-bonn.de/GAP6/

organized by Bernd Buldt (Konstanz), Benedikt Loewe (Amsterdam), Thomas
Mueller (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.

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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.