Conference: Philosophy and Foundations of Mathematics - Epistemological and Ontological Aspects, Uppsala May 5-8, 2009

First announcement:
A conference on
Philosophy and Foundations of Mathematics - Epistemological and Ontological Aspects
,

dedicated to Per Martin-Löf on the occasion of his retirement, is to be held in

Uppsala, Sweden, May 5-8, 2009 at the Swedish Collegium for Advanced Study.

Speakers:

Peter Aczel         Mark van Atten      Thierry Coquand
Peter Dybjer        Juliet Floyd        Jean-Yves Girard
Sten Lindström      Colin McLarty        Per Martin-Löf
Peter Pagin         Erik Palmgren       Jan von Plato
Dag Prawitz         Christine Paulin    Aarne Ranta
Michael Rathjen     Giovanni Sambin     Anton Setzer
Stewart Shapiro     Wilfried Sieg       Sören Stenlund
Göran Sundholm      William Tait



The aim of the conference is to bring together philosophers, mathematicians, and logicians to penetrate current and historically important problems in the philosophy and foundations of mathematics. Swedish logicians and philosophers have made important contributions to the foundations and philosophy of mathematics, at least since the end of the 1960s. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. A central philosophical question concerns the nature of the abstract entities of mathematics: do they exist independently of our epistemic acts (realism, or Platonism) or are they somehow constituted by these acts (idealism)?

Significant contributions have been made to the foundations of mathematics, for example in proof theory, proof-theoretic semantics and constructive type theory. These contributions have had a strong impact on areas of computer science, e.g. through Martin-Löf's type theory.

Two important alternative foundational programmes that are actively
pursued today are predicativistic constructivism and category-theoretic foundations.  Predicativistic constructivism can be based on Martin-Löf constructive type theory, Aczel's constructive set theory, or similar systems. The practice of the Bishop school of constructive mathematics fits well into this framework. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning as-use?

What can proof-theoretical analysis tell us about the scope and limits of constructive and (generalized) predicative mathematics? To what extent is it possible to reduce classical mathematical frameworks to constructive ones? Such reductions often reveal computational content of classical existence proofs. Is computational content enough to solve the epistemological questions?

A central concern for the conference will be to compare the different foundational frameworks - classical set theory, constructive type theory, and category theory - both from a philosophical and a logical point of view. The general theme of the conference, however, will be broader and encompass different areas of philosophy and foundations of mathematics, in particular the interplay between ontological and epistemological considerations.

    Peter Dybjer    Sten Lindström    Erik Palmgren
    Dag Prawitz     Sören Stenlund    Viggo Stoltenberg-Hansen

   (organization and programme committee)