Friday, 27 March 2009
Philosophy and Foundations of Mathematics : Epistemological and Ontological Aspects
SCAS, Uppsala, May 5-8, 2009. A conference dedicated to Per Martin-Löf on the occasion of his retirement.
*Mark van Atten
*Jan von Plato
Scope and aim
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.
The workshop will take place at the Swedish Collegium for Advanced Study (SCAS), Linneanum, Thunbergsvägen 2, Uppsala, Sweden. Map of Uppsala with a walking path from the Central Station indicated.
Organization and programme committee
Peter Dybjer, Sten Lindström, Erik Palmgren (Chair), Dag Prawitz, Sören Stenlund, Viggo Stoltenberg-Hansen.
The scientific programme starts at 10.00 on Tuesday, May 5 and ends at 16.00 on Friday, May 8. A conference dinner is planned for Friday evening. More details about the programme will appear in a few weeks.
Attendance is open, and there is no registration fee. However, anyone planning to attend should preregister by emailing PFM[at]math.uu.se no later than April 5, 2009.