5-8 May 2009
Uppsala, Sweden
First announcement
A conference on
Philosophy and Foundations of Mathematics -
Epistemological and Ontological Aspects,
dedicated to Per Martin-Lf 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 Lindstrm Colin McLarty Per Martin-Lf
Peter Pagin Erik Palmgren Jan von Plato
Dag Prawitz Christine Paulin Aarne Ranta
Michael Rathjen Giovanni Sambin Anton Setzer
Stewart Shapiro Wilfried Sieg Sren Stenlund
Gran 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-Lf'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-Lf 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-Lf. What is the relation between
proof-theoretical semantics in the tradition of Gentzen, Prawitz, and
Martin-Lf 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 Lindstrm Erik Palmgren
Dag Prawitz Sren Stenlund Viggo Stoltenberg-Hansen
(organization and programme committee)
Venue
The workshop will take place at the Swedish Collegium for Advanced
Study (SCAS), Linneanum, Thunbergsvgen 2, Uppsala, Sweden
Attendance
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.
A complete programme and further useful information will appear
on the web page
http://www.math.uu.se/PFM/
Sponsors
The conference is organised with the support of
Swedish Research Council,
Department of Mathematics, Stockholm University,
Department of Mathematics, Uppsala University,
Centre for Interdisciplinary Mathematics, Uppsala University,
Department of Philosophy, Uppsala University,
Department of Computer Science and Engineering, Chalmers University of
Technology and Gothenburg University,
The Swedish Collegium for Advanced Study, Uppsala,
Swedish National Committee for Logic, Methodology and Philosophy of Science
.