5-8 May 2009
Uppsala, Sweden
Philosophy and Foundations of Mathematics :
Epistemological and Ontological Aspects,
at the Swedish Collegium for Advanced Study,
Uppsala, May 5-8, 2009
- a conference dedicated to Per Martin-Lf
on the occasion of his retirement.
Speakers
Peter Aczel: TBA
Mark van Atten: Different times: Kant and Brouwer on real numbers
Steve Awodey: Type theory and homotopy theory
Thierry Coquand: Forcing and type theory
Peter Dybjer: Program testing and constructive validity
Juliet Floyd: Wittgenstein, Gdel and Turing
Jean-Yves Girard: Towards non-commutative foundations
Sten Lindstrm: The Curry-Fitch's knowability paradox revisited
Per Martin-Lf: Logic: epistemological or ontological?
Colin McLarty: Identity and existence in categorical foundations
Peter Pagin: Assertion, truth and judgment
Erik Palmgren: Formal topology and foundational problems
Christine Paulin-Mohring: Reasoning on randomized programs in Coq
Jan von Plato: Aristotles deductive logic: a proof-theoretical study
Dag Prawitz: TBA
Aarne Ranta: Levels of abstraction in language and logic
Michael Rathjen: The boundaries of intuitionistic type theory
Giovanni Sambin: A minimalist foundation of mathematics
Anton Setzer: Coalgebras as types determined by their elimination rules
Stewart Shapiro: An "i" for an i: singular terms, uniqueness
and reference
Wilfried Sieg: Reductive structuralism
Jan Smith: Can Hume's analysis of causality tell us something about the
rules of logic?
Sren Stenlund: On the notion finite numbers
Gran Sundholm: Three key-features of Martin-Lf's philosophy of logic
William Tait: The myth of intuition
Jouko Vnnen: Second order logic, set theory and
foundations of mathematics
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-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.
Venue
The workshop will take place at the Swedish Collegium for Advanced
Study (SCAS), Linneanum, Thunbergsvgen 2, Uppsala, Sweden.
Organization and programme committee
Peter Dybjer, Sten Lindstrm, Erik Palmgren (Chair), Dag Prawitz,
Sren Stenlund, Viggo Stoltenberg-Hansen.
Programme
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
Attendance is open, and there is no registration fee. However, anyone
planning to attend should preregister by emailing PFM@math.uu.se no
later than April 15, 2009. (For reasons of space the number of
participants will be limited to 90.)
Sponsors
Swedish Research Council (Vetenskapsrdet) - Department of
Mathematics, Stockholm University - Department of Philosophy,
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.
Webpage
http://www.math.uu.se/PFM/