From Plato to predicativity

Seminar on the Philosophy of Mathematics

This Intercity Seminar on the Philosophy of Mathematics is intended for anyone with at least a B.Sc in mathematics (hence especially for M.Sc and PhD students, whose research interests may lie elsewhere). The seminar takes place on alternate Friday afternoons from 14:00-16:30 h, beginning September 26th, 2008. We alternatively meet at the University of Utrecht (Mathematical Institute, Room 611, except 24 October) and at the Radboud Universiteit Ni2jmegen (location to be announced).

The relationship between mathematics and physical reality, and that between provability and truth have been studied from Plato till the present day. In the twentieth century these issues have receive
the attention of philosophers like Husserl, Russell and Wittgenstein, as well as of mathematicians like Hilbert, Brouwer and Goedel. The latter development within mathematics has increasingly focused on technical issues concerning axiomatic systems for the foundations of mathematics, whereas the former has essentially become part of analytical philosophy and has moved away from mathematics. In this seminar both lines will be represented by a variety of speakers whose backgrounds range from classical philosophy to quantum mechanics. Indeed, the eventual goal of the seminar is to bring basic philosophical questions back into contact with technical mathematical issues.

Special session November 3, 2009

Peter Hacker (Oxford), Proof in mathematics
Peter Koepke (Bonn), Mathematical proofs as derivation-indicators: theory and implementation

Program for 2009 (all sessions Friday 14:00-16:30 at Utrecht, MI.611)

January 30
H. Barendregt (RU), From mnemonics to proofs to lambda terms
K. Algra (UU), Cosmology and Mathematics in Aristotle and the Hellenistic schools

February 13
D. Corfield (Canterbury), Imre Lakatos: Proofs and Refutations
D. Corfield, Albert Lautman and Mathematical Reality

February 27
D. Isaacson (Oxford), Some comparisons between incompleteness in arithmetic and set theory
A. MacIntyre (London): The Impact of Incompleteness on Pure Mathematics

March 13 (Location: P.019, University of Amsterdam, Euclides building, Plantage Muidergracht 24, 1018 TV Amsterdam)
W. Hodges (Cambridge), Where Frege is coming from
J. Vaananen (UvA), Second order logic, set theory and the foundations of mathematics

March 27
C. Held (Erfurt), Frege and Second-Order Logic

April 17
N.-C. Short (Univ. Provence), Mathematical style: where symbolic concurrent structures and individual practice meet
W. Sieg (Carnegie Mellon University), Structural Proof Theory: Uncovering aspects of the mathematical mind

Program for 2008

September 26 (Utrecht, MI.611)
J. Kennedy (Helsinki): Some general remarks on the philosophy of mathematics (text available on request)

M. Keestra (UvA): Shying away from the mathematization of science. Setting the stage with Plato's idealism and Aristotle's quasi-empiricism of mathematical objects

October 10 (Nijmegen, HG.00.068)
H. Boukema (RU): Emergence, nature and decay of Russell's Platonism
W. Veldman (RU): Playing Brouwer's game

October 24 (Utrecht, Buys-Ballot Laboratorium 4.26)
A.S. Troelstra (UvA): Intuitionism
H. Philipse (UU): Platonism or psychologism in mathematics: A false dilemma? Frege, Husserl, and Wittgenstein on the philosophy of mathematics (Preliminary Reading: G. Frege, Grundgesetze der Arithmetik (Jena 1893) (Vorwort) .

November 7 (Nijmegen, Linnaeus Building LIN 4)
F.J. Dijksterhuis (UT): Mixta, Pura, Practica. The Landscape of Early Modern Mathematics
Tim Nicolaije (UT): Concepts of the usefulness of mathematics in the 17th century

The Linnaeus Building in Nijmegen is the low grey building located to the right of the Huygens Building (when facing the latter).

November 21 (Utrecht, MI.611)
H. Bos (UU/Aarhus): Descartes' attempt, in the 'Regulae,' to base the certainty of algebra on mental vision
K. Landsman (RU): Newton and Hilbert on the foundations of geometry: a case study in the philosophy of mathematics
Primary literature:
Newton, Preface to the reader (Auctoris Praefatio ad Lectorem) from Principia
Hilbert, Foundations of Geometry
Einstein, Geometry and Experience

December 12: no seminar

Juliette Kennedy
Klaas Landsman
Ieke Moerdijk