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The Continuum in Mathematics and Philosophy (Nov 2004, Copenhagen)

The Continuum in Mathematics and Philosophy

November 25 - 27 / 2004
The Carlsberg Academy, Copenhagen, Denmark

Organized by PHIS - The Danish Research School in Philosophy, The History
of Ideas and the History of Science (http://www.phis.ruc.dk) in
association with PHILOG

Aristotle struggled, in his physics, with a characterisation of the
continuum, and since then both philosophers and mathematicians have
continued the struggle. Even with the rigorous set theoretical
characterisation given by the end of the 19th century---a characterisation
which dominates modern mathematics---the difficulties still linger around.

The mathematician Rene Thom describes the problems in the following poetic
way: ``When you refer to a physical object, you mean an object which can
be scientifically described. I would accept that, in any kind of
description, we have a discrete element, because a true continuum has no
points. We are unable to specify anything in the continuum. The continuum
is something which cannot be described. It is a sort of unsayable. It is a
world in which one lives outside of symbolic description. But
nevertheless, it exists, despite the fact that we cannot describe it in
any sense.'' The physicist John Wheeler points in a similar intuitive way
to difficulties: ``Yet for daily work the concept of the continuum has
been and will continue to be as indispensable for physics as it is for
mathematics. In either field of endeavor, in any given enterprise, we can
adopt the continuum and give up absolute logical rigor, or adopt rigor and
give up the continuum, but we can't pursue both approaches at the same
time in the same application.''

The continuum hypothesis still haunts the foundations of mathematics and
as Thom, and many before him, says a true continuum can never be thought
of as a mere collection of points.

The 20th century has seen several new attempts to define the continuum in
a mathematical rigorous way more in accordance with our strong
philosophical intuitions. The aim of this conference is to throw light
upon the concept of the continuum, both in its systematic and its
historical aspects.

Historically, the main interpreters of continuity will be
discussed---Aristotle, Leibniz, Kant, Peirce, Cantor, Hilbert, Brouwer,
Weyl, etc. Systematically, there is a current wave of interest in the
philosophical and mathematical status of the continuum, and various
contemporary approaches and subjects will be presented and discussed,
including non-standard analysis, topos theory, constructivism, recent
positions pertaining to the continuum hypothesis, continuity as a derived
or primitive concept, the continuity or discontinuity of physical

The concept of the continuum is still in a process of fertile revision,
and it is our hope that this conference will contribute to shed light on
its role in mathematics and philosophy, and also in the special---natural
and human---sciences.


- Richard Arthur

- Pierre Aubenque

- Philip Ehrlich

- Frederik Stjernfelt

- Horst Osswald

- Jean Petitot

- Carl Posy

- Hugh Woodin


Program Committee

- Stig Andur Pedersen

- Nikolaj Oldager

- Frederik Stjernfelt

For more information, abstracts, time tables, conference registration,
etc. please refer to the conference homepage at
http://www.phis.ruc.dk/phisact/contconf.html and/or download the complete
conference booklet directly from http://www.phis.ruc.dk/continuum.pdf