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 space-time. 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. Speakers - 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