PILM 2002 will take place at the University of Nancy 2, home of the Poincaré Archives. The University is located near the centre of Nancy, and within a walking distance from the railway station.

Founded in 1992, the Laboratoire de Philosophie et d'Histoire des Sciences - Archives Henri Poincaré (LPHS-AHP) is an Unité mixte de Recherche du Centre National de la Recherche Scientifique (CNRS). Besides the conservation of Poincaré's writings and the collection of documents related to his work, its members conduct research projects concentrating on the philosophy and history of logic, mathematics and physics from 1850 to 1950. Following the International Congress - Henri Poincaré (Nancy 1994) and the Nelson Goodman Conference (Pont-à-Mousson 1997), the Logic Symposium of 2002 is the third large conference organized by the Archives.

Towards the end of the 20th century the following question arises: Is translatability into the language of set theory and logic really the exclusive form of justification and rigor in mathematics? Since Poincaré there have always been some outsiders who rejected the standard view about the foundations of mathematics. Formulated in modern terms, Poincaré held that the varieties of formal logical theories-which he thought to be considerably attached to set operations-don't express the structure which is essential for a genuine understanding of mathematics. One possible alternative were: "Mathematics without foundations," and it could be evidenced by the fact that the existence of formally undecidable propositions (within a given arithmetical system) or of problems unsettled by standard axioms (within set theory) does not obstruct the development of a viable and, in fact, powerful science. Accordingly, the foundational view of mathematics itself might then be suspect. Mathematics can and has to be understood from mathematical praxis alone.

Nevertheless, we would like to formalize truth, for classical model theory depends on truth definitions. As long as these definitions can only be given in a language of second-order or in set theory, model theory depends on second-order logic or set theory. But category theorists have defended the view that there are foundational operations different from set operations. Is this a way-out?

Further, recent years have witnessed a gradually increasing interest in the study of game-based semantics, such as GTS, dialogical logic, or Hintikka's IF-logic. Lately, these game-based approaches have been formulated with the help of mathematical game theory (van Benthem) and category theory (Hyland). In addition, they proved to be very effective for the formal study of linear, paraconsistent and non-monotonic logics, among others. By these developments, traditional views and received wisdom concerning the relations between syntax, semantics and pragmatics, between constructivist and classical positions, and the role of logic in foundations seem to be challenged.

Finally, most of the time the question concerning the foundations of mathematics tacitly assumes that what is to be founded is the mathematics as done by professional mathematicians of the 20th century. However, many historical, anthropological or sociological works have shown that mathematical activity is much more diverse than hitherto thought. If we accept, at least partially, that to found mathematics is relative to the practice of mathematics itself, then it is necessary to investigate the mathematics (and the mathematicians) of other cultures and other periods as well as their conception and practice of foundations.

The conference will features three sections in which the subject will be considered from a philosophical, historical or, if it comes with some philosophical insight, even technical point of view.

Section 1
Mathematical structures in foundations of mathematics: sets, categories and models

Section 2
Logical and cognitive aspects of foundations of mathematics: games, dialogues, and cognitive architecture

Section 3
Historical and Cultural Perspectives on foundations of mathematics.

Comité d'honneur: Paul Gochet, Gilles-Gaston Granger, Jaakko Hintikka, Kuno Lorenz, Roshdi Rashed, Christian Thiel.

Organisation Committee: Jean-Paul Amann, Johan van Benthem, Bernd Buldt, Dominique Fagnot, Dominique Flament, Jean-Louis Greffe, Gerhard Heinzmann, Ralf Krömer, François Lamarche, Philippe Nabonnand, Roger Pouivet, Shahid Rahman, Manuel Rebuschi, Laurent Rollet, Helge Rückert, Anne-Françoise Schmid, Joseph Vidal-Rosset, Henk Visser.

Scientific Committee: Michael Astroh, Michel Bourdeau, Karine Chemla, Gabriella Crocco, Jacques Dubucs, Catherine Goldstein, Marcel Guillaume, Jan Hogendijk, Theo M. V. Janssen, Jeffrey Ketland, Karel Lambert, Paolo Mancosu, Jean-Pierre Marquis, Jésus Mosterin, Jaroslav Peregrin, Philippe de Rouilhan, Gabriel Sandu, François Schmitz, Hourya Sinaceur, Max Urchs, Denis Vernant.

Invited Lectures:

• Patrick Blackburn
  Arthur Prior and the birth of hybrid logic
• Otávio Bueno
  The Theory of Valuations and the Foundations of Logic
• José Ferreirós
  Dogmas and the Changing Images of Foundations.
• Jean-Louis Gardies
  Les mathématiques grecques sous le regard de la théorie des types.
• Geoffrey Hellman
  Does category theory provide a framework for mathematical structuralism?
• Jaakko Hintikka
  Independence-friendly logic is classical logic.
• F. William Lawvere
  Was sind und was sollen die Kontinua?
• Kuno Lorenz
  Logic as a Tool of Science versus Logic as a Scientific Subject.

A selection of papers will be published with Kluwer.
Deadline for abstracts of contributed papers: December 20, 2001.

Participation

The conference fee is 84 € (for students and unemployed 38 €).

Please remit to the following bank account:
Name: "M. l'Agent comptable secondaire du CNRS délégation régionale du Nord Est"
IBAN (International Bank Account Number): FR76 1007 1540 0000 0030 0257 882
BIC (Bank Identification Code): BDFEFRPPXXX.
ETAB number: 10071
Guichet number: 54000
Account number: 00003002578 + 82.

You can also pay by check to the order of
"M. l'Agent comptable secondaire du CNRS délégation régionale du Nord Est"
to be sent to the address given below (foreign currency accepted).

The next circular will contain the program of the Symposium and a form for hotel booking. It is expected to appear in May 2002.

Registration Form

LPHS-Archives H. Poincaré
PILM 2002
Université de Nancy 2
BP 3397
F-54 015 Nancy
France

Tel/Fax : [33] 383 96 70 83

E-mail :
Manuel.Rebuschi@univ-nancy2.fr

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