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# Philosophy and Model Theory

June 2-5 2010

The conference is now over... but you may still find here

*** the general description of the conference,

*** the conference program, including slides for some of the talks.

Conference description

What? Where?

This is a conference on Model Theory from a philosophical perspective. The conference is supported by the University Université Paris Nanterre (Ireph and EA 373) and by the Agence Nationale de la Recherche (Logiscience program, supervised by P. Wagner at the Institute of History and Philosophy of Science and Technology). It will be held in Paris from June 2 to June 5 2010 at the University Université Paris Nanterre (June 2 and June 3) and at the Ecole Normale Supérieure (June 4 and June 5). Conference organizers are Denis Bonnay, Brice Halimi and Jean-Michel Salanskis.

Speakers

John Baldwin (University of Illinois at Chicago), Timothy Bays (University of Notre Dame), John Bell (University of Western Ontario), Denis Bonnay (Université Université Paris Nanterre), Thierry Coquand (University of Gothenburg), Philip Ehrlich (Ohio University) , Henri Galinon (Université Paris I, IHPST), Brice Halimi (Université Université Paris Nanterre), Joel Hamkins (CUNY), Martin Hils (Université Paris 7), Martin Kasa (University of Gothenburg), Paolo Mancosu (UC Berkeley), David Nicolas (Institut Jean Nicod), Alejandro Perez-Carballo (MIT), Bruno Poizat (Université Lyon I), Philippe de Rouilhan (IHPST), Jean-Michel Salanskis (Université Université Paris Nanterre), Hourya Sinaceur (IHPST), Jamie Tappenden (University of Michigan), Pierre Wagner (University Paris I), Sean Walsh (University of Notre Dame), Fernando Zalamea (Universidad Nacional de Columbia).

Model theory seems to have reached its zenith in the sixties and the seventies, when it was seen by many as virtually identical to mathematical logic. The works of Gödel and Cohen on the continuum hypothesis, though falling only indirectly within the domain of model theory, did bring to it some reflected glory. The works of Montague or Putnam bear witness to the profound impact of model theory, both on analytical philosophy and on the foundations of scientific linguistics.

Thirty or forty years later, the situation has decidedly changed, as other perspectives have all but replaced model theory, as for example in the areas of analytical philosophy and scientific linguistics mentioned above. Still, model theory has retained its function as a standard reference language for a wide variety of perspectives, fields and problems. At the same time, as a branch of mathematical logic, it has given rise to a number of important developments.

The aim of the conference is to take stock of the current situation, viewing it from a variety of perspectives, of which the following are but possible examples:*1) History*. Model theory now has a history, associated to a large extent with Tarski, who blazed the trail leading from the invention of logical semantics, in his famous 1935 paper, to the active promotion of what he himself called model theory. We would welcome any discussions shedding light on that evolution, as well as reflections on the avenues that have been opened up in the field beyond the pioneering work done by Tarski himself.

*2) Technicalities*. Over the course of its brief history, model theory (and logical semantics) have seen a number of significant innovations. The possible variation of interpretation structures for a given theory has been studied within the context of set theory, and model theory has intersected with a number of set theoretic themes (large cardinals, descriptive set theory, and so on). The fundamental core of model theory has been thought of as open to modifications, in particular so as to match category theory. As to logical semantics, different notions of model have been defined so as to allow for completeness theorems corresponding to different logics. Cogent discussions of these and related issues are also solicited.

*3) Applications*. Model theory and logical semantics have also been used as a kind of rational pattern and as a guide for scientific study in other areas. We invite talks having to do with all such applications of model theory -- in linguistics, cognitive science, economics, etc.

*4) Philosophy*. Finally, model theory and logical semantics, as Popper reports he discovered them,** **have been viewed as the most exact means with which to account for the fundamental philosophical problem of knowledge. Indeed, they have been thought to provide the most general and the most comprehensive way to describe what it is for a discourse to say the truth about reality. For that reason, numerous philosophical studies have come to depend on model theory. This is the case with the philosophy of mathematics, and a similar development may be seen in the way in which general epistemology has been molded, and also in the way questions in metaphysics, esthetics and general philosophy have been dealt with. Talks exploring such issues would be most welcome.

To conclude this tentative anticipation of some of the themes and questions that will be addressed, it seems to us that our work will be all the more relevant and fruitful if we keep in mind the distinction between logical semantics (let's say, the theory of truth as Tarski developed it around 1935) and model theory properly speaking which, in the realm of ZFC, studies the "degrees of freedom" that theories and their interpretation structures permit each other.

Slides or papers corresponding to most of the talks are now available online, just scroll down the schedule list to find the materials you are interested in.

Room L318

14:10--15:00 John Baldwin [slides] [references]

The impact of Modern Model Theory on Mathematics and Philosophy

15:00--15:50 Joel Hamkins [slides]

The set-theoretic multiverse: a model-theoretic philosophy of set theory

16:10--17:00 Philippe de Rouilhan [slides]

Quelle théorie des modèles ?

17:00--17:50 Paolo Mancosu [slides]

Tarski on semantical completeness, categoricity and logical consequence

Room L318

09:00--09:50 John Bell

What is categorical model theory?

09:50--10:40 Fernando Zalamea [slides]

Model theory of sheaves: a mathematical conspectus and a philosophical prospectus

11:00--11:50 Michel Olivier [paper]

La vérité ludique et la logique du premier ordre IF de Hintikka comme fondement alternatif du lien entre phrases et modèles

11:50--12:40 David Nicolas [handout]

Semantic theories for plurals

14:10--15:00 Bruno Poizat [slides]

Je positive !

15:00--15:50 Martin Hils [slides]

Imaginaries in Model Theory

16:10--17:00 Hourya Sinaceur [slides]

Etchemendy's objections to Tarski's concept of logical consequence

17:00--17:50 Pierre Wagner [slides]

Models and interpretations in the fifties: Kemeny and Carnap

Salle Cavaillès

09:00--09:50 Thierry Coquand [slides]

Model Theory and constructive mathematics

09:50--10:40 Sean Walsh [slides]

Interpreting Wilkie's Theorem

11:00--11:50 Jamie Tappenden

The geometric prehistory of model theory

11:50--12:40 Timothy Bays

Skolem on the foundations of mathematics

14:10--15:00 Martin Kasa [slides]

Some results on experimental logics

15:00--15:50 Henri Galinon

Vérité, principes de réflexion et preuves de cohérence

16:10--17:00 Alejandro Perez-Carballo

Models and semantics

17:00--17:50 Jean-Michel Salanskis

Two issues about Model Theory

Salle des Résistants

09:50--10:40 Philip Ehrlich [slides]

The absolute arithmetic continuum and the unification of all numbers great and small

11:00--11:50 Denis Bonnay [slides]

Logical consequence inside out

11:50--12:40 Brice Halimi [slides]

Categories of models

Mis à jour le 08 avril 2012