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# Representation and axiomatization: power and limits

The aim of the conference is to understand whether the formal analysis of mathematical proofs — as it has been developed by the proof-theoretical tradition of Hilbert and Gentzen — is compatible or not with the use of diagrammatical representations. More precisely, the idea is to investigate the articulation of these two different approaches with respect to two fundamental aspects of the mathematical practice of demonstration: assuming hypothesis and making inferences. Since axiomatic reasoning plays a crucial role with respect to these two aspects, the question can be rephrased as the problem of the compatibility between axiomatic thought and reasoning by representation. A particular attention will be given to the ontological import of these two practices.

The conference is organized by Jean Fichot (IHPST, Univ. Paris 1), Gerhard Heinzmann (Archives Henri Poincaré, Université de Lorraine), Alberto Naibo (IHPST, Univ. Paris 1), Marco Panza (IHPST, Univ. Paris 1), Mattia Petrolo (IHPST, Univ. Paris 1).

You can follow the live conference at http://live.univ-paris1.fr:8080/IHPST (Open stream in VLC).

### Program

#### Thursday 19th

**09h30 - 10h45** Dirk Schlimm (McGill University), "Axioms in mathematical practice"

**10h45 - 11h00** Coffee break

**11h00 - 12h15** Jean-Pierre Marquis (Université de Montréal), "Axiomatization as conceptual design"

**12h15 - 14h15 **Lunch

**14h15 - 15h30** Charles Parsons (Harvard University), "Concepts vs. objects"

**15h30 - 15h45** Coffee break

**15h45 - 17h00** Catarina Dutilh Novaes (University of Groeningen), "Mathematical proofs: between orality and writing"

**17h00 - 17h15** Coffee break

**17h15 - 18h30** Valeria Giardino (Institut Jean Nicod, École Normale Supérieure), "Towards a cognitive semiotics for mathematics"

#### Friday 20th

**9h00 - 10h15** Øystein Linnebo (University of Oslo), "Reference and criteria of identity"

**10h15 - 10h30 **Coffee break

**10h30 - 11h45** Georg Schiemer (University of Vienna), "The structuralist thesis"

**11h45 - 13h** Erich Reck (University of California at Riverside), "Axiomatics, modern logic, and structuralist mathematics"

**13h - 14h30** Lunch

**14h30 - 15h45** Wilfried Sieg (Carnegie Mellon University), "The concept of computation: an axiomatic characterization"

**15h45 - 16h** Coffee break

**16h - 17h15** Leon Horsten (University of Bristol), "How have we determined what arithmetic is about?"

**17h15 - 17h30** Coffee break

**17h30 - 18h45** Volker Halbach (University of Oxford), "Representing self-reference in arithmetic"

#### Saturday 21st

**9h00 - 10h15** Walter Carnielli (University of Campinas),"Formal plenitude and Curry’s paradox: Sketch of an expanded theory for arithmetical truth’’

**10h15 - 10h30** Coffee break

**10h30 - 11h45** Victor Pambuccian (Arizona State University), "Provability in axiom systems for weak arithmetic and geometry without actual proofs"

**11h45 - 13h** Robert Hale (University of Sheffield), "Definition by abstraction and real definition"

**13h - 14h30** Lunch

**14h30 - 15h45** Mattia Petrolo (IHPST, Paris), "Negation as an ideality: From conservativeness to constructibility"

**15h45 - 16h** Coffee break

**16h-17h45 **Göran Sundholm (Leiden University), "Axiom, assumption, presupposition"