PRESENTATION

Coordination: Vincenzo de Risi (CNRS, SPHERE), Paola Cantù (Centre G.-G. Granger)

PROGRAM

**Session of Tuesday November 6, 2018**: 4p.m. – 6p.m., University Paris Diderot, Room 371 Klein*.

- Georg Schiemer (University of Vienna)
*What are implicit definitions?*

The notion of implicit definition is a fundamental concept in modern mathematics, in particular in formal axiomatics. It is also ubiquitous in contemporary philosophical debates, ranging from the fields of philosophy of science and mathematics to philosophy of logic and language. Despite the relevance of this notion, it is commonly used in an informal way in these debates. The aim of this paper is to make more precise what implicit definitions actually are. We will address this issue by distinguishing between several types of definitions which are usually associated with the expression “implicit definition”. In particular, the focus here will be on a kind of definition given in structural or formal axiomatics, which in general terms is usually understood as providing a definition of the primitives terms of a given axiomatic theory. A central claim in the talk is that it is somewhat unclear how such definitions should be understood semantically. More precisely, we propose that both in modern mathematics and in subsequent philosophical debates one can distinguish between two types of understanding structural definitions semantically, namely, (i) as definitions of the meaning of the primitive terms of a theory and (ii) as definitions of types or concepts of mathematical objects or, alternatively, as their structures. The central aim in the following will be to survey these two conceptions of structural definitions both in the history of mathematics and in selected philosophical debates. The present work presents joint research with Eduardo Giovannini (CONICET Argentina).

- Discussion on future activities

**Session of Thursday April 11, 2019**, at Centre G.-G. Granger, Aix-Marseille University

**Study Day “Hilbert on the Foundations of Geometry", Saturday June 8, 2019**, University Paris Diderot

**Study Day , Tuesday March 17, 2020**, IHPST, Paris

Building Condorcet, University Paris Diderot, 4 rue Elsa Morante, 75013, Paris (map)

Calculate your itinerary with the public transport website RATP

Metro: lines 14 and RER C, stop: Bibliothèque François Mitterrand or line 6, stop: Quai de la gare. Bus: 62 and 89 (stop: Bibliothèque rue Mann), 325 (stop: Watt), 64 (stop: Tolbiac-Bibliothèque François Mitterrand)