PRESENTATION
Coordination : Vincenzo de Risi (CNRS, SPHERE), Paola Cantù (Centre G.-G. Granger)
PROGRAMME
Séance du mardi 6 novembre 2018 : de 16h à 18h, Université Paris Diderot, salle 371 Klein*
- Georg Schiemer (Université de Vienne)
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 sur les activités à venir
Séance du jeudi 11 avril 2019, au Centre G.-G. Granger, Aix-Marseille Université
Journée d’études “Hilbert on the Foundations of Geometry" du samedi 8 juin 2019, à l’Université Paris Diderot
Journée détudes, mardi 17 mars 2020, IHPST, Paris
INFORMATIONS PRATIQUES
Université Paris Diderot, bâtiment Condorcet, 4, rue Elsa Morante, 75013, Paris (map).
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