Logique, Mathématiques, Informatique, Raisonnement

Coordination scientifique : Hugo Cadière (IRPhiL Lyon 3) et Jean-Baptiste Joinet (IRPhiL Lyon 3 & IXXI)

Séminaire organisé avec le soutien de l’Institut des Systèmes Complexes Rhônalpin (IXXI) et la Maison des Sciences de l’Homme Lyon Saint-Étienne (MSH-LSE).

Au second semestre, le séminaire est plus spécifiquement consacré au thème "Indiscernabilité, Isomorphie, Identité".

Séminaire mensuel – Programme 2023-2024
 

MARS 2024

• Mardi 12/03/2024, 18h-19h30
  Site : Université Lyon 3, site des Quais (salle 206, 18 rue Chevreul)
  
  David RABOUIN (ERC Philiumm & SPHERE Sciences, Philosophie, Histoire – UMR 7219 CNRS/Université Paris Cité) & Filippo COSTANTINI (idem)
  "Identité et identification de Leibniz à la théorie homotopique des types"
   
• Mardi 05/03/2024, 18h30-20h
  Site : ENS de Lyon (AMPHI A / GRANDE NEF 1-2)
  
  Olivia CARAMELLO (University of Insubria (Como), Grothendieck Institute, Université de Paris-Saclay)
  "Relative toposes for the working mathematician"

JANVIER 2024

Mardi 30/01/2024, 18h-19h30, Salle 206, 18 rue Chevreul, Lyon

Andrei RODIN (Archives Henri Poincaré - Philosophie et Recherches sur les Sciences et les Technologies, UMR. 7117 CNRS-Université de Lorraine)
"L’Identité a-t-elle un sens ? / Does Identity Have a Sense?"
(Exposé donné en français, Diapositives en anglais)
► Écouter/voir l'intervention d'Andrei Rodin

Abstract:
Identity, i.e., "being the same as itself" is a key logical concept that has been a subject of hot philosophical debates during many centuries. Today this continuing philosophical discussion usually relies on the formal representation of the identity concept by standard means of symbolic logic where identity is construed as an equivalence relation (that is, a binary relation which is reflexive, symmetric and transitive) which satisfy the Indiscernibility of Identicals principle according to which identical things have the same (i.e. identical) properties.

This large formal framework admits many competing philosophical views on identity. Using this framework as a common ground logician and philosophers discuss whether or not the converse principle of Identity of Indiscernibles also holds, how to explain away the intuitively plausible preservation of identity through time and change (which at the surface contradicts InId since it allows the same thing to have different properties at different times), how to resolve classical paradoxes of identity such as the Ship of Theseus, and many other akin issues.

In my talk I shall explore some alternative formal approaches to representing identity that use Category theory and a modern version of Type theory called Homotopy Type theory (or HoTT for short) because of its intended interpretation in a branch of modern Algebraic Topology called Homotopy theory. As we shall see, in this alternative formal framework the identity concept is construed very differently, which sheds a new light on some long-lasted logical and philosophical puzzles. I shall make a special focus on a version of HoTT known as Directed Type theory (DTT for short) where identity comes in a directed non-symmetric form. This identity concept allows one to formalise the claim that today I am still the same person as I was 50 years ago when I was a boy without assuming that today that boy is the same person as myself.

Attending and understanding the talk does not require any previous knowledge of mathematical logic, of Type theory and Homotopy theory: all needed logical and mathematical concepts will be informally introduced and explained during the talk.

NOVEMBRE 2023

Le colloque du collectif interdisciplinaire NORMES (Logique/Informatique/Droit) et le colloque “Logique Linéaire et Philosophie” (organisés par JB Joinet & H. Cadière) étant prévus du mercredi 08/11 (à partir de 14h) au vendredi 10/11/2023, aucune séance du séminaire LMIR n’est prévue en novembre.

OCTOBRE 2023

Mardi 24/10/2023, 18h30-20h. ENS de Lyon, 15, Parvis René Descartes, Salle D2.004

Hugo CADIÈRE (IRPhiL Lyon 3 & Laboratoire junior TheoDem, ENS de Lyon)
“La notion d’égalité dans la théorie homotopique des types”

SEPTEMBRE 2023

Mardi 26/09/2023, 18h-19h30. Lyon 3, bât. du 18 rue Chevreul, 69007 Lyon, Salle 306

Jean-Baptiste JOINET (IRPhiL Lyon 3 & IXXI)
“Pour une ontologie computationnelle : sémantique actionnelle et individu algorithmique”