Métaphysique des modalités, in D. Lefebvre & K. Trego (éds), Les usages du possible, Peeters, 2023, p. 281-306.
Y a-t-il un sens à dire d’une situation impossible qu’elle aurait pu être possible? Ou bien d’une situation contingente, qu’il est possible qu’il soit nécessaire qu’elle soit contingente? De manière générale, les modalités d’ordre supérieur sont-elles admissibles? L’article initie une reconsidération positive de cette question, en montrant qu’elle est à la fois fondamentale et historiquement plus ouverte qu’on pourrait le penser.
A categorical aspect of the analogy between quantifiers and modalities, in Logic in Question, Birkhäuser, coll. «Studies in Universal Logic», 2023, p. 675-690.
The formal analogy between quantifiers and modalities is well-known. Its obvious limitation is, too: it holds on the condition of confining quantification to a single variable. This paper first presents that analogy in the terms of dynamic logic, which allows one to overcome the limitation just mentioned and to translate fragments of first-order logic into the language of propositional modal logic. It then sets out how the modal semantics for first-order logic which is established by dynamic logic lends itself to a classical algebraic development based on "cylindric algebras." Finally, it is shown how this algebraic semantics can be presented in a categorical setting, and how the algebraic counterparts of first-order structures correspond to subfibrations of the "syntactic fibration" representing first-order logic.
Geometric Modal Logic, Notre Dame Journal of Formal Logic, 64/3, 2023, p. 377-406.
This paper raises the issue of higher-order possible worlds, i.e., possible worlds about the way the (lower-order) possible worlds might be. It combines Kripke modal semantics and Riemannian geometry so as to formalize full-fledged higher-order possible worlds.
Une nouvelle sémantique de l’itération modale, Philosophia Scientiae 18/1, 2014, p. 185-203.
Saying that a proposition is necessarily necessarily true amounts to saying that the proposition is necessarily true whatever the range of all the possible worlds may be. This range then becomes a possible datum among others, which triggers the reference to higher-order possible worlds. This article aims at formalizing such a notion of high-order possible world, in sharp contrast to the Leibnizian heritage of a fixed closed totality of possible worlds, by using tools coming from Riemannian geometry.