The Paris-Nancy Colloquium in Logic and the Philosophy of Mathematics or PANALM is a forum for general expository talks accessible and relevant for all researchers in logic and the philosophy of mathematics. Speakers are invited to describe a whole research line or program that they have been pursuing and present the main results they have obtained in a synoptic and didactic way. PANALM is run jointly by the Institut d’Histoire et de Philosophie des Sciences et des Techniques (IHPST) and the Institut Jean Nicod (IJN) in Paris and the Archives Henri Poincaré (AHP) in Nancy. Each of these institutions will welcome one session of PANALM per semester. PANALM is open to anyone interested, from students to researchers in neighboring disciplines.
Title: The Euclidean programme
Abstract: The Euclidean Programme embodies a traditional sort of epistemological foundationalism, according to which knowledge—especially mathematical knowledge—is obtained by deduction from self-evident axioms or first principles. This talk, based on my book of the same name with Wesley Wrigley, will offer a detailed examination of Euclidean foundationalism, which, following Lakatos, we call the Euclidean Programme. In the talk, I will rationally reconstruct the programme’s key principles, showing it to be an epistemological interpretation of the axiomatic method. I will then assess the programme, exploring whether various areas of contemporary mathematics conform to it.
Location: Salle de réunion de l’Institut Jean Nicod, Rez-de-chaussé, Pavillon Jardin, 29 rue d’Ulm, 75005 Paris
Further reading: No reading is required prior to the talk. However, if you would like to prepare for the talk or go deeper afterwards, you may consult:
Alexander Paseau and Wesley Wrigley (2024). The Euclidean Programme, Cambridge University Press, Cambridge.
AHP Session Fall 2025: Sean Walsh (UCLA) - November 4, 2PM
Title: Model completions, model theory, and ideal elements
Abstract: Manders (1989) suggested that the model-theoretic notion of model completion could help conceptualize the rationale behind the choice of ideal elements in mathematics. Bellomo (2021) usefully compares and contrasts this to the idea of ‘domain expansion’ that one finds in the principle of permanence, which has many connections to the Hilbert program (cf. Detlefsen 2005). The Hilbert program has given rise to much within mathematical logic, and can be viewed through the lens of reverse mathematics (Simpson 1988, Simpson 1999). In this talk, we look at Manders’ preferred method of domain extension in the framework of reverse mathematics. It is one way of trying to understand how hard it is to find the types of models at issue in model completions when they exist.
Location: Amphithéâtre Léopold, Présidence Léopold, 34 cours Léopold, 54000 Nancy (link google maps)
Further reading: No reading is required prior to the talk. However, if you would like to prepare for the talk or go deeper afterwards, you may consult:
Bellomo, Anna, 2021. “Domain Extension and Ideal Elements in Mathematics.” Philosophia Mathematica, Series III 29 (3): 366–91.
Detlefsen, Michael, 2005. “Formalism.” In The Oxford Handbook of Philosophy of Mathematics and Logic, edited by Stewart Shapiro. Oxford University Press.
Manders, Kenneth, 1989. “Domain Extension and the Philosophy of Mathematics.” The Journal of Philosophy, 86 (10): 553–62.
S. G. Simpson, 1999. Subsystems of Second Order Arithmetic. Perspectives in Mathematical Logic. Springer- Verlag, Berlin.
S. G. Simpson, 1988. “Partial realizations of Hilbert’s program”. Journal of Symbolic Logic, 53(2):349–363.
Title: Refining epistemic logic via topology
Abstract: Epistemic logic is an umbrella term for a variety of modal logics whose main objects of study are knowledge and belief. As a field of study, epistemic logic uses mathematical tools to formalize, clarify, and address the questions that drive (formal) epistemology, and its applications extend not only to philosophy, but also to theoretical computer science, artificial intelligence, and economics. Research in epistemic logic has widely advanced based on the formal ground of normal modal logics and standard possible worlds semantics on relational structures as they provide a relatively easy way of modeling knowledge and belief. However, this mainstream approach is subject to well-known conceptual objections and open to extensions to better handle information. In this talk, I will focus on features of the standard (relational) possible worlds semantics that call for refinement/enrichment and provide an overview of topological approaches to epistemic logic. In particular, I will argue that topological spaces emerge naturally as information structures if one not only seeks an easy way of modeling knowledge and belief, but also aims at representing evidence and its relationship to these notions. Based on some of the topological semantics proposed in (Baltag et al, 2022; Özgün 2017), I will show that the topological approach enables fine-grained and refined representations of the aforementioned epistemic notions, highlighting several variations and extensions in the literature, and (time-permitting) applications in mathematical logic, formal epistemology, and formal learning theory.
Location: Salle de Conférence de l’IHPST, Université Paris 1 Panthéon-Sorbonne, Maison de la Philosophie-Marin Mersenne, 2nd floor, 13 rue du Four, 75006 Paris (link google maps)
Further reading: No reading is required prior to the talk. However, if you would like to prepare for the talk or go deeper afterwards, you may consult:
Baltag, A., Bezhanishvili, N., Özgün, A., and Smets, S., 2022. “Justified belief, knowledge, and the topology of evidence”. Synthese, 200, 1–51.
Özgün, A., 2017. Evidence in Epistemic Logic: A Topological Perspective. Ph.D. thesis, ILLC, Univerisity of Amsterdam.
Registration
The seminar is free and without registration. Everyone interested is welcome to attend.
For any questions, please send an email to the organizers.
Organizers
Acknowledgement and Support
The workshop is funded by by the Institut d’Histoire et de Philosophie des Sciences et des Techniques (IHPST), the Institut Jean Nicod (IJN) and the Archives Henri Poincaré (AHP).