Synthetic mathematics, logic-affine computation and efficient proof systems / Mathématiques synthétiques, calcul logique affine et systèmes de preuve efficients

Collection Synthetic mathematics, logic-affine computation and efficient proof systems / Mathématiques synthétiques, calcul logique affine et systèmes de preuve efficients

Organizer(s) Blechschmidt, Ingo ; Cohen, Liron ; Coquand, Thierry ; Negri, Sara ; Schuster, Peter

Date(s) 08/09/2025 - 12/09/2025

linked URL https://conferences.cirm-math.fr/3377.html

00:00:00 / 00:00:00

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Towards an internal construction of meaning

By Sophie d'Espalungue

I will share ideas underlying an internal approach I am developing to address the notion of meaning in mathematical language. I'll outline some expected benefits and explore how the syntax-semantics and analytic-synthetic dichotomies would fit into this framework. The idea is to organise mathematical objects and structures into a nested hierarchy, each level internalising the level below. The fundamental instance corresponds to the hierarchy of n-categories (proof of true, true, truth values, sets, categories, etc.). Given that this hierarchy includes the level of truth values, this approach further seeks to internalise the process of definition by formulating it at that very level, blurring the line between syntax and semantics. In this framework, no term is primitive: each object is defined as an element of an object at the next level up, built inductively from the levels below. The aim is to explore how meaning can emerge internally from the act of definition itself. My goal in this talk is to present this perspective, clarify intuitions, and invite discussion on its mathematical and philosophical implications.

Information about the video

Date of recording 09/09/2025
Date of publication 02/10/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20387903
Cite this video d'Espalungue, Sophie (09/09/2025). Towards an internal construction of meaning. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20387903
URL https://dx.doi.org/10.24350/CIRM.V.20387903

Domain(s)

Logic

Bibliography

D'ESPALUNGUE D'ARROS, S. (2023). Operads in 2-categories and models of structure interchange. Ph.D. thesis. - https://theses.hal.science/tel-04617115

MSC codes

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