Châtelet with Peirce. A Semiotic Conception of Category Theory
Bibliographic Data
| ID | 22430804 |
|---|---|
| Authors | Rocco Gangle (0000-0003-0545-9278, corresponding author) |
| Year | 2026 |
| Volume | 18 |
| Issue | 1 |
| Publication date | 2026-01-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | European Journal of Pragmatism and American Philosophy (JOURNAL) |
| Journal identifiers | ISSN: 2036-4091 • E-ISSN: 2036-4091 |
| Publisher | OpenEdition (PUBLISHER) |
| DOI | 10.4000/16kmc |
| OpenAlex | W7168272123 |
| Language | EN |
| References cited | 6 |
Gilles Châtelet aimed to provide a fresh philosophical point of view on the relationship between physics and mathematics by weaving together the concepts of diagram, gesture, and space in a new and creative configuration. He was especially intrigued by the possibilities inherent in using structures imported from one domain of mathematics as the basis for a diagrammatic notation in another domain, as evidenced by his discussion of knot theory in his ENS lecture of 1999. This paper elaborates and implements Châtelet’s ideas by combining a Peircean semiotic interpretation of Châtelet’s coordinated concepts of diagram and gesture with a novel point of view on the fundamental constructions of category theory in which the triadic structure of natural transformations takes on a certain priority of role that is analogous to the crucial role of the interpretant in Peirce’s triadic semiotics. This “natural transformations first” approach to category theory remains mathematically neutral but is highly suggestive for interpreting mathematical structures in terms of diagrammatic and gestural processes. It is shown how this approach to category theory can be readily represented using a convenient and intuitive string diagram calculus.
Category theory · Diagram · Diagrammatic reasoning · Iconicity · Notation · Semiotics · History and Theory of Mathematics · Mathematics Education and Teaching Techniques · Origins and Evolution of Life
| Citation velocity | historical |
|---|---|
| Highly cited | No |