Infinity and intensionality
We investigate the theory of infinite sets and intensional notions to develop a new synthesis.
Photo: Stephanie Abower.
About the project
The project “Infinity and intensionality: Towards a new Synthesis” investigates two clusters of questions so far only studied in isolation.
- The theory of infinite sets, which is the standard foundation for nearly all of today’s mathematics, but which is threatened by paradoxes.
- Intensional notion such as propositions, properties, and relations. Propositions are a central concern in linguistics, psychology, and philosophy.
Our overarching hypothesis is that real progress requires a new synthesis, where the two clusters of questions are tackled in a unified way. To address the first cluster, we supplement set theory with intensional notions of collection, number, and generality.
To develop satisfactory theories of intensional notions, we draw on concepts and theories developed by critics of infinitary set theory.
The project’s goals are:
- to develop a novel and distinctive philosophy of mathematics, which retains the theory of infinite sets but supplements it with intensional notions of collection, number, and generality
- to use concepts and methods from the critical views of infinity to develop new approaches to intensional phenomena, e.g., propositions and properties
- to offer a novel account of “large” totalities used in semantics and mathematics by developing an alternative notion of set
- to reshape the hotly debated hierarchical conception of reality by bringing to bear intensional conceptions of collection and generality
- to transfer ideas from the critical views of infinity to Cantor’s absolute infinity, thus retaining the strength of Cantorian set theory while incorporating insights from the critical views.
This project is funded by the Norwegian Research Council (NFR) with the project number 314435.
01.08.21 - 31.07.24