Uploaded November 2025 | Updated September 2026, 1 hour ago
Recorded as part of the CFvW Colloquium on November 12, 2025
The concept of predicativity emerged in the foundational debates of the early twentieth century and has inspired numerous developments in mathematical logic. Far from being univocal, it has received various formulations and characterisations. Perhaps the most influential is the Kreisel–Feferman– Schütte analysis of predicativity given the natural numbers, which precisely identifies the limit of this conception.
In constructive mathematics, however, certain constructions are commonly regarded as predicative, even though they do not qualify as such under the proof-theoretic account by Kreisel, Feferman, and Schütte. This more generous notion of predicativity finds full expression in Martin-Löf type theory. The aim of this talk is to clarify in what sense this provides a genuine notion of predicativity and to illustrate its philosophical and mathematical potential. I will also discuss the possibility of identifying a limit for constructive predicativity.
This is joint work with Ansten Klev.
Recorded as part of the CFvW Colloquium on November 12, 2025
The concept of predicativity emerged in the foundational debates of the early twentieth century and has inspired numerous developments in mathematical logic. Far from being univocal, it has received various formulations and characterisations. Perhaps the most influential is the Kreisel–Feferman– Schütte analysis of predicativity given the natural numbers, which precisely identifies the limit of this conception.
In constructive mathematics, however, certain constructions are commonly regarded as predicative, even though they do not qualify as such under the proof-theoretic account by Kreisel, Feferman, and Schütte. This more generous notion of predicativity finds full expression in Martin-Löf type theory. The aim of this talk is to clarify in what sense this provides a genuine notion of predicativity and to illustrate its philosophical and mathematical potential. I will also discuss the possibility of identifying a limit for constructive predicativity.
This is joint work with Ansten Klev.
