Abstract.In this note, I discuss U. Kohlenbach's work Applied Proof Theory. Proof Interpretations and their Use in Mathematics [#!Kohl!#] from a foundational and historical perspective. I put the emphasis on Kronecker's constructivist programme which is not mentioned by Kohlenbach and I show that Kronecker's idea of finitist foundations survives beyond Hilbert's programme in the foundations of mathematics. The idea of proof mining is meant to underline the project of extracting effective bounds from ineffective classical proofs in analysis. The logical tools used in that perspective are reviewed in a critical spirit.

Received: September 1, 2009

AMS Subject Classification: 03, 11, 30, 46

Key Words and Phrases: fixed-point theory, approximation theory, proof theory, Hilbert programme

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 56
Issue: 2