"It is like egg": Paul Lorenzen and the collapse of proofs of consistency

TL;DR

This paper explores Paul Lorenzen's 1947 crisis in his mathematical and philosophical work, analyzing his correspondence and writings to understand its origins and implications for proof theory and consistency.

Contribution

It provides a detailed translation and commentary on Lorenzen's 1947 autographed note, revealing the context and originality of his research during that period.

Findings

Lorenzen experienced a significant crisis in 1947 affecting his work.

Correspondence with contemporaries influenced his research direction.

The paper uncovers the origins of Lorenzen's innovative approach to proof and consistency.

Abstract

Paul Lorenzen, mathematician and philosopher of the 20th century, mentions October 1947 as the date of a crisis in his mathematical and philosophical investigations. An autograph dated 15 October 1947 documents this crisis. This article proposes a translation and a commentary of it and sketches the circumstances of its writing on the base of his correspondence with Paul Bernays. A letter from Lorenzen to Carl Friedrich Gethmann dated 14 January 1988 carves out the story of this crisis by showing how he soaks up the indications of his correspondents and transmutes them into an absolutely original research. Paul Lorenzen, math{\'e}maticien et philosophe du 20e si{\`e}cle, {\'e}voque le mois d'octobre 1947 comme la date d'une c{\'e}sure dans ses investigations tant math{\'e}matiques que philosophiques. Un {\'e}crit autographe dat{\'e} du 15 octobre 1947 marque cette c{\'e}sure. Cet article en propose une traduction et un commentaire ligne {\`a} ligne, puis esquisse les circonstances de son {\'e}criture sur la base de la correspondance avec Paul Bernays, figure tut{\'e}laire de la logique math{\'e}matique et l'un de ses principaux interlocuteurs {\`a} cette {\'e}poque, {\`a} l'instar de Heinrich Scholz et Oskar Becker. Une lettre de Lorenzen {\`a} Carl Friedrich Gethmann dat{\'e}e du 14 janvier 1988 {\'e}toffe le r{\'e}cit de cette c{\'e}sure en montrant comment il s'impr{\`e}gne des indications que lui fournissent ses correspondants pour les transmuter en une recherche absolument originale.