Les divers points de vue relatifs au concept mathématique de l’infini sont ordonnés en série croissante d’après le degré où l’on reconnaît ce concept en ses diverses complications. Cette série est divisée en trois groupes : la mathématique du fini, la « conception constructive », et la « conception en soi » de l’infini. D’après cette série, l’on explique le programme d"Hilbert, qui est de prouver que la mathématique est libre de contradiction, et l’on rapporte brièvement les méthodes qui sont (...) en question pour administrer cette preuve. (shrink)

Review of Eckart Menzler-Trott’s book, Logic’s Lost Genius: The Life of Gerhard Gentzen.

In his biography of Gerhard Gentzen, Eckart Menzler-Trott includes an extract from a letter written by Jean Cavaillès to his friend and fellow philosopher of mathematics Albert Lautman on 3rd Septe...

Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzen’s original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. They (...) underlie modern developments in computer science such as automated theorem proving and type theory. (shrink)