DOI: 10.4324/9780415249126-Y087-1
Version: v1, Published online: 1998
Retrieved March 29, 2024, from https://www.rep.routledge.com/articles/biographical/gentzen-gerhard-karl-erich-1909-45/v-1
Version: v1, Published online: 1998
Retrieved March 29, 2024, from https://www.rep.routledge.com/articles/biographical/gentzen-gerhard-karl-erich-1909-45/v-1
Article Summary
The German mathematician and logician Gerhard Gentzen devoted his life to proving the consistency of arithmetic and analysis. His work should be seen as contributing to the post-Gödelian development of Hilbert’s programme. In this connection he developed several logical calculi. The main device used in his proofs was a theorem in which he proved the eliminability of the inference known as ‘cut’ from a variety of different kinds of proofs. This ‘cut-elimination theorem’ yields the consistency of both classical and intuitionistic logic, and the consistency of arithmetic without complete induction. His later work was aimed at providing consistency proofs for less restricted systems of arithmetic and analysis.
Citing this article:
Peckhaus, Volker. Gentzen, Gerhard Karl Erich (1909–45), 1998, doi:10.4324/9780415249126-Y087-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/biographical/gentzen-gerhard-karl-erich-1909-45/v-1.
Copyright © 1998-2024 Routledge.
Peckhaus, Volker. Gentzen, Gerhard Karl Erich (1909–45), 1998, doi:10.4324/9780415249126-Y087-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/biographical/gentzen-gerhard-karl-erich-1909-45/v-1.
Copyright © 1998-2024 Routledge.