Repository | Book | Chapter
(2015) The road to universal logic II, Basel, Birkhäuser.
A note on the internal logic of constructive mathematics
the gel"fond-schneider theorem in transcendental number theory
Yvon Gauthier
pp. 297-306
The question of an internal logic of mathematical practice is examined from a finitist point of view. The Gel"fond–Schneider theorem in transcendental number theory serves as an instance of a proof-theoretical investigation motivated and justified by constructivist foundations of logic and mathematics. Constructivist notions are emphasized by contrasting the arithmetical proof procedure of infinite descent with the principle of transfinite induction. It is argued that intuitionistic logic cannot alone provide secure foundations for constructivist mathematics and a finitist logic is briefly sketched in the framework of polynomial arithmetic.
Publication details
DOI: 10.1007/978-3-319-15368-1_13
Full citation:
Gauthier, Y. (2015)., A note on the internal logic of constructive mathematics: the gel"fond-schneider theorem in transcendental number theory, in A. Koslow & A. Buchsbaum (eds.), The road to universal logic II, Basel, Birkhäuser, pp. 297-306.
This document is unfortunately not available for download at the moment.