皆様
ウィーン工科大学のMatthias Baaz先生の講演のお知らせです。 どうぞふるってご参加ください。
問合せ先： 石原 哉 北陸先端科学技術大学院大学 情報科学系 e-mail: [email protected] -----------------------------------------------
* JAIST Logic Seminar Series *
Date: Thursday 26, April, 2018, 11:00-12:30
Place: JAIST, Collaboration room 7 (I-56) (Access: http://www.jaist.ac.jp/english/location/access.html)
Speaker: Matthias Baaz (Vienna University of Technology)
Title: The concept of proof
Abstract: The concept of proof is one of the most fundamental building blocks of mathematics. The Hilbertian revolution at the beginning of the 20th century is based on an atomic notion of proof which is the foundation of the axiomatic method: "A proof is a finite sequence of formulas A1,..,An such that each Ai is instance of an axiom or follows by direct application of a rule from Ai1,..,Aik with all ij<i." No scientific revolution is however total, but there is a trend to disregard all alternatives to the successful method. In this lecture we discuss more global notions of proof, where subproofs are not necessarily proofs themselves. Examples are among others
1.protoproofs in the sense of Euler's famous solution to the Basel problem, which uses analogical reasoning and where additional external justifications are necessary. 2.circular notions of proof, where the concept of proof itself incooperates induction 3.sound proofs based on locally unsound rules 4.proofs based on abstract proof descriptions prominent e.g. in Bourbaki, where only the choice of a suitable result makes a verification possible.
We discuss the benefits of these alternative concepts and the possibility that innovative concepts of proof adapted to the problems in question might lead to strong mathematical results and constitute a novel area of Proof Theory.