Hilbert's Proof Theory and its modern Development


Seminar Paper, 2021

24 Pages, Grade: 1,0


Abstract or Introduction

David Hilbert first dealt with proofs as independent mathematical objects during the foundational crisis in mathematics at the beginning of the 20th century. Hilbert wanted to dispel all doubts about classical mathematical reasoning by a theory that makes mathematical proofs themselves to its objects (Hilbert, 1923). We examine the reasons and aims of Hilbert's proof theory and show how it came to a surprisingly sudden end.
Gerhard Gentzen continued proof theory in the spirit of Hilbert. We will see that Gentzen's system is more closely related to mathematical practice and get an outline how he succeeds in proving the consistency of number theory by means of new methods.
Attempts to grasp the real essence of proofs started afterwards. First we show how the important question of proof identity evolved in General Proof Theory. Second, how formal proofs can be represented in a new language by mathematical category theory and the lambda calculus to derive new identity criteria.

Details

Title
Hilbert's Proof Theory and its modern Development
College
University of Hagen
Course
Philosophy of Mathematics
Grade
1,0
Author
Year
2021
Pages
24
Catalog Number
V1174078
ISBN (Book)
9783346592897
Language
English
Keywords
Philosophy, Mathematics, Proof Theory, Hilbert, Gentzen, Prawitz, General Proof Theory, Brouwer, Intuitionism, Set theory, Natural deduction
Quote paper
Ralf Ille (Author), 2021, Hilbert's Proof Theory and its modern Development, Munich, GRIN Verlag, https://www.grin.com/document/1174078

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