Hilbert's program. An essay on mathematical instrumentalism
type: Item
instance of: scholarly article
title: Hilbert's program. An essay on mathematical instrumentalism
zbMATH Open document ID: 0641.03001
published in: Synthese Library
publication date: 1986-01-01T00:00:00Z
review text: The main philosophical idea of Hilbert's program, viz. to prove the security, i.e. consistency of non-trivial ``ideal'' mathematical methods using only very elementary and thence obviously secure ones, i.e. ``finitary'' methods, often is claimed to be refuted by Gödel's incompleteness theorems, especially by the second one. In the present essay the author carefully analyzes the (pre-)suppositions which are - or have to be - used to prove such claims. His goal is to show that at present all those claims which have been made in the relevant literature (seem to) use some dubitable principles and hence cannot be taken as really disproving the Hilbertian aims. Of course, it is impossible to establish in such a way what Hilbert originally intended. But the author successfully localizes essential points in anti-Hilbertian argumentations which should be discussed in more detail. The book is well written and recommended reading for everyone interested in the philosophical dimensions of technical results from foundations of mathematics and pure logic.
Mathematics Subject Classification ID: 03-02
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 00A30
Mathematics Subject Classification ID: 03B99
Mathematics Subject Classification ID: 03F99
zbMATH DE Number: 4043803
zbMATH Keywords: finitary methods
zbMATH Keywords: mathematical epistemology
zbMATH Keywords: Hilbert's program
zbMATH Keywords: consistency
zbMATH Keywords: Gödel's incompleteness theorems
zbMATH Keywords: anti-Hilbertian argumentations
author: Michael Detlefsen
reviewed by: Siegfried J. Gottwald
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4043803