Hilbert's formalism and arithmetization of mathematics
type: Item
instance of: scholarly article
title: Hilbert's formalism and arithmetization of mathematics
zbMATH Open document ID: 0933.01014
DOI: 10.1023/A:1004919107087
published in: Synthese
publication date: 2000-03-29T00:00:00Z
review text: The main concern is Hilbert's understanding of axiomatics, especially as deployed in his Grundlagen der Geometrie (1899), and in later sources such as a lecture course on foundations in 1904-1905 (not `a long lecture of 1905' of p. 3). The author shows that in some ways Hilbert was opposed to kinds of formalism in mathematics, and should have mentioned that Hilbert never used the word ``Formalismus'' to characterise his position; it was imposed by Brouwer, as a criticism. The author brings out by examples the model-theoretic aspects of Hilbert's philosophy. Various items of primary and historical literature in German are cited in the footnotes and references -- with a mass of spelling mistakes.
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 00A30
Mathematics Subject Classification ID: 03-03
zbMATH DE Number: 1322778
zbMATH Keywords: D. Hilbert
zbMATH Keywords: metamathematics
author: Judson Chambers Webb
reviewed by: Ivor Grattan-Guinness
MaRDI profile type: Publication
full work available at URL: a:1004919107087
OpenAlex ID: W1591170770
description: scientific article; zbMATH DE number 1322778