title: Hilbert's axiomatic method and Carnap's general axiomatics.
abstract: This paper compares the axiomatic method of David Hilbert and his school with Rudolf Carnap's general axiomatics that was developed in the late 1920s, and that influenced his understanding of logic of science throughout the 1930s, when his logical pluralism developed. The distinct perspectives become visible most clearly in how Richard Baldus, along the lines of Hilbert, and Carnap and Friedrich Bachmann analyzed the axiom system of Hilbert's Foundations of Geometry—the paradigmatic example for the axiomatization of science. Whereas Hilbert's axiomatic method started from a local analysis of individual axiom systems in which the foundations of mathematics as a whole entered only when establishing the system's consistency, Carnap and his Vienna Circle colleague Hans Hahn instead advocated a global analysis of axiom systems in general. A primary goal was to evade, or formalize ex post, mathematicians' 'material' talk about axiom systems for such talk was held to be error-prone and susceptible to metaphysics.
authors.affiliation: Department of Philosophy, University of South Carolina, Columbia, SC 29208, USA. Electronic address: stoeltzn@sc.edu.
authors.forename: Michael
authors.initials: M
authors.lastname: Stöltzner
mesh_terms: D049673:History, 20th Century; D019359:Knowledge; D008433:Mathematics / Q000266:history*; D010684:Philosophy / Q000266:history; D010825:Physics / Q000266:history
keywords: Axiomatic method; Axiomatization of geometry; Carnap's general axiomatic; Categoricity; Completeness of an axiom system; Hilbert school