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HILBERT, DUALITY, AND THE GEOMETRICAL ROOTS OF MODEL THEORY

Published online by Cambridge University Press:  29 December 2017

GÜNTHER EDER  and
GEORG SCHIEMER
GÜNTHER EDER*
Affiliation:
Department of Philosophy, University of Salzburg
GEORG SCHIEMER*
Affiliation:
Department of Philosophy, University of Vienna
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF SALZBURG FRANZISKANERGASSE 1 A-5020 SALZBURG, AUSTRIA E-mail: guenther.eder@univie.ac.at
†DEPARTMENT OF PHILOSOPHY UNIVERSITY OF VIENNA UNIVERSITÄTSSTRAßE 7 A-1010 VIENNA, AUSTRIA E-mail: georg.schiemer@univie.ac.at
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Abstract

The article investigates one of the key contributions to modern structural mathematics, namely Hilbert’s Foundations of Geometry (1899) and its mathematical roots in nineteenth-century projective geometry. A central innovation of Hilbert’s book was to provide semantically minded independence proofs for various fragments of Euclidean geometry, thereby contributing to the development of the model-theoretic point of view in logical theory. Though it is generally acknowledged that the development of model theory is intimately bound up with innovations in 19th century geometry (in particular, the development of non-Euclidean geometries), so far, little has been said about how exactly model-theoretic concepts grew out of methodological investigations within projective geometry. This article is supposed to fill this lacuna and investigates this geometrical prehistory of modern model theory, eventually leading up to Hilbert’s Foundations.

Keywords

03A0500A30Hilberthistory of geometryearly metatheoryhistory of model theorymodern axiomatics
Type
Research Article
Information
The Review of Symbolic Logic , Volume 11 , Issue 1 , March 2018 , pp. 48 - 86
Copyright
Copyright © Association for Symbolic Logic 2017 

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