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PROJECTIVE DUALITY AND THE RISE OF MODERN LOGIC

Part of: Philosophical aspects of logic and foundations History of mathematics and mathematicians

Published online by Cambridge University Press:  26 July 2021

GÜNTHER EDER
GÜNTHER EDER*
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF VIENNA UNIVERSITÄTSSTRAßE7 1010VIENNA, AUSTRIAE-mail: [email protected]
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Abstract

The symmetries between points and lines in planar projective geometry and between points and planes in solid projective geometry are striking features of these geometries that were extensively discussed during the nineteenth century under the labels “duality” or “reciprocity.” The aims of this article are, first, to provide a systematic analysis of duality from a modern point of view, and, second, based on this, to give a historical overview of how discussions about duality evolved during the nineteenth century. Specifically, we want to see in which ways geometers’ preoccupation with duality was shaped by developments that lead to modern logic towards the end of the nineteenth century, and how these developments in turn might have been influenced by reflections on duality.

Keywords

dualityreciprocityearly metatheoryprojective geometry

MSC classification

Primary: 01A55: 19th century
Secondary: 01A60: 20th century 03A05: Philosophical and critical
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 27 , Issue 4 , December 2021 , pp. 351 - 384
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Copyright
The Author(s), 2021. Published by Cambridge University Press on behalf of Association for Symbolic Logic

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