Review of Symbolic Logic 11 (1):48-86 (2018)

Authors
Günther Eder
University of Vienna
Georg Schiemer
University of Vienna
Abstract
The article investigates one of the key contributions to modern structural mathematics, namely Hilbert’sFoundations of Geometry 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, 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’sFoundations.
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DOI 10.1017/s1755020317000260
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References found in this work BETA

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Citations of this work BETA

Cassirer and the Structural Turn in Modern Geometry.Georg Schiemer - 2018 - Journal for the History of Analytical Philosophy 6 (3).
XV—On Consistency and Existence in Mathematics.Walter Dean - 2021 - Proceedings of the Aristotelian Society 120 (3):349-393.
Projective Duality and the Rise of Modern Logic.Günther Eder - 2021 - Bulletin of Symbolic Logic 27 (4):351-384.

View all 6 citations / Add more citations

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