Article ID: CBB484264044

Frege and the origins of model theory in nineteenth century geometry (2021)


The aim of this article is to contribute to a better understanding of Frege’s views on semantics and metatheory by looking at his take on several themes in nineteenth century geometry that were significant for the development of modern model-theoretic semantics. I will focus on three issues in which a central semantic idea, the idea of reinterpreting non-logical terms, gradually came to play a substantial role: the introduction of elements at infinity in projective geometry; the study of transfer principles, especially the principle of duality; and the use of counterexamples in independence arguments. Based on a discussion of these issues and how nineteenth century geometers reflected about them, I will then look into Frege’s take on these matters. I conclude with a discussion of Frege’s views and what they entail for the debate about his stance towards semantics and metatheory more generally.

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Authors & Contributors
Belna, Jean-Pierre
Boos, William
Heijenoort, Jean van
Frege, Gottlob
Barnes, Jonathan
Besson, Corine
History and Philosophy of Logic
Revue d'Histoire des Sciences
Archive for History of Exact Sciences
Harvard University Press
Librairie Philosophique J. Vrin
Vittorio Klostermann
Cambridge University Press
University of California, Irvine
Philosophy of mathematics
Signs and symbols
Frege, Gottlob
Gödel, Kurt
Riemann, Georg Friedrich Bernhard
Leibniz, Gottfried Wilhelm von
Hilbert, David
Dedekind, Richard
Time Periods
19th century
20th century, early
20th century
18th century

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