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Article ID: CBB484264044

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

Eder, Günther (Author)

Synthese
Volume: 198
Issue: 6
Pages: 5547-5575

URI: https://doi.org/10.1007/s11229-019-02421-4

DOI: 10.1007/s11229-019-02421-4

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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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