Frege and the origins of model theory in nineteenth century geometry

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.

Automated summary

This article aims to contribute to a better understanding of Frege's views on semantics and metatheory by examining his take on several themes in nineteenth century geometry. By focusing on three key issues, the article explores Frege's perspective on these matters, ultimately concluding with a discussion of what his views entail for the debate about his stance towards semantics and metatheory more generally.