Abstract
Abstract
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.
Publisher
Springer Science and Business Media LLC
Subject
General Social Sciences,Philosophy
Reference73 articles.
1. Andersen, K. (2007). The geometry of an art: The history of the mathematical theory of perspective from Alberti to Monge. Berlin, Heidelberg: Springer.
2. Antonelli, A., & May, R. (2000). Frege’s new science. Notre Dame Journal of Formal Logic, 41, 242–270.
3. Arana, A., & Mancosu, P. (2012). On the relationship between plane and solid geometry. The Review of Symbolic Logic, 5(2), 294–353.
4. Awodey, S., & Reck, E. (2002). Completeness and categoricity, part 1: Nineteenth-century axiomatics to twentieth-century metalogic. History and Philosophy of Logic, 23, 1–30.
5. Badesa, C., Mancosu, P., & Zach, R. (2009). The Development of mathematical logic from Russell to Tarski, 1900–1935. In L. Haaparanta (Ed.), The development of modern logic. Oxford: Oxford University Press.
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