Eder Günther
Department of Philosophy, University of Vienna, Universitätsstrasse 7, 1010 Vienna, Austria.
Synthese. 2021;198(6):5547-5575. doi: 10.1007/s11229-019-02421-4. Epub 2019 Oct 10.
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.
本文旨在通过考察弗雷格对19世纪几何学中几个对现代模型论语义学发展具有重要意义的主题的看法，来促进对他的语义学和元理论观点的更好理解。我将聚焦于三个问题，在这些问题中，一个核心的语义观念，即重新解释非逻辑术语的观念，逐渐开始发挥重要作用：射影几何学中无穷远点的引入；转移原理的研究，尤其是对偶原理；以及独立性论证中反例的使用。基于对这些问题以及19世纪几何学家对它们的思考的讨论，我将接着探究弗雷格对这些问题的看法。最后，我将讨论弗雷格的观点，以及它们更广泛地对关于他在语义学和元理论立场的争论所蕴含的意义。
