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Ghost world: A context for Frege's context principle

In Michael Beaney & Erich Reck (eds.), Gottlob Frege: Frege's philosophy of mathematics. London: Routledge. pp. 157-175 (2005)

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  1. Frege on the Foundation of Geometry in Intuition.Jeremy Shipley - 2015 - Journal for the History of Analytical Philosophy 3 (6).
    I investigate the role of geometric intuition in Frege’s early mathematical works and the significance of his view of the role of intuition in geometry to properly understanding the aims of his logicist project. I critically evaluate the interpretations of Mark Wilson, Jamie Tappenden, and Michael Dummett. The final analysis that I provide clarifies the relationship of Frege’s restricted logicist project to dominant trends in German mathematical research, in particular to Weierstrassian arithmetization and to the Riemannian conceptual/geometrical tradition at Göttingen. (...)
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  • The Frege–Hilbert controversy in context.Tabea Rohr - 2023 - Synthese 202 (1):1-30.
    This paper aims to show that Frege’s and Hilbert’s mutual disagreement results from different notions of Anschauung and their relation to axioms. In the first section of the paper, evidence is provided to support that Frege and Hilbert were influenced by the same developments of 19th-century geometry, in particular the work of Gauss, Plücker, and von Staudt. The second section of the paper shows that Frege and Hilbert take different approaches to deal with the problems that the developments in 19th-century (...)
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  • Frege on intuition and objecthood in projective geometry.Günther Eder - 2021 - Synthese 199 (3-4):6523-6561.
    In recent years, several scholars have been investigating Frege’s mathematical background, especially in geometry, in order to put his general views on mathematics and logic into proper perspective. In this article I want to continue this line of research and study Frege’s views on geometry in their own right by focussing on his views on a field which occupied center stage in nineteenth century geometry, namely, projective geometry.
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  • Frege's natural numbers: Motivations and modifications.Erich Reck - 2005 - In Michael Beaney & Erich Reck (eds.), Gottlob Frege: Critical Assessments of Leading Philosophers, Vol. III. London: Routledge. pp. 270-301.
    Frege's main contributions to logic and the philosophy of mathematics are, on the one hand, his introduction of modern relational and quantificational logic and, on the other, his analysis of the concept of number. My focus in this paper will be on the latter, although the two are closely related, of course, in ways that will also play a role. More specifically, I will discuss Frege's logicist reconceptualization of the natural numbers with the goal of clarifying two aspects: the motivations (...)
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  • Frege and Russell: Does Science Talk Sense?Mark Wilson - 2007 - European Journal of Analytic Philosophy 3 (2):179-190.
    Over the course of the nineteenth century mathematicians became vividly aware that great advances in intuitive “understanding” could be obtained if novel definitions were devised for old notions such as “conic section”, for one thereby often gained a deeper appreciation for why old theorems in the subject had to be true. From a naïve philosophical standpoint, such definitional alterations look as if they must properly displace the “propositional contents” of the very theorems they seek to illuminate. Haven’t our reformers merely (...)
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