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  1. Frege’s Philosophy of Geometry.Matthias Schirn - 2019 - Synthese 196 (3):929-971.
    In this paper, I critically discuss Frege’s philosophy of geometry with special emphasis on his position in The Foundations of Arithmetic of 1884. In Sect. 2, I argue that that what Frege calls faculty of intuition in his dissertation is probably meant to refer to a capacity of visualizing geometrical configurations structurally in a way which is essentially the same for most Western educated human beings. I further suggest that according to his Habilitationsschrift it is through spatial intuition that we (...)
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  2. Frege’s ‘On the Foundations of Geometry’ and Axiomatic Metatheory.Günther Eder - 2016 - Mind 125 (497):5-40.
    In a series of articles dating from 1903 to 1906, Frege criticizes Hilbert’s methodology of proving the independence and consistency of various fragments of Euclidean geometry in his Foundations of Geometry. In the final part of the last article, Frege makes his own proposal as to how the independence of genuine axioms should be proved. Frege contends that independence proofs require the development of a ‘new science’ with its own basic truths. This paper aims to provide a reconstruction of this (...)
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  3. 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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  4. Frege and Hilbert.M. Hallett - 2010 - In Michael Potter Tom Ricketts (ed.), The Cambridge Companion to Frege. Cambridge University Press. pp. 413--464.
  5. Objectivité et principe de dualité : Le paragraphe 26 des Fondements de l'arithmétique de Frege.Jean-Pierre Belna - 2006 - Revue d'Histoire des Sciences 2 (2):319-344.
    The idea of objectivity is primary in Gottlob Frege’s thought, not only for his conception of logic and mathematics, but also for his philosophy as a whole. He deals with the topic for the first time in 1884, in Grundlagen der Arithmetik, precisely in paragraph 26. He distinguishes the objective from the subjective, of course, but also from the real, what he calls the actual (wirklich in German). In order to be perfectly understood, he gives as example the colors but, (...)
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  6. What Frege Meant When He Said: Kant is Right About Geometry.Teri Merrick - 2006 - Philosophia Mathematica 14 (1):44-75.
    This paper argues that Frege's notoriously long commitment to Kant's thesis that Euclidean geometry is synthetic _a priori_ is best explained by realizing that Frege uses ‘intuition’ in two senses. Frege sometimes adopts the usage presented in Hermann Helmholtz's sign theory of perception. However, when using ‘intuition’ to denote the source of geometric knowledge, he is appealing to Hermann Cohen's use of Kantian terminology. We will see that Cohen reinterpreted Kantian notions, stripping them of any psychological connotation. Cohen's defense of (...)
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  7. Frege on Axioms, Indirect Proof, and Independence Arguments in Geometry: Did Frege Reject Independence Arguments?Jamie Tappenden - 2000 - Notre Dame Journal of Formal Logic 41 (3):271-315.
    It is widely believed that some puzzling and provocative remarks that Frege makes in his late writings indicate he rejected independence arguments in geometry, particularly arguments for the independence of the parallels axiom. I show that this is mistaken: Frege distinguished two approaches to independence arguments and his puzzling remarks apply only to one of them. Not only did Frege not reject independence arguments across the board, but also he had an interesting positive proposal about the logical structure of correct (...)
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  8. Geometry and Generality in Frege's Philosophy of Arithmetic.Jamie Tappenden - 1995 - Synthese 102 (3):319 - 361.
    This paper develops some respects in which the philosophy of mathematics can fruitfully be informed by mathematical practice, through examining Frege's Grundlagen in its historical setting. The first sections of the paper are devoted to elaborating some aspects of nineteenth century mathematics which informed Frege's early work. (These events are of considerable philosophical significance even apart from the connection with Frege.) In the middle sections, some minor themes of Grundlagen are developed: the relationship Frege envisions between arithmetic and geometry and (...)
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  9. Frege: The Royal Road From Geometry.Mark Wilson - 1992 - Noûs 26 (2):149-180.
  10. Frege and Kant on Geometry.Michael Dummett - 1982 - Inquiry: An Interdisciplinary Journal of Philosophy 25 (2):233 – 254.
    In his Grundlagen, Frege held that geometrical truths.are synthetic a priori, and that they rest on intuition. From this it has been concluded that he thought, like Kant, that space and time are a priori intuitions and that physical objects are mere appearances. It is plausible that Frege always believed geometrical truths to be synthetic a priori; the virtual disappearance of the word ‘intuition’ from his writings from after 1885 until 1924 suggests, on the other hand, that he became dissatisfied (...)
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  11. Freges Analyse der Hilbertschen Axiomatik.Peter Hinst - 1977 - Grazer Philosophische Studien 3 (1):47-57.
    Gegen die vielfach vertretene Auffassung, Frege habe die Hilbertsche Axiomatik nicht verstanden, wird nachzuweisen versucht, daß Frege die neue Methode nicht nur verstanden, sondem auch begrifflich präzise analysiert hat. Er definiert eine formale Theorie im Hilbertschen Sinn als eine Klasse von logisch beweisbaren Wenn-dann-Sätzen, die freie Variable enthalten und deren Wenn-Satz eine Konjunktion der Axiome im Hilbertschen Sinn ist. Er untersucht ferner das Verhältnis zwischen einer Hilbertschen Theorie und ihren Modellen (Anwendungen) und wendet seine allgemeinen Ergebnisse in erhellender Weise auf (...)
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  12. Freges Analyse der Hilbertschen Axiomatik.Peter Hinst - 1977 - Grazer Philosophische Studien 3 (1):47-57.
    Gegen die vielfach vertretene Auffassung, Frege habe die Hilbertsche Axiomatik nicht verstanden, wird nachzuweisen versucht, daß Frege die neue Methode nicht nur verstanden, sondem auch begrifflich präzise analysiert hat. Er definiert eine formale Theorie im Hilbertschen Sinn als eine Klasse von logisch beweisbaren Wenn-dann-Sätzen, die freie Variable enthalten und deren Wenn-Satz eine Konjunktion der Axiome im Hilbertschen Sinn ist. Er untersucht ferner das Verhältnis zwischen einer Hilbertschen Theorie und ihren Modellen und wendet seine allgemeinen Ergebnisse in erhellender Weise auf Hilberts (...)
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  13. The Frege-Hilbert Controversy.Michael David Resnik - 1974 - Philosophy and Phenomenological Research 34 (3):386-403.
  14. Frege Und Die Grundlagen der Geometrie. [REVIEW]Michael Resnik - 1971 - Journal of Symbolic Logic 36 (1):155-155.
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  15. On the Foundations of Geometry. Tr. By M.E. Szabo.Gottlob Frege - 1960 - Philosophical Review 69 (1):3-17.
  16. Frege and Hilbert on the Foundations of Geometry (1994 Talk).Susan G. Sterrett - unknown
    I examine Frege’s explanation of how Hilbert ought to have presented his proofs of the independence of the axioms of geometry: in terms of mappings between (what we would call) fully interpreted statements. This helps make sense of Frege’s objections to the notion of different interpretations, which many have found puzzling. (The paper is the text of a talk presented in October 1994.).
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