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  1.  11
    Space, Number, and Geometry From Helmholtz to Cassirer.Francesca Biagioli - 2016 - Springer Verlag.
    This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of intuitions, which lie at the foundation of mathematical knowledge. The success of his philosophical account of space was due not least to the fact that Euclidean geometry was widely considered to be a model of certainty at his time. However, such (...)
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  2.  13
    Ernst Cassirer’s Transcendental Account of Mathematical Reasoning.Francesca Biagioli - forthcoming - Studies in History and Philosophy of Science Part A.
  3.  27
    Articulating Space in Terms of Transformation Groups: Helmholtz and Cassirer.Francesca Biagioli - 2018 - Journal for the History of Analytical Philosophy 6 (3).
    Hermann von Helmholtz’s geometrical papers have been typically deemed to provide an implicitly group-theoretical analysis of space, as articulated later by Felix Klein, Sophus Lie, and Henri Poincaré. However, there is less agreement as to what properties exactly in such a view would pertain to space, as opposed to abstract mathematical structures, on the one hand, and empirical contents, on the other. According to Moritz Schlick, the puzzle can be resolved only by clearly distinguishing the empirical qualities of spatial perception (...)
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  4.  6
    Cohen and Helmholtz on the Foundations of Measurement.Francesca Biagioli - 2018 - In Christian Damböck (ed.), Philosophie Und Wissenschaft Bei Hermann Cohen/Philosophy and Science in Hermann Cohen. Springer Verlag. pp. 77-100.
    It is well known that Hermann Cohen was one of the first philosophers who engaged in the debate about non-Euclidean geometries and the concept of space. His relation to Hermann von Helmholtz, who played a major role in the same debate, is an illuminating example of how some of the leading ideas of Marburg neo-Kantianism, although motivated independently of scientific debates, naturally led to the examination of scientific works and scientists’ epistemological views. This paper deals with Cohen’s view of magnitudes (...)
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  5.  59
    What Does It Mean That “Space Can Be Transcendental Without the Axioms Being So”?: Helmholtz’s Claim in Context.Francesca Biagioli - 2014 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 45 (1):1-21.
    In 1870, Hermann von Helmholtz criticized the Kantian conception of geometrical axioms as a priori synthetic judgments grounded in spatial intuition. However, during his dispute with Albrecht Krause (Kant und Helmholtz über den Ursprung und die Bedeutung der Raumanschauung und der geometrischen Axiome. Lahr, Schauenburg, 1878), Helmholtz maintained that space can be transcendental without the axioms being so. In this paper, I will analyze Helmholtz’s claim in connection with his theory of measurement. Helmholtz uses a Kantian argument that can be (...)
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  6.  17
    Ernst Cassirer on Historical Thought and the Demarcation Problem of Epistemology.Francesca Biagioli - 2021 - British Journal for the History of Philosophy 29 (4):652-670.
    Cassirer’s neo-Kantian epistemology has become a classical reference in contemporary history and philosophy of science. However, the historical aspects of his thought are sometimes seen to be in so...
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  7.  25
    Hermann Cohen and Alois Riehl on Geometrical Empiricism.Francesca Biagioli - 2014 - Hopos: The Journal of the International Society for the History of Philosophy of Science 4 (1):83-105.
    When non-Euclidean geometry was developed in the nineteenth century, both scientists and philosophers addressed the question as to whether the Kantian theory of space ought to be refurbished or even rejected. The possibility of considering a variety of hypotheses regarding physical space appeared to contradict Kant’s supposition of Euclid’s geometry as a priori knowledge and suggested the view that the geometry of space is a matter for empirical investigation. In this article, I discuss two different attempts to defend the Kantian (...)
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  8. Alois Riehl’s Epistemological Argument for Realism About Things in Themselves.Francesca Biagioli - 2021 - In Rudolf Meer & Giuseppe Motta (eds.), Kant in Österreich: Alois Riehl Und der Weg Zum Kritischen Realismus. De Gruyter. pp. 73-96.
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  9. Intuition and Conceptual Construction in Weyl’s Analysis of the Problem of Space.Francesca Biagioli - 2019 - In Carlos Lobo & Julien Bernard (eds.), Weyl and the Problem of Space. Springer Verlag.
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  10. Neo-Kantian Perspectives on the Exact Sciences.Francesca Biagioli & Marco Giovannelli (eds.) - forthcoming - Routledge.
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  11.  25
    Between Kantianism and Empiricism: Otto Hölder's Philosophy of Geometry.Francesca Biagioli - 2013 - Philosophia Scientiae 17 (17-1):71-92.
    La philosophie de la géométrie de Hölder, si l’on s’en tient à une lecture superficielle, est la part la plus problématique de son épistémologie. Il soutient que la géométrie est fondée sur l’expérience à la manière de Helmholtz, malgré les objections sérieuses de Poincaré. Néanmoins, je pense que la position de Hölder mérite d’être discutée pour deux motifs. Premièrement, ses implications méthodologiques furent importantes pour le développement de son épistémologie. Deuxièmement, Poincaré utilise l’opposition entre le kantisme et l’empirisme comme un (...)
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  12.  14
    Between Kantianism and Empiricism: Otto Hölder’s Philosophy of Geometry.Francesca Biagioli - 2013 - Philosophia Scientae 17:71-92.
  13.  15
    Limits of Knowledge Between Philosophy and the Sciences.Francesca Biagioli - 2013 - Rivista di Storia Della Filosofia 68 (2):393-398.
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  14.  7
    J Tyler Friedman and Sebastian Luft, Eds. The Philosophy of Ernst Cassirer: A Novel Assessment. Berlin: De Gruyter, 2015. Pp. Vi+475. $154.00. [REVIEW]Francesca Biagioli - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (1):164-167.
  15.  8
    Between Kantianism and Empiricism: Otto Hölder’s Philosophy of Geometry.Francesca Biagioli - 2013 - Philosophia Scientiae 17 (1):71-92.
    La philosophie de la géométrie de Hölder, si l’on s’en tient à une lecture superficielle, est la part la plus problématique de son épistémologie. Il soutient que la géométrie est fondée sur l’expérience à la manière de Helmholtz, malgré les objections sérieuses de Poincaré. Néanmoins, je pense que la position de Hölder mérite d’être discutée pour deux motifs. Premièrement, ses implications méthodologiques furent importantes pour le développement de son épistémologie. Deuxièmement, Poincaré utilise l’opposition entre le kantisme et l’empirisme comme un (...)
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