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Ernst Cassirer's transcendental account of mathematical reasoning

Francesca Biagioli

Studies in History and Philosophy of Science Part A 79 (C):30-40 (2020)

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Neo-Kantian conceptualism: between scientific experience and everyday perception.Katherina Kinzel - forthcoming - British Journal for the History of Philosophy:1-24.details This paper reconstructs the major transformations in the Marburg neo-Kantian account of experience. By focusing on the problem of ‘conceptualism’, it traces connections between four issues that are central to the transcendental projects of the Marburg philosophers: the interpretation of Kant, the critique of experiential givenness, the account of objective cognition in science, and the relation between scientific and pre-scientific experience. My historical narrative identifies two shifts. The first is from Cohen's conceptualist answer to the threat of subjectivism to Cassirer's (...) Download Export citation Bookmark
Loop quantum gravity in the light of neo-Kantian philosophy.Luigi Laino - 2021 - Kant E-Prints 16 (2):231-255.details The paper surveys the possibility of keeping a neo-Kantian approach in the face of Loop Quantum Gravity. Together with a preliminary analysis of Cassirer’s re-interpretation of Kantian philosophy that allowed him to harmonize the a priori cognitions with the theory of relativity and quantum mechanics, it will focus on the distinction between constitutive and regulativea priori. In this way, the paper will suggest that despite Rovelli’s refutation of Kant’s interpretation of space and time, he seems, at least implicitly, to hold (...) Download Export citation Bookmark
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.details 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 some tension with his defence of a priori elements of knowledge. This paper reconsiders Cassirer’s strategy to address this tension by positing functional dependencies at the core of the notion of objectivity. This requires the epistemologist to account for the determination of the objects of knowledge within given scientific theories, but also for (...) conceptual changes over time. (shrink) Download Export citation Bookmark 1 citation
(1 other version)Avicenna on Syllogisms Composed of Opposite Premises.Behnam Zolghadr - 2021 - In Mojtaba Mojtahedi, Shahid Rahman & MohammadSaleh Zarepour (eds.), Mathematics, Logic, and their Philosophies: Essays in Honour of Mohammad Ardeshir. Springer. pp. 433-442.details This article is about Avicenna’s account of syllogisms comprising opposite premises. We examine the applications and the truth conditions of these syllogisms. Finally, we discuss the relation between these syllogisms and the principle of non-contradiction. Download Export citation Bookmark
Structuralism and Mathematical Practice in Felix Klein’s Work on Non-Euclidean Geometry†.Biagioli Francesca - 2020 - Philosophia Mathematica 28 (3):360-384.details It is well known that Felix Klein took a decisive step in investigating the invariants of transformation groups. However, less attention has been given to Klein’s considerations on the epistemological implications of his work on geometry. This paper proposes an interpretation of Klein’s view as a form of mathematical structuralism, according to which the study of mathematical structures provides the basis for a better understanding of how mathematical research and practice develop. Download Export citation Bookmark 1 citation

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