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Carl Posy (2008). Intuition and Infinity: A Kantian Theme with Echoes in the Foundations of Mathematics.

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  1.  41
    When Series Go in Indefinitum, Ad Infinitum and in Infinitum Concepts of Infinity in Kant’s Antinomy of Pure Reason.Silvia De Bianchi - 2015 - Synthese 192 (8):2395-2412.
    In the section of the Antinomy of pure Reason Kant presents three notions of infinity. By investigating these concepts of infinity, this paper highlights important ‘building blocks’ of the structure of the mathematical antinomies, such as the ability of reason of producing ascending and descending series, as well as the notions of given and givable series. These structural features are discussed in order to clarify Ernst Zermelo’s reading of Kant’s antinomy, according to which the latter is deeply rooted in the (...)
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  2.  38
    Kant's A Priori Intuition of Space Independent of Postulates.Edgar J. Valdez - 2012 - Kantian Review 17 (1):135-160.
    Defences of Kant's foundations of geometry fall short if they are unable to equally ground Euclidean and non-Euclidean geometries. Thus, Kant's account must be separated from geometrical postulates. I argue that characterizing space as the form of outer intuition must be independent of postulates. Geometrical postulates are then expressions of particular spatializing activities made possible by the a priori intuition of space. While Amit Hagar contends that this is to speak of noumena, I argue that a Kantian account of space (...)
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