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Arithmetic and Combinatorics: Kant and His Contemporaries

Southern Illinois University Press (1985)

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  1. Kant and Aristotle: Epistemology, Logic, and Method.Marco Sgarbi - 2016 - Albany, NY, USA: State University of New York Press.
    A historical and philosophical reassessment of the impact of Aristotle and early-modern Aristotelianism on the development of Kant’s transcendental philosophy. Kant and Aristotle reassesses the prevailing understanding of Kant as an anti-Aristotelian philosopher. Taking epistemology, logic, and methodology to be the key disciplines through which Kant’s transcendental philosophy stood as an independent form of philosophy, Marco Sgarbi shows that Kant drew important elements of his logic and metaphysical doctrines from Aristotelian ideas that were absent in other philosophical traditions, such as (...)
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  • Kant on the `symbolic construction' of mathematical concepts.Lisa Shabel - 1998 - Studies in History and Philosophy of Science Part A 29 (4):589-621.
    In the chapter of the Critique of Pure Reason entitled ‘The Discipline of Pure Reason in Dogmatic Use’, Kant contrasts mathematical and philosophical knowledge in order to show that pure reason does not (and, indeed, cannot) pursue philosophical truth according to the same method that it uses to pursue and attain the apodictically certain truths of mathematics. In the process of this comparison, Kant gives the most explicit statement of his critical philosophy of mathematics; accordingly, scholars have typically focused their (...)
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  • Kant on the possibilities of mathematics and the scope and limits of logic.Frode Kjosavik - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 65 (6):683-706.
    ABSTRACT I suggest how a broadly Kantian critique of classical logic might spring from reflections on constructibility conditions. According to Kant, mathematics is concerned with objects that are given through ‘arbitrary synthesis,’ in the form of ‘constructions of concepts’ in the medium of ‘pure intuition.’ Logic, by contrast, is narrowly constrained – it has no objects of its own and is fixed by the very forms of thought. That is why there is not much room for developments within logic, as (...)
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  • Kant on concepts and intuitions in the mathematical sciences.Michael Friedman - 1990 - Synthese 84 (2):213 - 257.
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