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 (...) tendency of the mind of producing “creative progress” and “inclusive closure”. The aim of this paper is to explain in which sense and why Kant’s treatment of the antinomies attracts the attention of Zermelo in the early 1900s and which aspects of his second axiomatic system have been inspired by Kant’s philosophy. Thus, by reading Kant’s antinomy ‘through Zermelo’s eyes’—with emphasis on the concept of regressive series in indefinitum and on that of regressive series ad infinitum – this paper identifies the echoes of Kant’s work in the making of the ZFC set theory. (shrink)

This essay argues that the key to understanding Kant's transcendental idealism is to understand the transcendental realism with which he contrasts it. It maintains that the latter is not to be identified with a particular metaphysical thesis, but with the assumption that the proper objects of human cognitions are “objects in general” or “as such,” that is, objects considered simply qua objects of some understanding. Since this appears to conflict with Kant's own characterization of transcendental realism as the view that (...) (mistakenly) regards appearances as if they were things in themselves, the essay explicates the connection between the concepts of an object (or thing) considered as such and a thing considered as it is in itself. In light of this, it maintains that Kant's transcendental idealism is compatible with a robust empirical realism and that many of its critics are tacitly committed to a misguided transcendental realism. (shrink)