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The Ontic and the Iterative: Descartes on the Infinite and the Indefinite

In Igor Agostini, Richard T. W. Arthur, Geoffrey Gorham, Paul Guyer, Mogens Lærke, Yitzhak Y. Melamed, Ohad Nachtomy, Sanja Särman, Anat Schechtman, Noa Shein & Reed Winegar (eds.), Infinity in Early Modern Philosophy. Cham: Springer Verlag. pp. 27-44 (2018)

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  1. Three Infinities in Early Modern Philosophy.Anat Schechtman - 2019 - Mind 128 (512):1117-1147.
    Many historical and philosophical studies treat infinity as an exclusively quantitative notion, whose proper domain of application is mathematics and physics. The main aim of this paper is to disentangle, by critically examining, three notions of infinity in the early modern period, and to argue that one—but only one—of them is quantitative. One of these non-quantitative notions concerns being or reality, while the other concerns a particular iterative property of an aggregate. These three notions will emerge through examination of three (...)
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  • The infinite, the indefinite and the critical turn: Kant via Kripke models.Carl Posy - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 65 (6):743-773.
    I thank the editors for inviting me to contribute to this issue on critical views of logic. Kant invented the critical philosophy. He fashioned its doctrines (Understanding versus Reason, synthetic...
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  • The indefinite in the Descartes-More correspondence.Tad M. Schmaltz - 2021 - British Journal for the History of Philosophy 29 (3):453-471.
    In this article, I consider Descartes’ enigmatic claim that we must assert that the material world is indefinite rather than infinite. The focus here is on the discussion of this claim in Descartes’ late correspondence with More. One puzzle that emerges from this correspondence is that Descartes insists to More that we are not in a position to deny the indefinite universe has limits, while at the same time indicating that we conceive a contradiction in the notion that the universe (...)
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  • Kant’s Mereological Account of Greater and Lesser Actual Infinities.Daniel Smyth - 2023 - Archiv für Geschichte der Philosophie 105 (2):315-348.
    Recent work on Kant’s conception of space has largely put to rest the view that Kant is hostile to actual infinity. Far from limiting our cognition to quantities that are finite or merely potentially infinite, Kant characterizes the ground of all spatial representation as an actually infinite magnitude. I advance this reevaluation a step further by arguing that Kant judges some actual infinities to be greater than others: he claims, for instance, that an infinity of miles is strictly smaller than (...)
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