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Leibniz’s Actual Infinite in Relation to His Analysis of Matter

In David Rabouin, Philip Beeley & Norma B. Goethe (eds.), G.W. Leibniz, Interrelations Between Mathematics and Philosophy. Springer Verlag (2015)

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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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  • What Does God Know but can’t Say? Leibniz on Infinity, Fictitious Infinitesimals and a Possible Solution of the Labyrinth of Freedom.Elad Lison - 2020 - Philosophia 48 (1):261-288.
    Despite his commitment to freedom, Leibniz’ philosophy is also founded on pre-established harmony. Understanding the life of the individual as a spiritual automaton led Leibniz to refer to the puzzle of the way out of determinism as the Labyrinth of Freedom. Leibniz claimed that infinite complexity is the reason why it is impossible to prove a contingent truth. But by means of Leibniz’ calculus, it actually can be shown in a finite number of steps how to calculate a summation of (...)
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  • Leibniz’s Argument Against Infinite Number.Filippo Costantini - 2019 - History of Philosophy & Logical Analysis 22 (1):203-218.
    This paper deals with Leibniz’s well-known reductio argument against the infinite number. I will show that while the argument is in itself valid, the assumption that Leibniz reduces to absurdity does not play a relevant role. The last paragraph of the paper reformulates the whole Leibnizian argument in plural terms to show that it is possible to derive the contradiction that Leibniz uses in his argument even in the absence of the premise that he refutes.
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