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 (...) central figures in the period: Locke, Descartes, and Leibniz. (shrink)

The main objective of the paper is to give initial answers to three important questions. Why did Leibniz visit Spinoza? Why did his preparation for this meeting include a modification of the ontological proof of God? What is the philosophical result of the meeting and what do possible worlds have to do with it? In order to provide answers, three closely related manuscripts by Leibniz from November 1676 have been compared and the slow conceptual change of his philosophical apparatus has (...) been analyzed. The last of these manuscripts was presented and read in front of Spinoza. Around that time Leibniz abandoned the idea of plurality of worlds (cf. Tschirnhaus) and instead proposed the idea of possible worlds, thus introducing possibility into the (onto/theo)logical structure itself in order to avoid the “precipice” of Spinoza’s necessity. What is interesting, however, is how exactly this conceptual change occurred at the end of 1676 and what its philosophical and methodological implications are. (shrink)