Leibniz's Early Encounters with Descartes, Galileo, and Spinoza on Infinity

O. Nachtomy

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


This chapter seeks to highlight some of the main threads that Leibniz used in developing his views on infinity in his early years in Paris (1672–76). In particular, I will be focusing on Leibniz’s encounters with Descartes, Galileo, and Spinoza. Through these encounters, some of the most significant features of Leibniz’s view of infinity will begin to emerge. Leibniz’s response to Descartes reveals his positive attitude to infinity. He rejects Descartes’s view that, since we are finite, we cannot comprehend the infinite and therefore should refrain from studying it. Likewise, Leibniz rejects Descartes’s view that the term ‘infinite’ should be reserved to God alone, as well as Descartes’s distinction between the infinite and the indefinite. Leibniz’s encounter with Galileo brings out his rejection of infinite number in response to Galileo’s paradox. This, in turn, leads him to face another formidable challenge, viz., to defend the claim that an infinite being is possible, while an infinite number is not. Leibniz’s encounter with Spinoza, I suggest, highlights the way he is approaching this problem by distinguishing between quantitative and non- quantitative senses of infinity. The strategy of employing different senses of infinity in different contexts will remain central in Leibniz’s approach to infinity for the rest of his career
Original languageEnglish
Title of host publicationInfinity in Early Modern Philosophy
EditorsO. Nachtomy, R. Winegar
Place of PublicationCham
Edition1st ed
ISBN (Electronic)3319945564
ISBN (Print)3319945556
StatePublished - 2018

Publication series

NameNew synthese historical library


Dive into the research topics of 'Leibniz's Early Encounters with Descartes, Galileo, and Spinoza on Infinity'. Together they form a unique fingerprint.

Cite this