Leibniz and the History of Infinity

Leibniz (1646-1716) is an excellent starting point for investigating the intellectual history of infinity in the early modern period. He was not only an extremely original and influential thinker but also a prominent citizen in the Republic of Letters, maintaining a vast network of correspondences that open a window into the intellectual landscape of his time. While infinity was embraced by Epicurus and Lucretius in antiquity, for over a millennium, infinity was shunned from nature and ascribed to God alone. The received view was that God is infinite and creatures are finite. As the fate ofGiordano Bruno illustrates, invoking infinity circa 1600 was dangerous. Yet, in Leibniz’ s letters infinity already figures prominently and becomes essential to understanding many features of nature, including its most fundamental constituents. As Leibniz writes: “I am so much in favor of actual infinity that, instead of admitting that nature rejects it, I hold that it affects it everywhere, for better marking the perfections of its author” (to Foucher, GP I:416). While he sought to introduce infinity into our description of nature, Leibniz flatly rejects infinite quantities. Leibniz’s nuanced use of infinity and his attempt to introduce infinity into nature presents intriguing questions. As time permits, I will present some of these issues.