Nicholas of Cusa and the Finite Universe

Nicholas of Cusa and the Finite Universe* TYRONE LM IN 1440, NICrIOLAS OF COSA PUBLmrmD his De Docta Ignorantia in which one of the chapters was headed with the statement: "From propositions already established the unity and infinity of the universe is inferred. (Correlaria praeambularia ad inferendum unum infinitum universum.)" 1 Many have taken Cusa to espouse a belief in an infinite universe somewhat similar to the one later championed by Giordano Bruno. Kepler, referring to Galileo's "Sidereal Message," asks, "If its author intended to lie about new planets, why, may I ask, did he not invent infinite planets around infinite fixed stars, to agree.., with the Cardinal of Cusa?" 2 Descartes, in a letter to his friend Chanut, says that "the Cardinal of Cusa and several other Divines have supposed the world to be infinite." 3 However, it has not been always clear in exactly what way Nicholas of Cusa thought of the universe as infinite. "Cusanus' conception of the physical universe is not completely clear in the Docta lgnorantia,'" wrote one author recently, "but it seems to be without spatial limitation.'" 4 Dijksterhuis, in his book The Mechanization of the Worm Picture is more definite; he says, "The Universe [as Nicholas of Cusa sees it] is infinite in the same sense as the series of natural numbers: there is no end to it." 5 Koyrd agrees that an interpretation of Cusa is difficult 6 but he thinks that according to Nicholas of Cusa, the universe "is not infinite (infinitum) but 'inter- * In writing this paper, I have benefited much from an unpublished paper of my teacher, Piero Ariotti, to whom I wish to express my most grateful thanks. Nicholas of Cusa, De Docta lgnorantia, cd. E. Hoffmann and R. Klibansky (Leipzig, 1932), Bk. II, Chap. 1. English translation by Germain Heron, O/ Learned Ignorance (London: Routledge & Kegan Paul, 1954). Passages quoted from Heron in this paper have been checked against the original; these are indicated by giving the title in English. 2 See Edward Rosen, Kepler's Conversation with Galileo's Sidereal Messenger. (New York: Johnson Reprint Corp., 1965), p. 64, n. 56. s Descartes" Philosophical Letters, trans. Anthony Kenny (Oxford: the University Press, 1970), p. 221. 9 Paul E. Sigmund, Nicholas of Cusa and Medieval Political Thought (Cambridge, Mass.: Harvard University Press, 1963), p. 257. s E. J. Dijkstcrhuis, The Mechanization of the World Picture, trans. C. Dikshoom (London: 1961), p. 228. 6 Alexandre Koyr6, From the Closed World to the Infinite Universe (New York: Harper Torchbooks, 1958), p. 13. [161] 162 HISTORY OF PHILOSOPHY minate' (interminatum), which means not only that it is boundless and is not terminated by an outside shell, but also that it is not 'terminated' in its constituents, that is, that it utterly lacks precision and strict determination." 7 Thus, according to Koyr6, Cusa does not assert the "positive infinity" of the universe although he was the first to reject the medieval cosmos-conception,s The purpose of the present note is to show, through a clarification of the different concepts of infinity that Cusa employs, that he thinks of the world as no other than finite so far as its extent is concerned. If Cusa was instrumental in reintroducing the concept of an infinite universe, it was not something, it seems to me, that he intended. His description that the universe is infinite or interminate is quite compatible with his thinking that the actual extent of the universe is finite. There is at least one place in De Docta Ignorantia at which Cusa says simply that the universe is finite. In Book II, Chap. 8, he says: Mundus necessario contractus ex contingenti fin#us est. Now, one may not wish to attach too much importance to just one statement but it is significant that previous to this statement in the same paragraph, Cusa did entertain the possibility that God could have created the world infinite, but he ruled out this possibility because, to him, the world was a "contracted" being (esse contractum) and being such it was necessarily finite. It is useful to bear in mind here Cusa's doctrine of contractio. The universe is a reflection of God but in...