Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

34 infinity as a transformative concept in science and theology1.4.2.3 Actual Infinity and the Watershed of Its Rational Understanding:Nicholas of CusaNicholas of Cusa was deeply influenced by Pseudo-Dionysius. He was the author mostoften quoted in Nicholas of Cusa’s writings. 78 He was especially influenced by theAreopagite’s approach to apophatic theology. First of all, Nicholas of Cusa agreed withthe Areopagite that God is infinite. 79,80 Secondly, he also equated God’s infinity withGod’s unity, which means that God’s infinity and unity are identical (Schulze 1978,p. 95). 81,82Now the question is in what way he differed from the tradition of apophatic theology.That is, how did he differ with respect to the constraints that the limitations of language,the categories, and logic put on the human ability to have access to infinity?Regarding language, Nicholas of Cusa agreed with Pseudo-Dionysius, who said inhis early writing about the “docta ignorantia” that God cannot be reached by means oflanguage. 79With regard to the applicability of the Aristotelian categories to infinity, he raisedthe question as to how to relate the category of quantity to infinity. He argued thatinfinity defies any characterization in terms of the category of quantity.Furthermore, there is a question as to how traditional logic, or other axioms ofreasoning in the finite realm, such as “the whole is larger than the parts,” can be appliedto infinity (Knobloch 2002, p. 227). Are the rules of logic valid in an infinite realm,which at the same time – as we have seen – coincides with unity? For instance, how canthe rule of contradiction be used in an infinite unity, given that contradiction requiresat least two propositions, which cannot be found in a nonquantitative infinite unity? 80Despite these obstacles to a rational account of infinity, however, Nicholas of Cusawent beyond the apophatic tradition, insofar as he attempted by means of symbolicexpressions to find an intellectual understanding of God’s infinity. This developmentmust be explained in more detail, because this innovative intellectual and theologicalendeavor exercised an enormous impact on the subsequent understanding of infinity,as well as on natural science and mathematics.1.4.2.3.1 Nicholas of Cusa’s New Approach to Infinity. First of all, Nicholas ofCusa held that God is infinite, just as Gregory and the Areopagite did. 81 However, heintroduced a new and quite innovative thought about this infinity, which is not found inthe writings of either Gregory or Pseudo-Dionysius. He himself described this thoughtas “never heard before” (“prius inaudita”; Nikolaus von Kues 1964, book II, chap. 11,78 For example, in “docta ignorantia” (Nikolaus von Kues 1964, book I, chaps. 18, 24, 26).79 “Docuit nos sacra ignorantia Deum ineffalbilem; et hoc, quia maior est per infinitum omnibus, quae nominaripossunt; et hoc quidem quia verissimum, verius per remotionem et negationem de ipso loquimur, sicutiet maximus Dionysius, qui eum nec veritatem nec intellectum nec lucem nec quidquam eorum, quae dicipossunt, esse voluit” (Nikolaus von Kues 1964, book I, chap. 26, p. 292).80 “Infinitas est ipsa simplicitas omnium, quae dicuntur, contradiction sine alteratione non est. Alteritasautem in simplicitate sine alteratione est, quia ipsa simplicitas” (Nikolaus von Kues 1967, chap. 13,p. 148).81 For literature on Cusanus’s concept of infinity, see Enders (2002).82 “Debet autem in his profundis omnis nostril humani ingenii conatus esse, ut ad illam se elevet simplicitatem,ubi contradictoria coincident” (Flasch 1998, p. 46).