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

from potential infinity to actual infinity 35p. 388; cf. Flasch 1998, p. 47). He qualified the infinity of God as the “coincidentiaoppositorum,” the falling together of contradictions or opposites. 82 In different writingshe approached infinity from different angles, such as language, the category of quantity,and even logic. In his “docta ignorantia,” he related general notions of language, suchas “maximum” and “minimum,” to the “coincidentia oppositorum.” 83 Elsewhere, heassociated infinity with the category of quantity, claiming that infinity is not a matterof quantification. 84There is an inherent limitation to understanding infinity with the category of quantity.It is a limitation because this category cannot be applied ontologically to infinity,and also because human rationality operates epistemologically within the categoryof quantity. For example, notions such as “bigger,” “smaller,” and “unequal” cannotbe related to infinity. 85 Infinity cannot be quantified, as it is beyond the categoryof quantity. 86 This understanding also puts constraints on mathematics in its reach forinfinity, because all mathematical operations are based on this very category of quantity(Nikolaus von Kues 1967, pp. 362, 364; cf. Knobloch 2002, p. 225). There is no wayfrom quantity to infinity; 87 therefore, infinity, the maximum, and the minimum are alltranscendent terms. 88 Ontologically, there is no relation of finiteness – finite quantity –to infinity. Therefore, he objected to Aristotle’s understanding of infinity as potentialinfinity, because that is based on an infinite progression of quantities (Knobloch 2002,p. 228). 89Epistemologically, infinity has no relation to our rationality (“intellectus”), whichworks by measuring quantities and finding proportions. 90 Infinity cannot be measured.However, it is the measure of everything else. 91 Furthermore, in considering the relationof infinity to logic, especially to the principle of contradiction, Nicholas of Cusa claimedthat the infinite unity defies any logical treatment, because logical procedure requiresat least a duality of entities, which is not the case in a unity. 92 Much more could be83 “Maximum itaque absolutum unum est, quo de omnia; in quo omnia, quia maximum. Et quoniam nihil sibiopponitur, secum simul coincidit minimum” (Nikolaus von Kues 1964, book I, chap. 2, p. 198).84 “Quia infinitum non habet partes, in quo maximum coincidit cum minimo” (Nikolaus von Kues 1964, bookI, chap. 17, p. 246).85 “Infinitum ergo nec est dato quocumque aut maius aut minus aut inaequale. Nec propter hoc est aequale finito,quia est supra omne finitum, hoc est per se ipsum, tunc infinitum est absolutum penitus et incontrahibile”(Nikolaus von Kues 1967, chap. 13, p. 152).86 “Infinita quantitas non est quantitas, sed infinitas” (Nikolaus von Kues 1967, chap. 13, p. 152).87 “Hoc ex regula doctae ignorantiae constat, quae habet, quod in recipientibus magis et minus non est deveniread maximum et minimum simpliciter” (Nikolaus von Kues 1967, p. 326).88 “Maximum autem et minimum, ( . . . ), transcendentes absolute significationis termini existunt, ut supraomnem contractionem ad quantitatem molis aut virtutis in sua simplicitate absoluta omnis complecantur”(Nikolaus von Kues 1964, book I, chap. 4, p. 206).89 “Finiti ad infinitum nulla est proportio” (Nikolaus von Kues 1967, chap. 23, p. 200).90 “Quomodo potest intellectus te capere, qui es infinitas? Scit se intellectus ignorantem et te capi non posse,quia infinitas es. Intelligere enim infinitatem est comprehendere incomprehensibile" (Nikolaus von Kues1967, chap. 13, p. 148).91 “Infinitum non est mensurabile, quia infinitum est interminum. Non igitur potest claudi terminis cuiuscumquemensurare, sed ipsum est mensura omnium” (Nikolaus von Kues 1967, chap. 11, p. 686).92 “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).