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

from potential infinity to actual infinity 29theological suppositions. This was exactly the way Gregory pursued. He did so in atwofold way:1. He claimed that the of God is not a trait of the , but it is only aproperty. Given this different interpretation of God, it follows that the whole argumentof Eunomius collapses. 642. Gregory went further and designed a new concept of God. On the one hand, this newconcept made it impossible to set up the logical inferences of Eunomius, and on the otherhand, it allowed a logical deduction as to the Son’s divinity based on the compatibilityof the and the . This feat was accomplished by introducing the ideaof infinity ( and ) as a decisive trait of God. In order to avoid thecounterargument of a pure ad hoc hypothesis, he had to make sure that the idea of God’sinfinity could be substantiated by reasonable arguments.The second part of the argument will be the focus here, and Gregory’s argumentwill be followed in some detail. In the first part of the argument, Gregory wanted tomake sure that the human mind cannot grasp the of God at all. Given this point,Eunomius’s logical inference can no longer be upheld. Gregory introduced the notionof infinity – as actual infinity ( and ) – into God’s . As we shallsee later, infinity is a notion to which the human rationality cannot be applied. Gregoryhad to show that the relating of this notion to the essence of God was not just anargument based on an ad hoc hypothesis. First of all, he did this by substantiating itwith biblical quotations (Ps. 144: 3b + 5a) (Mühlenberg 1966, p. 102 [sect. 103, 38,21sq]; p. 160 [4, 9sq]). Secondly, and more convincingly, he used the common groundof the God of Greek metaphysics and its properties, on which Eunomius also agreed.By a logical inference, Gregory showed that the two metaphysical properties of Godin the Greek tradition, simplicity and inalterability (), necessarily entailGod’s infinity (Aristotle 2003, 1073a11). According to Ekkehard Mühlenberg (1966,pp. 121–22), the argument based on God’s unchangeability runs as follows: 651. Logical Presupposition: With regard to mercy, power, wisdom, and so on, a limitationcan only be obtained by the respective opposite.2. Metaphysical Presupposition: The divine nature is unchangeable ().Logical conclusions are as follows:1. Because God is unchangeable, there is no opposite in his essence.2. If God in this way is superior to the realm of opposites, where nonbeing and evil arealso located, then he must be perfect.3. Because, according to presupposition (i), God cannot be limited in his goodness, he isunlimited.4. Being without limits is identical with infinity.As the next logical step, in agreement with Greek metaphysical heritage,Gregory claimed that infinity is not accessible by reason (Gregory of Nyssa 1960b,64 For further elaboration of this argument see Mühlenberg (1966, p. 101) and Gregory of Nyssa (1960b, p. 101,13–14).65 For the argument based on God’s simplicity, see Mühlenberg (1966, p. 125).