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

from potential infinity to actual infinity 27apophatic theology. In fact, he may have deeply influenced the Cappadocian Fathers:Basil, Gregory of Nyssa, and Gregory of Nazianzus. However, if God is infinite,how can one think about him in a rational way? Later Christian theology paved theway for struggling in a new way with this question (Armstrong 1954–55; Sweeney1957).1.4.2 Gregory of Nyssa, Dionysius the Areopagite,Nicholas of Cusa, and Georg Cantor1.4.2.1 Gregory of NyssaThe biblical writings do not refer directly to God as infinite, although some texts alludemetaphorically to God’s infinity. 57 The first well-known Christian theologian, Origen,was still within the conceptual framework of Aristotle. Surprisingly, Origen indirectlyclaimed in his De Principiis that God is finite. 58 St. Augustine held that thinking ofGod must include infinity, as a result of his divine omniscience and foreknowledge.The latter attributes cannot be thought of without presupposing that God himself isinfinite. He substantiated his claim for God’s infinity on biblical grounds in his Cityof God. 59 Augustine illustrated his argument for God’s foreknowledge by the exampleof the infinite number of integers that is present in God’s mind. Although he arguedthat God’s infinite mind comprehends the infinite number of integers, he rejected theidea of an actual infinity (“quamvis infinitorum numerorum nullus sit numerus”). Itis interesting that St. Augustine did not make his claim for God’s infinity from areligious experience, as did his Neo-Platonic brother Plotinus, to whom he owes, inother respects, so much. Rather, St. Augustine made his claim from a rational argumentthat was based on biblical resources. Minucius Felix 60 and Clement of Alexandria 61also thought about God in terms of infinity.57 For instance in Ps. 143:3 and Ps. 145:5, Ps. 90:2, Ps. 139:7–12, Ps. 147:5, Job 38–41, Is. 51:6, and Deut.33:27, often the word “ōlām” is attributed to God, which can mean eternity or a far distant time.58 There is no direct quotation of Origen contending the finiteness of God. However, the overall schema of histhought points to this direction. One statement in his De Principiis (“Fecit autem (=God) omnia numero etmensura; nihil enim deo vel sine fine vel sine mensura est”; Origen, De principiis, IV, 4, 8) can be interpretedin this sense (Origenes 1992, pp. 808–9).59 “Absit itaque ut dubitemus quod ei notus sit omnis numerus cuius intelligentiae, sicut in psalmo canitur,non est numerus. Infinitas itaque numeri, quamvis infinitorum numerorum nullus sit numerus, non est tameninconprehensibilis ei cuius intelligentiae non est numerus. Quapropter si quidquid scientia conprehenditurscientis conprehensione finitur, profecto et omnis infinitas quodam ineffabili modo Deo finite est quia scientiaeipsius inconprehensibilis non est” [Let us then not doubt that every number is known to him “of whoseunderstanding” as the psalm goes, “there is no set number” (Ps. 147:5). Accordingly, the infinity of number,although there is no set number of infinite numbers, nevertheless is not incomprehensible to him “of whoseunderstanding there is no set number.” Wherefore, if whatever is comprehended by knowledge is limitedby the comprehension of him who knows assuredly all infinity also is in some ineffable way finite to Godbecause it is not incomprehensible for his knowledge] (Augustine 1988, IV, Book XII, 19). Among othersources St. Augustine discusses with Faustus about the infinity of God with relation to the problem of evil isContra Faustum Manicheum, libri triginta tres 25, 1–2.60 “Hic (= Deus) non videri potest: visu clarior est; nec conprehendi potest nec aestimari: sensibus maior est,infinitus inmensus et soli sibi tanuts, quantus est, notus, nobis vero ad intellectum pectus angustum est, etideo sic cum digne aestimamus, dum inaestimabilem dicimus” (Felix 1977, 18, 8).61 “For the One is indivisible; wherefore also it is infinite, not considered with reference to inscrutability, butwith reference to its being without dimensions, and not having a limit” (Clemens Alexandrinus 1968, V, 12).