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

278 god and infinitychallenge until the revolution in mathematics in the nineteenth century. Aristotle began,as those before him, by considering infinity as a negative quality, that is, as somethinglacking: “(I)ts essence is privation.” 5 But he altered the concept of infinity to mean anunending and incomplete process: “(T)he infinite has this mode of existence: one thingis always being after another, and each thing that is taken is always finite, but alwaysdifferent.” 6 Here the only infinity considered possible is potential infinity: somethingcapable of being endlessly divided or added to, but never fully actualized as infinite. Forexample, consider the series of unending succession of natural numbers, the endlesssuccession of the seasons, or the continuous division of a line interval into smallerand smaller portions. 7 Aristotle thought of these as potentially infinite, given that theseries can be continued endlessly while remaining finite; these series are never actuallyinfinite. Going through successive elements in a series, we never get beyond the finitesteps in the series to reach their limit, the actually infinite. We never view the infiniteseries as a whole. 8Early Christian writers were informed by this more “positive” conception of infinityas they developed the doctrine of God. 9 In time the attribution of infinity to Godbecame a standard cornerstone of Christian theology. Augustine (354–430), throughhis debt to Plotinus, believed that because God is infinite, God must know all numbersand must have limitless knowledge of the world. 10 Gregory of Nyssa (335–394) alsoargued that God is infinite in the context of his Christological debates against suchArians as Eunomius. 11 Writing a millennium after Augustine and drawing on thephilosophy of Aristotle, Thomas Aquinas (1225–74) believed that only God is infiniteand all creatures are finite. Yet even God, whose power is infinite, “cannot make anabsolutely unlimited thing.” 12 Turning to contemporary theology, most theists inheritthis tradition, affirming that God creates and sustains the world in existence whileutterly transcending it. God alone is infinite, and the world is finite. God’s infinity is5 See Physics, III.7.207b35 in McKeon (1941).6 Aristotle, Physics, III.6.206a26-30.7 Aristotle, Physics, III.4.204b1-206a8.8 Aristotle, Physics, III.5.206a5b.9 In his very illuminating contribution to this volume, “A (Partially) Skeptical Response to Hart and Russell,”Denys Turner offered the following criticism of my reference to a positive notion of the infinite: “I confess tonot being clear about what is meant by a ‘positive’ notion of the divine infinity . . . (W)e need to distinguishbetween two sorts of predicates of God: those that can be said to be ‘positive’ (predicates) – such as ‘goodness,’‘wisdom,’ ‘intelligence’ – and are known ‘by analogy’ from what we know of such predicates as affirmed ofcreatures, and those that are . . . ‘regulative’ – such as ‘infinity’ and ‘simplicity’ – which are known to be trueof God only by denial of what we know of creatures” (p. 4). I am appreciative of Turner’s distinction betweenthese two types of predicates of God. Using Turner’s, together with Pannenberg’s, terminology, the regulativepredicates are appropriate for discussing those divine attributes that define the God who acts (i.e., tell us what“God” means), while the positive predicates are appropriate for discussing those divine attributes that describeGod’s actions (i.e., tell us what God does). See my discussion of Pannenberg in “The infinity of God in relationto the divine attributes,” below. Regarding my comment on early Christian writers, what I meant to suggest isthat these writers were informed by a positive concept of infinity through Aristotle’s understanding comparedwith that of Plato. For the latter, God could never be said to be infinite. (See the chapter by Hart in this volume,sections 2 and 3.)10 Augustine, City of God, XII 18.11 Thomas Aquinas, Summa Ia, 7, 2–4.12 We shall see that Galileo’s insight was to play a key role in the discovery of “transfinite” numbers by GeorgCantor in the nineteenth century (see Galileo 1954).