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

a (partially) skeptical response to hart and russell 291so related into a finite community of difference that contains them. As Thomas himselfoften says, reporting Aristotle, eadem est scientia oppositorum (Peri Hermeneias, 6,17a, 31–33): to know what counts as not-p is the same knowledge as knowing whatcounts as p. If we can say in what God differs from creatures (from “stone” or “wood”)or, which is to say the same, if we can characterize how “other” God is, then, as Thomasputs it, we end up having to deny the divine infinity and the divine transcendencealtogether. God becomes reduced to just another existent alongside our finite, creaturelyexistence, a “this” or “that,” because there would have to be something in commonbetween God and creatures that they differ as. Nor would it help to say that God differsfrom this and that in this way and that, only infinitely so. For, as Hart rightly says, itis only as finite that things can differ in one way or another, by howsoever much. Anyinfinity defined in terms of contrast with finiteness would have to be a created infinity,such as that, as Russell explains, of Cantor’s transfinites. Moreover, as Hart puts it(in very different terms), it is for want of seeing this that the Heideggerian “onticoontologicaldifference” between God and creatures is obliterated in onto-theologicalidolatry (Hart, Chapter 12).Recognizing this, some theologians have sought a way out of the dilemma of thedivine transcendence by saying that God is not “other” than creatures in any particularrespect (in “this” way rather than “that”) but is “wholly other,” or, as one might say,“infinitely other,” “other” in every respect. But this way out is no way out at all –not, at any rate, as it stands, and certainly not for Christian theologians in the classicaltraditions. Such a notion of “otherness” is entirely vacuous. To be “other” in everyrespect is to be nothing in any respect, and to be “other” in no particular respect is notto be “other” at all. Moreover, the “wholly other” is not just contentless in itself. Anynotion of the divine “infinity” that is connected with it will itself be wholly vacuous, andwe are back, once again, with that classical Greek notion of infinity, as of “otherness,”as pure indeterminacy. Being back to that problem, we are back where Gregory of Nyssastarted: how do you get a notion of an “infinite being,” or of a being that is “infinitelygood,” from a notion of infinity as absolute indeterminacy? In short (no doubt tooshort), it would seem that you can buy the divine infinity at the price of evacuating it ofall determinate content. But if you want determinate content to the divine “difference,”you must sell off your interest in the divine infinity. To put it another way, if you wantto say that God contains all “perfections,” you will have to sacrifice his/her infinity –or vice versa. Either way, on a purely negative concept of infinity, for example, on thatof Plato, who thought of the infinite as formless imperfection, it would seem that youcan make no sense of an infinite existent – hence, none of an infinite God.I am not at all sure that the chapters by Hart and Russell – Hart proposing that away out of this dilemma was found at least in some classical theologies, and Russellsuggesting that the problem is soluble on an analogy provided by Cantor’s distinctionbetween the Absolute Infinite and the transfinite – are, as they stand, entirely convincing.Certainly both are right that Christian theologians, or at least some of them, didacknowledge the problem and faced up to it. Apart from Gregory of Nyssa, Thomasfaces up to it squarely, as we have seen. So, in their different but related ways, doMeister Eckhart and Nicholas of Cusa. On the other hand, I am not entirely sure thatHart is right in saying that from Descartes, through Kant and Hegel, the dilemmais eliminated because one of its horns is removed, by means of retreat into a purely