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

296 a (partially) skeptical response to hart and russellOtherwise, we could never get analogy going at all. If, as Russell suggests in hischapter, we knew God’s “absolute” infinity by analogy from creaturely infinity, ona model of the way in which Cantor’s “transfinites” enable knowledge of AbsoluteInfinity, then it could not serve, in the manner just described, as a quasi-operatorwithin language about God, to contribute to the structure of analogical utterance aboutGod. The infinite/finite distinction defines the gap that analogy has to cross; it is notan analogical means of crossing it. If the absolute “infinity” of God were known byanalogy from any creaturely “finite” infinity, then we would need another term, notpredicated by analogy and defined only negatively, as a “qualifier” over the supposedly“substantive” notion of “infinity,” and so on. Such a procedure would be like tryingto define “square of ...”bymeans of the values it generates. Just as “square of ...”operates over numbers, and so itself cannot be a number, so “infinite,” it seems to me,is a second-order qualifier, operating over our affirmations of substantive attributes ofGod, but is not itself a substantive “attribute” in the way that “ ...isgood” and “ . . . iswise” are.However, if the divine “absolute” infinity is not a positive attribute, known by analogyfrom the more limited infinities of creaturely experience, but only by negation of thosemore limited infinities, it is important to distinguish, as the Pseudo-Dionysius does,between “ordinary negation” and “negation by transcendence” (Mystical Theology).Thus, it is important in itself to distinguish types of “negativity,” but it is also importantif we are to be precise about the nature of the disagreement I have with Hart and Russell.I suspect that the reason why both are resistant to conceding that “infinity” as predicatedof God is a negative concept is because they suppose that the negativity involved couldbe only of the Pseudo-Dionysius’s “ordinary” kind. Now as the Pseudo-Dionysius says,there is all the difference in the world between saying “God is not good,” in the senseentailing the “ordinary” negation of “God is good,” namely, “God is evil,” and saying“God is not good,” as meaning “God is not one of the good things that there are, forGodisthecause of all the good things that there are, and what is the cause of all cannotbe one of the things thus caused.” Now, if you supposed that to say that the infinity ofGod is “only negative” meant nothing more than is entailed by “ordinary negation,”then, of course, you would have every reason for denying that the infinity of God is buta negative concept. To adopt Russell’s comparison, this would reduce the theologicalnotion of divinity to nothing more than the equivalent of Cantor’s transfinites, whichmay, of course, be serially endless, but being only the endless extrusions of series offinite numbers, or else of sets of finite numbers, are each finite as a whole. To get at theinfinity of God, we would have to “get at” some intelligible content to the notion ofan infinite being, and that we cannot get at. We possess no concepts and no language,except that of negation, for doing so. Such a notion is utterly incomprehensible, beyondany power of expression, negative “by transcendence.”How, then, does “negation by transcendence” differ logically from “ordinary” transcendence– in what way, that is, relevant to the logic of predicating infinity of God?If we are to speak of the divine infinity, it seems necessary to distinguish betweeninfinity understood as the simple negation of the finite such as yields its correspondingcontradictory, namely, that of the infinite understood as endlessness – whether ofmathematical or of temporal seriality – and the infinity that is yielded by the negationof the negation between the finite and the infinite as so understood in mathematics.