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

12 introductionIn its own way, David Bentley Hart’s chapter, “Notes on the Concept of the Infinitein the History of Western Metaphysics,” is as intensely technical as W. Hugh Woodin’s“The Realm of the Infinite” or Harvey Friedman’s “Concept Calculus: Much BetterThan.”Hart feels that the starting point of the metaphysical notion of infinity is the notionof absolute indeterminacy. He also remarks that the metaphysical infinite is a domainin which the principle of noncontradiction fails, and both A and the negation of A canbe true. Waxing a bit territorial, he says that things such as numbers, matter, space,or time can never really attain to a truly metaphysical infinitude. As he puts it, “Wesee here, then, that between the mathematical and the metaphysical senses of ‘infinite’there exists not merely a distinction, but very nearly an opposition ...any possibleanalogy is at best pictorial, affective, and immeasurably remote.”Given the richness of the metaphysical thoughts that Hart goes on to describe, Iwould hope that he’s overstating his case that the metaphysical infinity bears no fruitfulrelations to the infinites of mathematics and physics. He describes some wonderfullyjuicy and intricate distinctions to be found in the metaphysicians’ writings, and I’d liketo think that some mathematical logician of the order of Harvey Friedman or W. HughWoodin might find some formal applications of these arcane metaphysical notionsafter all.Hart views the Christian “Logos” as being like an intermediate divinity betweenGod and the mundane world. He speaks of there being a certain pathos to the notion ofa higher One that lies completely outside of our world – this notion is tragic because,in order to reach the divine, ordinary mortals need to discard or at least forget theirordinary lives.In discussing Erich Przywara’s analogia entis, Hart presents a possible resolutionto our distancing from the divine Infinite. Here we regard of God as living within usand we view our behaviors as in some way mirroring those of the Creator. As Hartputs it, “Every creature exists in a state of tension between essence and existence,in a condition of absolute becoming, oscillating between what it is and that it is,striving toward its essence and existence alike, receiving both from the movementof God’s grace while possessing nothing in itself . . . sharing in the fullness of beingthat God enjoys in infinite simplicity, and so infinitely other than the source of itsbeing.”Marco Bersanelli’s “Infinity and the Nostalgia of the Stars” includes a somewhatsimilar remark: “The belief that each human being is in a direct relationship withthe Infinite provides a solid foundation to irreducible dignity of the single person, afoundation that is hard to maintain otherwise.”Although Cantor himself seems to set metaphysics apart from mathematics andphysics, I still have hopes that theological notions can enrich mathematical thoughtand vice versa. I was heartened to notice that Hart writes quite a bit about Gregoryof Nyssa, whom I mentioned earlier for his anticipation of the set-theoretic reflectionprinciple. Hart refers to Gregory as one of the first early thinkers to “attribute to God,or to develop a philosophical description of, positive infinity,” that is, of an infinity thatis discussed in terms of “fullness of the whole” rather than in terms of the “fecundityof chaos.”