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

292 a (partially) skeptical response to hart and russellnegative conception of the infinite (i.e., I am not sure that that is what is wrong withtheir accounts of infinity, although what is wrong with them is another story). In anycase, my main problem with Hart’s chapter is that what he identifies as the “historical”solution in patristic and medieval theology (requiring the simultaneous affirmationof “infinity” and “perfection,” and so of “infinity” and “determinacy”) seems not toamount to anything much more than simply attempting to have it both ways, withoutformally removing what is prima facie the inconsistency of so doing. Although I thinkthat the inconsistency can be removed, I doubt whether it can be removed just byworking with what Hart calls a “positive” notion of infinity.Russell’s chapter, on the other hand, while developing what seems to me to be a mostilluminating parallel between Cantor’s account of the relationship of the AbsolutelyInfinite to the transfinite and that of the divine infinity to the creaturely finite, doesnot, in the end, demonstrate what he claims for this parallel, namely, that there is anyreal analogy to be found there. For, as Hart shows, an analogical relationship betweenp and q depends on a relationship of participation one in the other, and I cannot seehow sense can be made of any created infinity’s participating in the divine infinity.However, given that both Hart and Russell rest their distinct cases on the theologicalnecessity of a “positive” notion of infinity, I will direct my comments principally tothe discussion of that notion. I think that such a notion is neither possible logically nornecessary theologically in the defense of the divine infinity.A single example will illustrate what I mean. Hart says, rightly, that Christianswill want to say things like the following (this is Hart in explication of Gregory’s“solution”):The insuperable ontological difference between creation and God – between the dynamismof finitude and an infinite that is eternally dynamic – is simultaneously an implication ofthe infinite in the finite, a partaking by the finite of that which it does not own, but withinwhich it moves – not dialectically, abstractly, or merely theoretically – but through itsown endless growth in the good things of God (In Canticum Canticorum VI).(Hart, Chapter 12)However, my problem with being able to say such things (and as a Christian theologianI, like Hart, want to be able to say them) is that the defensibility of such theological talkrequires the demonstration that the following two propositions are not inconsistent:(a) “God is without opposition, as he is beyond nonbeing or negation, transcendent ofall composition or antinomy” (Hart, Chapter 12); and (b) “Difference within being,that is, corresponds precisely as difference to the truth of divine differentiation” (Hart,Chapter 12).The problem is that (a) is the proposition that God is “wholly other,” that is, abeing beyond “difference,” “transcendent of all composition and antinomy,” as Hartsays. To be “beyond antinomy,” of course, is to be “beyond” any relation of oppositionwith anything else. To escape the antinomies of “this” rather than “that” is to escapethe clutches of the Aristotelian eadem est scientia oppositorum. It follows that such anotion of the “otherness” of God has therefore to be that of the “wholly other.” On theother hand, (b) seems to set creaturely differences in at least an “analogical” relationwith the “divine differentiation,” so that our creaturely “differentiations” in some wayparticipate in the “divine differentiation” that is the plenitude of all perfections. Hart’s