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

250 god and infinity: directions for future researchdivine attributes are actually infinite without undermining the kinds of considerations towhich orthodox cosmological arguments appeal in attempting to establish that God exists?Indeed, more generally, are there conceptions of the infinite that can sustain the claimthat God is actually infinite, and the claim that the magnitudes of the divine attributesare actually infinite tout court? Moreover, if there is a conception of the infinite that cansustain the claim that God is actually infinite, can this conception of the infinite alsosustain the idea of an incarnate God, and the idea that there is an afterlife in which peopleshare the same abode as God?(Oppy 2006)As I noted at the end of the previous section, it seems to me that there are pressures thatdrive theologians in the direction of claiming that God possesses some properties toan unquantifiable – “more than proper class many,” “On” – extent. But, if that is right,then it seems that theologians should not look with any fondness on those philosophicalviews that deny that we can form a coherent conception of actually infinite domainsand actually infinite magnitudes. Rather than side with formalists, or radical finitists,or constructivists, or intuitionists, or those who insist that there are none but merelypotential infinities, believers in God should say instead that there can be domainsand properties that are “unquantifiably infinite,” that is, not measurable by any of thecardinalities that are to be found in Cantor’s paradise. Thus, I take it, the directionof thought that is expressed in the first two paragraphs of the quotation is acceptablewithout qualification (although there is much more to be said in defense of the maintheses outlined therein). Furthermore – and for the same reasons – I take it that the lineof thought that is expressed in the first part of the third paragraph is also acceptable.However, when we turn to the question of traditional arguments for the existenceof God, matters are rather more interesting than the above compressed presentationallows. What is true is that there are some traditional arguments for the existence ofGod (e.g., one a priori version of the kalām cosmological argument) in which it isexplicitly assumed that there can be no actual infinities. Those arguments cannot bedefended consistently with the adoption of the conception of divine infinity articulatedin the previous section. Of course, there are many other arguments, including manyother cosmological arguments, that make no such (implicit or explicit) assumptionabout the impossibility of actual infinities. These arguments are not impugned bythe considerations about infinity to which I have been here adverting. (They may beimpugned by other considerations about infinity, but that’s another story.) It would bean interesting project to run an inventory of arguments about the existence of God, todetermine where considerations about infinity come up, and to check to see how thosearguments fare under the kinds of considerations that were adduced earlier.When we turn to matters such as the idea of an incarnate God and the idea that thereis an afterlife in which people share the same abode as God, there is yet a further raftof considerations that comes into view. It is not easy to reconcile the suggestion thatGod is actually infinite with the idea that God took on a finite physical form. It is noteasy to reconcile the idea that God’s abode is infinite with the idea that that abode isinhabited by finite physical creatures (such as ourselves). At the very least, there isclearly an interesting possible project that investigates the ways in which particularChristian doctrines – concerning, for example, incarnation, trinity, atonement, and soforth – are affected by particular theories about the ways and respects in which God