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

244 god and infinity: directions for future researchWhat goes for omniscience goes for the other properties that I listed in the previoussection. On plausible interpretations of the simple subject-predicate sentences that Ilisted, it is highly natural to suppose that the truth of any one of those sentences bringswith it a commitment to infinite domains of objects and/or infinite magnitudes ofdegreed properties. At the very least, it is prima facie plausible to suppose that thereare infinitely many different possible actions that an omnipotent being can perform,and that there are infinitely many different tasks that have been carried out by a solecreator of all contingently existing things; it is prima facie plausible to suppose thata four-dimensionally omnipresent being is present to an infinite volume of spacetime(and this because it is plausible to suppose that the universe is open in the future); it isprima facie plausible to suppose that an eternal being is present to an infinite extent oftimes (again because it is plausible to suppose that the universe is open in the future); itis prima facie plausible to suppose that a perfectly good creator has created a world ofinfinite value (because it would be unworthy of such a being to create a world of lesservalue than some other world that it might have created); and so forth. Moreover, ofcourse, the commitment to infinite magnitudes of degreed properties seems evident onits face in the case of the claim that God is infinite (although see the following sectionfor discussion of some of the difficulties that are raised by this claim).Considerable recent philosophical activity has sought to apply recent mathematicaldiscussions of infinity to the divine attributes that are currently under discussion. Inparticular, there is a considerable literature on omniscience that draws on Cantoriantheories of the infinite (mostly drawing on or discussing ideas that were first canvassedby Patrick Grim [1991]). However, even in the case of omniscience, there has been nosystematic study of the kind that would be needed to address the kinds of questions thatI have been raising in this section. There is a large program of research here waiting tobe carried out.11.5 God and InfinityAmong the various claims listed for consideration in the previous section, the claimthat God is infinite raises special difficulties. As we noted initially, some might supposethat this claim is only to be interpreted in a loose or metaphorical sense: what it reallymeans to say is that God is imperishable, or unchanging, or the source of everything,or the like. Of course, if this is all that the claim that God is infinite is taken toreally mean, then understanding of the claim that God is infinite will not be enhancedby considerations drawn from an investigation of “limits” and “bounds” as a subjectmatter in its own right. But I do not think that it is plausible to suppose that this is allthat those who now claim that God is infinite mean to assert; certainly, it is not all thatmany of those who now claim that God is infinite mean to assert. From this point, Ishall proceed under the assumption that those who claim that God is infinite mean toassert something that is susceptible of explanation in terms of considerations drawnfrom an investigation of “limits” and “bounds” as a subject matter in its own right.Perhaps the most plausible way to interpret the claim that God is infinite is to take itto be the claim that God is infinite in certain respects. Some might think that it shouldbe taken to be the claim that God is infinite in every respect, but unless we have some