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

242 god and infinity: directions for future researchhave been inclined to make that suggest that those who wish to investigate “the ultimatesource of everything” do need to equip themselves with the fruits of an investigation of“limits” and “bounds” as a subject matter in its own right. On the one hand, believersoften claim that God is infinite. On the other hand, believers often claim that God isomnipotent, omniscient, omnipresent, eternal, perfectly good, the sole creator of theuniverse, and so forth. All these claims, when interpreted in a straightforward andliteral way, strongly suggest that believers must actually be relying on the results ofinvestigations of “limits” and “bounds” as subject matters in their own right.Now, of course, it might be said that these various claims should not be interpreted ina straightforward and literal way. However, I take it that the discussion in the previoustwo sections of this chapter strongly supports the view that believers ought not to takesuch a line. While believers can perfectly well maintain that a complete characterizationof God is beyond our imaginative and conceptual capacities, such believers are obligedto allow that we have the capacity to provide an intelligible – literal, straightforward –description that fixes the referent of the name “God.” Of course, some will not bepersuaded that this is so. No matter; those not persuaded should think of this inquiryas conditional in form: what should those who suppose that it is straightforwardly andliterally true that God is omnipotent, omniscient, and so forth, allow that investigationsof “limits” and “bounds” as subject matters in their own right contribute to theirunderstanding of these claims?There are straightforward ways in which literal interpretations of the claims thatGod is omnipotent, omniscient, and so on, suggest involvement with investigationsof “limits” and “bounds” as subject matters in their own right. To say that God isomnipotent is, at least roughly, to say that it is within God’s power to do anythingthat it is logically possible for God to do. To say that God is omniscient is, at leastroughly, to say that God knows the truth status of every proposition for which it islogically possible that God know the truth status of that proposition. To say that Godis omnipresent is to say that every spatiotemporal location is present (“available”) toGod. To say that God is eternal is to say that every time is present (“available”) toGod. (Some say, rather, that God is sempiternal, i.e., that God exists at every time.My formulation is neutral on the question of whether God is in time.) To say that Godis perfectly good is to say, inter alia, that there is no moral obligation, moral duty, ormoral good to which God fails to pay due accord. To say that God is the sole creator ofthe universe is to say that God is the sole original creator of all contingently existingthings. And so forth. In every case, the attribution of one of these properties to Godbrings with it quantification over a domain of objects, and, in each case, there is then aserious question to address concerning the measure or cardinality of that domain.Consider the case of omniscience. If we suppose that God knows the truth statusof every proposition for which it is logically possible that God know the truth statusof that proposition, 5 then a natural question to ask is, how many propositions are5 Note that if we suppose that God knows the truth status of every proposition for which it is logically possiblethat God know the truth status of that proposition, we do not suppose – but rather take no stance on the claim –that there are propositions for which it is not logically possible that God know their truth status. My formulationhere is meant to be neutral on, for example, the question of whether Gödel’s limitative theorems would haveapplication in the case of God.