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

236 god and infinity: directions for future researchMoreover, the same point holds true for serious textbook discussions of infinities inlogic, mathematics, and the physical sciences: there is no theological prolegomenonthat is required for examinations of Conway numbers, renormalization in quantumfield theory, Kripke models for intuitionistic logic, or any other particular topic in thisdomain.But what about the other direction? Does the investigation of “limits” and “bounds”as a subject matter in its own right have some essential or ineliminable significance forthe investigation of “the ultimate source of everything”? It is, of course, well knownthat some of those who have investigated “limits” and “bounds” as a subject matter inits own right have supposed that this investigation does have important consequencesfor the investigation of “the ultimate source of everything.” (This is true, for example,of Cantor.) But the question that I wish to take up, in the remainder of this chapter,is whether it is true – and, if so, in what ways it is true – that those who wish toinvestigate “the ultimate source of everything” need to equip themselves with the fruitsof an investigation of “limits” and “bounds” as a subject matter in its own right.11.2 Predicates and PropertiesThose who believe that there is a unique “ultimate source of everything” exhibit arange of different views concerning the language that they use when talking about thisultimate source. We can illustrate some of the range of views by considering simplesubject-predicate sentences of the form “God is F,” where “F” is a relatively simpleand unstructured predicate.There are, of course, questions about the interpretation of the word “God.” Giventhat I don’t wish to focus on those questions here, I shall simply assume that we can takeit for granted that “God” is a proper name, and that the reference of this name is fixedby the description “the ultimate source of everything.” (Others who accept the generalaccount that is suggested here will prefer different reference-fixing descriptions: e.g.,“the omnipotent, omniscient, perfectly good creator of the world ex nihilo” [Swinburne1979, p. 8] or “the thing that is, in an objectively normative manner, the proper objectfor religious attitudes” [Sobel 2004, p. 10]. For the purposes of the present discussion,nothing turns on the exact phrasing of the reference-fixing description.) Of course, thisaccount leaves it open that there is nothing that satisfies the reference-fixing description;if there is nothing that satisfies the reference-fixing description, then the name is empty.Among those who suppose that “God” is not an empty name, there is a wide rangeof views about the understanding that it is possible for people to have of the propertiesthat are possessed by the being who bears the name. Some suppose that we cannot grasp(apprehend, understand) any of the properties of God. Others suppose that we cannotfully grasp (apprehend, understand) any of the properties of God, but that we can havea partial or incomplete grasp (apprehension, understanding) of some of the propertiesof God. Yet others suppose that, while we can fully grasp (apprehend, understand)some of the properties of God, there are other properties of God of which we can – as amatter of logical or metaphysical necessity – have no more than a partial or incompletegrasp. And, perhaps, there are some who suppose that, while there are properties ofGod of which we remain – and will always remain – ignorant, there is no logical or