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

a (partially) skeptical response to hart and russell 293case for a “positive infinity” rests on showing how (a) and (b) are consistent, or at thevery least on demonstrating that the question of formal consistency is undecidable.But you could not demonstrate that “undecidability” if you had not first seen off anyarguments purporting to demonstrate formal inconsistency, such as that which Thomasoffers. What I am not sure about, then, is whether Hart’s version of how historicallytheologians have dealt with the problem – as Thomas raises it – shows that they have,in fact, seen the objection off.The grounds of my skepticism lie in the proposition, claimed by both Hart andRussell, that Christian theology not only historically originated but also logicallyrequires a “positive” notion of infinity. I confess to not being clear about what is meantby a “positive” notion of the divine infinity. The best I can make of this notion isthat of an actually existent infinite being, or of an infinitely good existent, and soforth. Although I am far from having any quarrel with Hart and Russell over thosepropositions – after all, they are central to any Christian theology – I do not see how,just by virtue of that certain truth, it follows that “infinity” is, as they want to say, a“positive” attribute of God.At any rate, my uncertainty about this (perhaps it is just a failure of clarity on my part)arises from a feeling that we need to distinguish between two sorts of predicates of God:those that can be said to be “positive,” such as “goodness,” “wisdom,” “intelligence,”and are known “by analogy” from what we know of such predicates as affirmedof creatures, and those that are, as I shall say, “regulative,” such as “infinity” and“simplicity,” which are known to be true of God only by denial of what we know ofcreatures. Let me explain.When we say that God is “simple,” we mean to say of God something we knowwe cannot say of any creature at all: that everything true of God is God. If I am good,there is an I and there is my goodness: these are distinct. I could not come to be good,nor could I cease to be good, if I and my goodness were identical, for were I, beingonce good, to become less so, then the I who was less good would not be the same Iwho was once better. A being identical with an attribute cannot cease to possess thatattribute without ceasing to be that being. Now when we say that God is “simple,” wemean to say that any of the attributes we affirm positively of God belong to God insuch a way that God would cease to be God were s/he to lose them. And when I saythat a predicate affirmed of God in the way that “simple” is has a “regulative,” ratherthan an “attributive,” character, I advert to this fact of the logic of such terms: thedivine “simplicity” refers not to some substantive attribute, on a par with “goodness,”“beauty,” and so forth, but to how such positive attributes are predicated of God; thatis to say, they are predicated of God minus any implication of complexity carried overwith such positive attributes from their applications to creatures.We can see this if we note how the logic of “complex” as predicated of creaturesparallels that of “simple” as predicated of God. Of course, any creature is, bycontrast with the simplicity of God, “complex.” However, there is a sort of categorymistake in supposing that the following is a logically homogeneous list of substantiveattributes of a creature: “Peter is good, strong, handsome, intelligent, and complex.”For whereas “good,” “strong,” and so forth, are “positive” attributes of Peter, having“positive content,” Peter’s being “complex” is not another attribute of Peter alongsidethe others and on all fours with them logically. Peter’s being “complex” is rather a