Your pun on Sophie’s Choice (a choice between two bad options) reveals that you haven’t yet grasped the theory of middle knowledge, for God doesn’t create such a choice for Himself. The counterfactuals of creaturely freedom which confront Him are outside His control. He has to play with the hand He has been dealt.
A good place to begin is by asking ourselves, “Does the number 3 exist?” Certainly there can be three apples, for example, on the table; but in addition to the apples does 3 itself exist? We’re not asking whether the numeral “3” exists (the symbol borrowed from the Arabs to represent the quantity three). Rather we’re asking whether the number 3 itself exists. Are there such things as numbers? Do numbers really exist?
Some people might think that this question is so airy-fairy as to be utterly irrelevant. But in fact it raises a fundamental theological issue whose importance can scarcely be exaggerated. For if we say that numbers do exist, where did they come from? Christian theology requires us to say that everything that exists apart from God was created by God (John 1:3). But numbers, if they exist, are almost always taken to be necessary beings. They thus would seem to exist independently of God. This is the view called Platonism, after the Greek philosopher Plato.
Someone might try to avoid this problem by espousing a modified Platonism, according to which numbers were necessarily and eternally created by God. But then a problem of vicious circularity arises: explanatorily prior to God’s creating the number 3, wasn’t it the case that the number of persons in the Trinity was 3? Of course; but then the number 3 existed prior to God’s creating the number 3, which is impossible!
I remember the sense of panic that I felt in my breast when I first heard this objection raised at a philosophy conference in Milwaukee. It seemed to be an absolutely decisive refutation of theism. I didn’t see any way out.
The way out, I discovered, is to deny the Platonist view that abstract objects like numbers exist. My first inclination was to adopt some sort of Conceptualism which construes abstract objects as ideas in God’s mind. This may still be the route I’ll take, but the more I’ve studied the problem the more attracted I’ve become to various Nominalistic or anti-realist views of abstract objects which flatly deny their existence rather than re-interpret their existence in terms of conceptual realities. As you note, Conceptualism seems to be a sort of realism which identifies numbers with thoughts in God’s mind. Such thoughts are concrete objects, not abstract objects, even though they are immaterial. Such an identification seems problematic in a number of ways, which I needn’t go into here. If, on the other hand, the Conceptualist does not take numbers to be actual thoughts God is having, then he seems to be really embracing some anti-realist view like Fictionalism.
Sentences like “2 + 2 = 4” are like statements concerning fictional characters, such as “Santa Claus lives at the North Pole.” Such sentences fail to correspond to reality because they have vacuous terms in them. Because they thus fail to correspond to reality, they are literally false. Since there is no such person as Santa Claus, he cannot literally live at the North Pole. Since there are no such things as two and four, it is not literally true that four is the sum of two twos. What is true to say, however, is that Santa Claus lives at the North Pole according to the usual story of Santa Claus; he does not, according to that story, make his home in East Peoria. Similarly, it is true to say that 2 + 2 = 4 according to the standard account of mathematics. This saves the Fictionalist from the embarrassment of stating flatly that “2 + 2 = 4” is false, for he agrees that such a statement is true in the standard model of arithmetic. But he denies that that model corresponds to any independent reality. It is a mistake to think that mathematical practice commits us to the literal truth of mathematical theories, for the ontological question concerning the reality of mathematical objects is a philosophical question which mathematics does not itself address. At most our practice commits us to holding that certain statements are true according to the standard account in the relevant area.
So not only must God play the hand he’s been dealt, but he was dealt that hand from a fictitious deck by a fictitious dealer!
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