Dr. Vallicella, over at his blog, had been discussing the notion of whether "World + God = God." He took time out to address a comment made by blogger and commenter The Big Henry, criticizing Henry's numerical analogy. (Read this post to learn the details.) I stepped in to comment and left the following remarks:
I don't know what Henry had in mind when he made his analogy, but it sounds at least somewhat consistent with something I'd read, once, in a textbook on philosophy of religion.* In the textbook, the metaphor of an infinite bookshelf is used: imagine a bookshelf that stretches forever to your left and to your right. On this shelf is an infinity of books that alternate between red and black covers, i.e., every other book is black, and every other book is red. That's the setup for the thought experiment.
If I pluck a single book, of either color, from this shelf, how many books remain on the shelf? An infinity of books! In that sense, perhaps we can say that "infinity minus one is still infinity." If I were somehow able to remove all the red books from the shelf, how many books would I remove? Why, an infinity of books. And how many books would still be on the shelf? An infinity! So it may be legitimate to say that, at least in this case, "infinity minus infinity equals infinity." Were I to add an infinity of green books to this shelf, such that the books now alternated "black-red-green, black-red-green, etc.," how many books would be on the shelf? An infinity! So perhaps "infinity plus infinity equals infinity," too.
I don't know, but perhaps it's to this additive oddness that Henry is referring, and as for "God is not a set," well... no matter what analogy we try to use when talking about God, it's a safe bet that, in any "God:X" analogy, God is not an X.
Henry replied with this comment:
That is essentially the infinity I had in mind when I offered my analogy for Bill's consideration. And, indeed, Bill is correct in noting that I had not considered Cantor's work on the concept of infinity. Bill's claim that, "Since Cantor we have an exact mathematics of infinity", however, is questionable. As the greatest mathematician of all time (Johann Carl Friedrich Gauss) noted, "Infinity is nothing more than a figure of speech which helps us talk about limits. The notion of a completed infinity doesn't belong in mathematics".
The analogy I suggested was not meant to imply that God is humanly conceivable by any analogy. From the only philosophy course I ever took as an undergrad (philosophy of religion) I remember that God's attributes are deemed to be "wholly other". That is to say (to use another mathematical analogy) if human attributes are real numbers, then God's are complex numbers.
Finally, in the spirit of Bohr's response to Einstein, if God wants to be a "set" or any "X" you care to mention, God can be whatever He wants to be.
It was that final sentence about God that snagged my attention. So I wrote:
[slightly edited for style]
"God can be whatever He wants to be."
Fascinating theological claim. My inner Sunday-school student wants to accept this unquestioningly because, after all, God can do anything.
But can He really?
What if God says to Himself, in the spirit of Rachel Dolezal's claiming to be black, "You know... I want to be a deer. And you know what else? I think I am a deer! So be it!" So God transforms Himself into a deer, and does so in such a thorough, complete way that He is now wholly a deer, i.e., an animal with no deific attributes at all, which further means that God now lacks the ability to turn Himself back into the God of all creation. At this point, having only a deer's powers of cogitation, God is no longer in a position to say about Himself, "Well, shit... now I'm a deer. What the hell do I do?" Even that thought is beyond Him.
If God's omnipotence includes the ability to become something less-than-God so completely that God loses His God-ness, then the claim that "God can be whatever He wants to be" can be true only once. Otherwise, if God turns into a deer but retains the deific power to revert back to being fully God, then God has not truly become a deer in full: He's kept an ontological escape clause.
I realize you were just being playful with your Bohr/Einstein remark, but I saw an opportunity to engage in some theological whimsy. Apologies.
I should note that, technically speaking, nothing I wrote above invalidates Henry's claim that "God can be whatever He wants to be." The modal can refers to potential. If we think spatiotemporally, and if we assume God does exist, we can further safely assume that God hasn't exercised His prerogative to become a deer just yet: that remains a potential action. The fact that God can perform this action only once (because becoming a deer means abandoning the universe) doesn't undermine the notion that God can become whatever He wants to become. The claim becomes invalid after God's first—and only—transmogrification.
[NOTE TO NEW READERS: I don't believe in a literal God of the Bible. I am, in fact, about as far from being a classical theist as it's possible to be. At the same time, I wouldn't call myself an outright atheist, either; I prefer to call myself, in the language of nondualism, a nontheist. Ultimate reality is apophatic—ineffable, inexpressible—in nature. Even saying that much about ultimate reality is saying too much, and saying it misleadingly.]
*Stairs, Allen, and Christopher Bernard. A Thinker’s Guide to the Philosophy of Religion. New York: Pearson Education, Inc., 2007.