God's Infinite Properties

A student and playground regular is working on a senior thesis with me about natural language uses of utterances referring to the infinite. He's got an interesting puzzle that I figured I'd throw out there for everyone to play with.

There are two types of transfinite numbers -- cardinals and ordinals. A cardinal number is an amount. I have five bananas. An ordinal number is the rank of something. Stan Musial's jersey was not saying he had 6 of anything, but that if you lined up everyone in order according to what was on the back of the jersey, he would be 6th in line. Of course, that would mean he played for the St. Louis Ordinals, not the St. Louis Cardinals.

If we consider the three classic properties attributed to God -- omniscience, omnipotence, and omnibenevolence -- which notion of the infinite is implicit in each?

With omniscience, the idea of being all-knowing implies that God knows every fact, that we could take all of the facts, number them, come up with an infinite number and attribute knowledge of all of them to God. It appears to be a cardinality claim.

With omnipotence, on the other hand, it is not saying that God could do everything on an infinitely long list of actions, but rather that being all powerful means that no matter how powerful you are, God is always more powerful than that. God in front of you in the power line-up. It seems to be an ordinal notion.

But what about omnibenevolence? What does it mean to be all good or all loving? Is it that if you listed out everything, God would love everything on the list? Or if you listed every possible action, God would always do the right one? Or is it that no matter how much you love a thing, God always loves everything more? there doesn't seem to be a quantity of anything to count, but there also doesn't seem to be a scale here to make God the holder of the ultimate degree. What does it mean to say that God is infinitely good or all loving?