There’s a lot to be said about the use of the concept of infinity in theology, which I will write about once I’m not traveling. Different major theologians have thought that it was a wonderful way to think about God; others have disliked the usage for various reasons. Nicholas of Cusa, one of the fans, had diagrams meant to convey the impossibility of finite minds grasping God. Others thought other things.
To be clear, I'm one of the ones who doesn't like the concept of infinity as applied to God, ironically because I think it is too limiting. Mathematicians talk about infinities as having different sizes, which there are good proofs for but which I also think is wrong.
Infinities crop up regularly in physical calculations, and you can just cancel them out when they do: if you get an infinity on one side and another on the other, you can cross them out like you would an "x" in algebra. The calculations work just fine. It doesn't matter if the infinites are "countable" or not, which is the point the mathematicians are making about them being of different sizes. Maybe that has to do with infinity as applied to physical reality, as opposed to within the theory of math. I hold with Aristotle, however, that actual infinities -- physically real ones included -- are impossible. The Church strictly disagrees with me, and Aristotle, on this point. So do many (most?) modern mathematicians. They are persuaded by the same evidence as me in the opposite direction: since we can use the infinities algebraically, they must be actual. My sense is that since we can use them so in spite of their allegedly (provably!) different sizes, they aren't actual infinities but a place where our mathematical models are reaching their limits. There's no reason to think our mathematical models are right, and very good reasons to think they aren't quite. One such: no human beings before us have ever made mathematical models that really were quite right when applied to reality.
The impossibility of an actual infinity is an important feature of the proof of God given by Avicenna, which Aquinas gives in brief in the Summa Theologica in spite of the fact that he ends up endorsing actual infinity. To put it in basic terms, every existent thing gets its existence from something else that already exists. You came to be because your parents already were, and they were able to bring you about. If an infinite series were possible, then there is no need for a thing-that-exists-without-being-made to have started the chain. God's necessity stands on the fact that divine existence is necessary in order to account for everything else that follows: the whole chain needs to be rooted, grounded, on something that already existed before anything was made. (There is a second proof along this line as well, in which Avicenna is pleased to say that it just wouldn't be determined if everything actually existed without the necessary divine existant; I'll leave that as an exercise for very interested readers.)
The fact is that infinity as we know how to discuss it is a feature of reality, meaning that we understand it as well as we do because of concepts that pertain to this world. Perhaps, as Pythagoras said, the math is what makes the world; perhaps, it is our model of the world. Either way, it belongs to this world and not to the eternity beyond the world. A transcendent God that genuinely exists beyond our reality would not be bound by it, and it is not helpful -- I think, against the Church's considered opinion which any devout Catholic should take as authoritative in spite of my dissent -- to try to apply it to God.
We generated these ideas from our own ideas about mathematics and how they work. All of that belongs to this place and our experience of it. I don't believe it translates beyond the wall of creation. It might, but I see no reason why it must. I'm not entirely convinced we are correct about how it applies here, and I see no reason to believe that it ought to apply there.
4 comments:
Renormalization isn't quite as trivial as "cancelling infinities". I agree that predicted physical infinities speak of problems with the modeling (how do you measure something that's infinite?).
As to aspects of God being infinite, yes, probably an apophatic approach is better: if you think you understand what "infinite goodness" means, you haven't quite wrapped your mind around either word.
Forgive me; I don’t mean to trivialize. Like others, I was just trying to make the matter accessible to a broader audience. Avicenna gives the proof I summarized over several pages of the 13th book of his major work; but I reduced it to a paragraph summary. Aquinas gives it in a sentence.
Let readers understand that there is very much more to be said; almost infinitely more.
The discussion at D29's place was about whether human beings do or do not have "infinite dignity," or if only God does. You can infer from this discussion that I think that God's dignity is beyond the concept of infinity, but transcendent in a way that our mathematical concepts don't really apply to it.
Humans, however, might arguably. Because they are beloved of God, whose love for them is unlimited and whose mercy towards them is inexhaustible provided they do not themselves reject it, infinity looks like a defensible theological concept here. On the other hand, since it can be rejected, there is a limit; but that isn't dispositive, because infinities can exist within limits. For example, the concept of 'one' has a clear limit, but one is infinite in the sense that it is infinitely divisible.
This is the sort of theological debate that people mock, like the 'how many angels can dance on the head of a pin?' one that is the classic example. But it's kind of interesting to think about.
I wonder if human dignity is infinite, but our human understanding is finite, possibly irretrievably so. Thus, we might deny the infiniteness of our dignity, including insisting that there is nothing to deny. That, though, would not mean we lack an infinite dignity, but merely confirm that we don't understand it.
Eric Hines
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