In mathematics, there are many definitions of infinity, because there are many different infinities. The infinity that describes the number of points on a line is infinitely greater than the infinity that describes the number of integers that exist. But one particular definition of infinity has intrigued me in its ability to be turned into a metaphor.
The formal definition of a limit at infinity is this. Let 
be a function defined on an interval that contains 
, except possibly at 
. Then we say that 
if for every number 
there is some number 
such that 
whenever 
. What does this mean? Essentially, if we pick any number, now matter how large it is, then if we move 
close enough to the point , then will be bigger. Infinity is defined as the entity that is bigger than any number. Its definition is, given a number M, infinity is bigger than M. It is an indirect definition, because it cannot be directly defined.
I’m told and believe that “God’s love is infinite.” Given any love we can observe, hope for, or even imagine, God’s love is larger, it is deeper. He is impossible to fully imagine because of the nature of who He is and the nature of who we are. Anselm described God as “That which nothing greater can be conceived.” Later, he elaborates that this implies that He is “That which is greater than can be conceived.” It is definitionally impossible to imagine the goodness of God, because whatever we imagine, God is greater. How marvelous! How worthy of marvel!
And how convicting. We are called by Christ to follow Christ, to reflect Christ, to imitate Christ. We are called to have infinite love, as He did. Therefore, given any level of love we have, our calling is higher. We have never arrived at our goal, because to think so is to misunderstand infinity. Then a universal negative can, in fact, be found: It is never true that our love is enough.
Not only have we failed, but we have failed infinitely. Infinity minus a number is infinity; that is, the difference between our love and God’s love is infinite. This is our mired state! This is our pitiable home!
Are we then to despair in our infinite failure? Or is this yet another failure? Can any progress be made if we are perpetually in unimaginable failure? Of course progress can be made! One hundred is greater than fifty, though both are infinitely far away from infinity. Growth is possible and beautiful.
But still, is this only forgetting our guilt? Is wallowing a failure or a wisdom? God, in His infinite love, became the Incarnate and redeemed us to Himself. What does this mean! It is surely a boundless source of mystery and confusion, but it is just as surely true. Therefore our infinite failure is a testament to His infinite mercy! It would seem that rejoicing is the proper posture! Hallelujah, Lord!
And yet, this whole discussion of the infinitude of God feels somewhat… lacking. I really believe it all, but if part of the definition of God’s love is that it is greater than what I can understand, then I clearly cannot understand it. That means that whenever I’m talking about God’s love, the thing I’m talking about is not truly God’s love.
I can understand how this could be seen as a comfort. It wrenches control from our incompetent hands and puts it in the hands of the Most Competent. But when I think of this doctrine, it feels like it kicks out all meaning from the words I use. What do the words “God’s love is infinite” mean? Whatever we say they mean is not what they mean, because God’s love is infinite. It is just shy of a self-defeating statement.
Although, perhaps my difficulty is just an unbounded ego who demands, absurdly, that I must understand God. I admit this is surely me. And it is indeed absurd, even hilarious. For this reason, I try to adopt Augustine’s and Anselm’s phrase, “I do not seek to understand so that I may believe, but I believe so that I may understand.” Now, this does not eliminate the issue, it merely allows us to approach the issue rightly.
But what is really the issue? What bugs me is not exactly that we cannot understand God. It is that we cannot understand God, and yet he is clearly the most relevant and important thing we could ever talk about, so we talk about him. But #28 of Apothegms 12 says, “The wise man does not speak on an issue unless he has a clear grasp of it.” Therefore, if I desire to be consistent, then I ought to say that the wise man does not speak of God’s love, because he knows that he cannot have a clear grasp of it.
That apothegm is probably overstated. But the general idea stands that any speech of God is insufficient. And in fact, there is some precedent to this idea. What did God say of himself? “I am who I am.” No other words were sufficient descriptors. I believe this is a consequence of what Kierkegaard meant by there being an infinite qualitative distinction between God and man. C.S. Lewis conveys something similar in his Footnote to All Prayers:
He whom I bow to only knows to whom I bow
When I attempt the ineffable Name, murmuring Thou,
And dream of Pheidian fancies and embrace in heart
Symbols (I know) which cannot be the thing Thou art.
Thus always, taken at their word, all prayers blaspheme
Worshiping with frail images a folk-lore dream,
And all men in their praying, self-deceived, address
The coinage of their own unquiet thoughts, unless
Thou in magnetic mercy to Thyself divert
Our arrows, aimed unskillfully, beyond desert;
And all men are idolaters, crying unheard
To a deaf idol, if Thou take them at their word.
Take not, O Lord, our literal sense. Lord, in thy great
Unbroken speech our limping metaphor translate.
Why, then, can we think speech has value? Perhaps it can rouse our minds towards God, and then when we get sufficiently close, our minds can leave the words, and focus only on the real God.
But how mystical is that! God deemed it proper to give us a Bible that contained words about him and the world he made, which includes us and the story of our creation, fall, redemption, and glorification. Am I saying that these words are mere metaphors, and do not really contain any truthful truths? That sounds as if the only truth contained in Scripture is in how they are interpreted. But then, couldn’t the interpretation of other non-canon books brings us truth just as true as the interpretation of the Bible? Then what is the point of keeping the Bible around?
In addition, it seems to not make sense to believe in something I do not understand. What, exactly, am I believing in? I can only believe in an idea, but if a certain idea that I can understand, and therefore believe, is that another idea, the Divine Being, cannot be understood, then if I believe that idea, then I am believing that I cannot believe in God.
But of course, the Divine Being is not an idea, he is a being. He is a subject, as opposed to an object. So this idea, the idea that He is not an idea but a being, allows me to understand how I can believe in Him while understanding that I cannot understand who He is.
Furthermore, for most of this discussion I have ignored that fact that I can partially understand something without fully understanding it. This seems reasonable to apply to God. I do understand that I am sinful and that he sent himself to die for me. Of course, even this simple example contains many mysteries, such as the Trinity and the nature of our salvation. But I can somewhat grasp it. I can use metaphors, at the very least.
When I started this post, I was expecting to be able to resolve the difficulties I found in believing that God’s love is infinite. I thought it would be something like the scientific culture we live in is obsessed with obliterating the deep, beautiful, and holy complexities of real religion. But it turns out that I have stumbled upon one of those exceedingly difficult ideas in theology, and that is why it is difficult for me. Theologians since the beginning of time have been assailed by God, and of course! As it should be!
So, yeah. I a bit gave up on that goal, as I feel profoundly unqualified. Maybe I should just delete this whole thing. But no, I still find it to be interesting. If you so desire, here are a few Wikipedia articles that convinced me that I am profoundly unqualified. Enjoy.
Thoughts of a Novice 