In short, if God is infinite, then he cannot be known, even by himself, because to know something is to render it finite, and God cannot be something other than God, i.e., infinite.
Take for example, number. Does God know the last number? Of course not. Numbers go on forever. There is no end and therefore no boundary in which to enclose them.
To exist requires boundaries, which is why it is proper to say that God doesn't "exist" to begin with. Creatures exist. The Creator does not. "Existence" is a property of, or analogy to, something else.
Schuon defines matter as "the sensible manifestation of existence as such." This implies that there are insensible manifestations of existence, which indeed there are. That is to say, all matter in existence is suffused with boundaries which are the effect of ideas.
Or in other words, as Schuon writes, "form is the manifestation of an 'idea,'" or "of a particular possibility." Thus, both form and substance, idea and matter, are limitations on possibility, rendering the infinite finite.
Even so, there is always nonlocal unity beneath the local diversity, which one might say is a shadow of the Absolute.
For example, although number goes on forever, there is no conceivable number that could be so far out as to become "detached" from the rest. Underneath the diversity of mathematics is always a continuum of unity; math is just multiples of one, or the endless variety of One-ness: unity prolonged. Even a fraction -- i.e., less than one -- must still partake of oneness, or it couldn't be defined.
Ah, but what about irrational numbers such as pi? Pi has "no solution." It has no end and therefore no boundary. As such, even God cannot know it, since it trails off into infinity, just as he does. So, does pi exist?
I don't know. I've never thought about it before. I would say that this only goes to show that there exist truths that cannot be proved with strict logic. In other words, we know that there must be a constant ratio between the diameter and circumference of a circle, even if it cannot be reduced to a fully rational expression.
Maybe the problem is that circles don't actually exist, any more than points or lines do. Rather, these are mental abstractions, pure forms that are never seen in matter. Or to plagiaphrase Benoit Mandelbrot, clouds aren't spheres, mountains aren't cones, coastlines aren't circles, and bark isn't smooth.
Speaking of Mandelbrot, one of his bestest ideas is that -- and I'm expressing this in my own way -- the immanent is just as infinite as the transcendent. For example, a coastline is not actually a finite boundary, but rather, is infinite. Thus, Tonga, for instance, is actually "enclosed in infinity."
How can that be, since infinity by definition cannot be closed? Well, let's say you are tasked to measure the coastline(s) of Tonga. Now, we all know that Tonga consists of 176 islands. Forget about that. We just want you to measure one of them. How would you begin? With a big tape measure? What about all the little nooks and crannies along the coastline, all the individual grains of sand, not to mention the molecules, atoms, and subatomic particles?
It turns out that nature is such a rough place that even the toughest Tongan couldn't possibly measure it, because
"the measured length of a stretch of coastline depends on the scale of measurement. Empirical evidence suggests that the smaller the increment of measurement, the longer the measured length becomes. If one were to measure a stretch of coastline with a yardstick, one would get a shorter result than if the same stretch were measured with a one-foot (30cm) ruler.
"This is because one would be laying the ruler along a more curvilinear route than that followed by the yardstick. The empirical evidence suggests a rule which, if extrapolated, shows that the measured length increases without limit as the measurement scale decreases towards zero" (Professor Wiki, emphasis Professor Wacky).
Wo. Let's pause here for a moment so as to allow you to assimilate this wonderful orthoparadox: the more accurately we measure something, the longer it is, to the point that perfect measurement equates to infinity?
CIBSPFY! (Can I buy some pot from you?)
This truth can be depicted visually via fractals. Magnify the itsiest bitsy of a fractal and you will see another beautiful fractal. There is no "last fractal," any more than one could find the last snowflake before they start repeating themselves. Or write the last poem. Or compose the last melody. Or bleat the last blog post.
(Which reminds me a line from the Wake that sez When a part so ptee does duty for the holos we soon grow to use of an allforabit.)
Again: the infinitude proceeds both up, into transcendence, and down, into immanence. And I would suggest that the same principle can assist us in thinking about God, who overflows and spills into and out of everything, just as Meister Eckhart claimed.
What exactly did he claim? Oh, for example, "Every single creature is full of God and is a book about God. Every creature is a word of God. If I spent enough time with the tiniest creature -- even a caterpillar -- I would never have to prepare a sermon. So full of God is every creature."
Or "Earth cannot escape heaven. Flee it by going up, or flee it by going down, heaven still invades the earth..."
Or "God forever creates and forever begins to create, and creatures are always being created and in the process of beginning to be created."
I guess that's the "end," even if no such thing is possible...