We apply logical processes in order to try to understand the universe. In any logical explanation or theory, we start with an axiomatic foundation and build on top of this foundation. Axioms about the universe take the form of physical laws and models. For example, in order to explain observations about the chemistry of elements, we postulate the existence of atoms as a model, and we devise as our axioms physical laws such as energy and momentum conservation and quantum theory. This allows us to explain why physical matter behaves as it does. If we delve deeper, we find we must postulate the existence of subatomic particles and physical laws describing their interactions. Deeper still, we postulate quarks and quantum chromodynamics.
Layer upon layer, we delve deeper, hoping to uncover the true nature of the universe. As soon as we discover a new layer of models and axioms, we inquire into the intrinsic nature of the elemental components of the model, thus revealing a new layer beneath it. But because our logical processes require certain unexplained underpinnings as a foundation, the process never ends. Each foundation we uncover serves also as the top of a new layer of description. It is the nature of any logical process that this be so.
We seem to be caught in an infinite series of explanations. Like the fabled paradox of Xeno, we continually make progress toward our goal but never seem to reach it. We make a step toward it in each iteration of theory, but each step reveals new territory to be uncovered. Some infinite series do converge, however . We know that if Xeno starts at position 0, with position 1 as his goal, and in each time interval covers half of the remaining distance, then he will get ever closer to his goal. If he had infinite time, he would reach his goal.
Xeno's paradox is usually phrased in the following way: given the fact that he covers half the remaining distance in each time interval, how long will it take for him to reach his goal? If we attempt to solve this problem iteratively, or arithmetically, that is, by separating it into parts and considering each time interval separately, computing the amount of time required for a given step, and summing the individual time intervals, we encounter an infinite series. This is somewhat analogous to our approach to physical description of the universe. Each layer of description is an iteration in an infinite series. We quickly discern that we are stepping along in an infinite series. If we had infinite time, we could solve the problem. Unfortunately, we are impatient and cannot wait that long.
With Xeno's paradox, we take a step back, out of the iterative. Another way to phrase the paradox is as follows. If Xeno starts at X=0, covers ½ mile in the first hour, 1/4 mile in the second hour, 1/8 mile in the third hour, and so on, and if Xeno could live forever and had the patience to continue the experiment for that long, then how far would he travel? In other words, what is the limit of the infinite series "Sum 1/n for n = 1 to infinity". An iterative approach toward solving the problem won't work, it would take far too long. Instead, we take a step back, reason about it for a second, and decide that Xeno will eventually travel 1 mile. With a level of reasoning at a higher level than the arithmetic, one can prove this result.
It takes a quantum leap, from arithmetic reasoning in the iterative vein, to a higher level in order to resolve the problem of Xeno's paradox. Following our analogy from Xeno's paradox to the problem of an infinite series of layers of description of the universe, is there a way to "take a step back", to apply a higher level of reasoning to the problem? Some might answer that the infinite series does not converge, that there is no ultimate explanation, that there is just a never ending sequence of layers.
But if one accepts this, one must also accept the premise that the universe is ultimately unexplainable and incomprehensible. We are stuck forever in the arithmetic, iterative mode. All the clues which the universe leaves about its nature; the order and regularity it exhibits, are blind alleys. They are meaningless. God does indeed seem to be malicious.
It is not more palatable to imagine some as yet undiscovered reasoning process, a quantum leap above the logical processes we employ in our theories, which could be used to resolve the problem? The question really becomes that of asking whether or not God allows the universe to be understood. All evidence we see leads us to believe that the universe is understandable. There are definite regularities and physical laws. If the universe were not understandable, why should these regularities exist? Why should the universe not be a totally random, magical place where anything can happen? If we accept that God is not malicious, that the universe is explainable, and if we accept that conventional reasoning processes cannot bring about that explanation, then we must conclude that there is some "meta-logic" which can produce the explanation. This meta-logic is as yet undiscovered. Perhaps there is an infinite series of logic levels, each coming closer to an ultimate explanation. In such a case, there must be a m-logic squared to resolve that infinite series.
Whatever the nature of the thought processes necessary to understand the universe, at the end stands God. I have stated before that God is the end of all infinite series. Once we acquire the thought processes necessary to understand the universe, we will be well on our way to understanding God. It won't be a clear understanding, since these thought processes alone tell us nothing of God's goals. We will know how God accomplishes his goals, but not why. Perhaps reasoning alone is not sufficient to understand why, but we will always try.