Skeptics ask whether Jesus could be both omniscient and ignorant. How is it that God could retain his property of being all-knowing while also experiencing fear, doubt, and not knowing when he would return. The answer, surprisingly, comes from the Kalam Cosmological Argument.
In the Kalam argument, the proponent argues that the past cannot be infinite because an infinite number of things cannot exist in the real world (and to say that distances are composed of an infinite number of points is begging the question). When David Hilbert evaluated the role of infinite quantities such as
. These quantities are used in abstract thought, so that we can make generalized statements that apply to all numbers. The problem is that as soon as you start performing operations with these numbers, you run into paradoxes like Hilbert's hotel.
Worse, operations like
-
or
/
are undefined. You cannot perform inverse operations on actual infinites, but if actual infinites existed in the real world, there would be nothing stopping you from performing these operations.
The question then arises: how is God omniscient? If God knows an infinite number of propositions, wouldn't that contradict these mathematical laws? It seems they would.
Therefore, we need to think of omniscience not as knowledge of distinct propositions, but as some kind of non-propositional super-thought, from which he can derive propositions.
Another question relates to the biblical teaching about the soul and how it relates to neuroscience. The Bible repeatedly teaches that the body and the immaterial soul are two distinct things. This view, called dualism-interactionism, has come under fire from philosophers. If our soul is different, then why do we lose consciousness when we are hit over the head? Why do things that damage the brain also affect memory, and why is it when you are knocked unconscious for surgery, that you have no recollection of the passage of time? There are also numerous instances of people able to obtain information and have conscious experiences at times when their are brain dead.
All of these problems are answered by a single solution. When the soul is left on its own, the soul has its own mental faculties, such as reason and memory. That is why people can know about conversations across the street even when they are brain dead. When the soul is connected to a brain, it relies on the brain's faculties, even if they are damaged. The soul will not rely on its own faculties until it is completely severed from the brain.
Think about how this applies to the incarnation. Jesus had the super-thought from which he was able to derive propositions, until he became incarnate, at which point he relied on the faculties of his human brain. Since the human brain does not have the ability to derive propositions from the divine super-thought, that is how he could be both omniscient and ignorant.