A Simple Case for Countably Infinite God
C: set of all knowledge possible to man. C is countably infinite.
G: set of all knowledge possible. Assume God knows this. G could be countably infinite or uncountably infinite.
Case 1: G is countably infinite. Now the intersection of C and G is C. From God’s perspective there is a small subset out of G, which man understands. This inadvertently puts some attribute of God known to man, which makes God less of a God. Note that, man cannot yet find a mapping between G to C, as G-C is still beyond man’s reach. God is safe. Now by Kantian Synthetic a priori capability of man, can ever man know anything in G-C? Assuming complexity of knowledge of man has some upper limits in correlation with the neural hardware of man, and C contains every knowledge within this limits, G-C is still unreachable to man.
Case2: G is uncountably infinite. Still the intersection of C and G is C. Still from God’s perspective, there is a small subset out of G which man understands. This inadvertently puts some attribute of God known to man, which makes God less of a God. But the bigger problem is how will God deal with an uncountably infinite set. He can’t; by the definition of uncountably infinite set. If he can’t, then he is not God. It means the presence of God or an uncountably infinite set of theorems ever possible.
It is probable the presence of God with a countably infinite G. As there could be some ever fast growing map between God’s capability and man’s capability. If there is no such map, God and man are in different realms with no means of connecting between. If this is the case, it is as good as the absence of God.
The bottom line is simple. God and man must be in the same realm to even say that God is all powerful. At the best, God’s capability is some exponentially more than that of man’s.
By exponentially, what I mean is not the mathematical exponential function, but a function that grows faster than any other functions man ever deviced.
