Gödel's theorem applied to God (essay)
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There is one proposition which no deity possessed of godlike powers would ever be able to know the truth of, and that is whether it itself is simply a construct within an even greater reality beyond its perception. This may sound odd and impossible, but let us think this through. First, imagine a point in space. Now imagine that a straight line begins at that point and extends infinitely onward in one direction from that point. Flat space, please, don't want that line curving around and becoming itself. Now imagine a second point right next to the first, with a parallel infinite line extending infinitely outward in one direction. So now you've got infinite nonintersecting lines. If either line could be aware of its own infinitude, it might imagine itself to be the only thing in existence capable of being infinite. Now, let us take the second infinite line and move its starting point backwards an inch relative to the other line. Now you have two infinite lines, but one is an inch longer than the other.
Now let's take that longer line and stretch it along a second dimension, making it a flat plane with a few inches of height (and still infinite length). We keep it parallel to our first line, so they still never intersect; the first line still has every reason to believe itself to be uniquely infinite, even though it is right next to a thing that is not only an inch longer, but has an entire additional dimension of substance. And now we will take the second object (which is now a plane) and curve it into a cylinder which completely surrounds the first line, but continues never touching it. And just for the sake of it, we'll take that end of the cylinder that goes past the first point and curve its edges toward one another, into a sort of hemispherical cap which closes off that end of the cylinder (still without touching the original infinite line). Indeed we could do all of these operations to the first line and make into an infinitely long tube with one end beginning with a hemisphere, and still have it completely contained within a slightly larger tube with which it never intersects.
Now you might at this point be thinking, 'yes but the gods envisioned by human faiths are not mathematical constructs, they are not tubes; so what's the point?' Well, you would be correct that man-described deities tend not to be mathematical constructs, but human ideas of the ultimate are necessarily constructs nonetheless, for they are invariably described in human languages, and with human words and concepts such as 'infinite' and 'absolute' (and really those are concepts which, if not outright mathematical, are subject to mathematical discussion). Lest we delve too close to describing perfectly spherical gods in a vacuum, let us get straight to the heart of the capacities philosophically ascribed to deity-models. Able to do anything; possessed of all knowledge. But wait, there's the catch. No matter how much knowledge a god possesses, it is impossible for it to know that it is not missing some knowledge of which it is unaware, such as the existence of a greater surrounding entity which contains it. It's like this....
Remember Neo, in The Matrix; once the nature of the Matrix was revealed to him, he found that while outside of it he was a normal human, but inside of it he had, essentially, superpowers. But how could Neo outside the Matrix know he was really outside the Matrix? After all, though things smelled and tasted and felt different, all of that could simply be another trick of the computer, sending signals which let Neo to think that he was experiencing those differences. Naturally, the lack of superpowers in the 'real' world (and existence of superpowers in the 'false' world) would be trivially easy to conjure up through the signals sent to Neo's brain (if he has a 'brain' at all, for Neo's entire existence could be as a subroutine within a larger program, one programmed to believe itself to be an independent organic entity). And no amount of contemplation would then allow him to peel back the falsity of the 'real' world outside the one he already knew to be false. But suppose instead of being programmed to believe himself to be a superpowered human, Neo was programmed to believe himself to be an omnipotent/omniscient deity? Anything which he wished to bring about would instantly present itself to him as having transpired; any knowledge he wished to have would instantly manifest itself in his mind. If he wished to set forth living planets orbiting burning stars to fill hundreds of trillions of galaxies, and know the every movement past and future of every atom in them, he could (if sustained within a powerful enough system) do so with a thought. But none of this would prove that it was Neo's inherent godliness causing such things to come about, for it could always be an even greater being, an imperceptibly nonintersecting surrounding cylinder of a being, providing all of these experiences.
Even if in some relative sense the Bible or the Qu'ran or the Baghavad Gita were true (such that there was a Creator entity which set forth all that we humans are able to perceive at least, and all the events recounted transpired as set forth there), even this Creator entity could never know that everything it was doing was not part of some infinitely greater Creator-entity's thought experiment. (Here is an inverse proof of this -- imagine a true all-powerful being not sustained within anything greater than itself; such a being could, by definition, create a slightly lesser being which believed itself to be the true 'only all-powerful being,' and which would by dint of the true all-powerful being's all-powerfulness, be absolutely unable to detect the greater being of which it was part).
And if no hypothetical Creator of our entire Universe could possibly actually know whether it was the ultimate being, then surely we spatially and temporally and intellectually limited humans can have no inkling as to what the truth is of such a thing. And here's the even greater rub; supposing that there was a god of this or that scriptural type, and that this god was unknowingly simply an entity sustained in existence within a greater being (and perhaps one of many so sustained), then the greater being within which it was sustained would itself have no way to be sure that it wasn't merely the thought experiment or subroutine or what have you of an even greater thing than itself, a cylinder within the cylinder, within perhaps inestimable layers like a neverending Russian doll. And that is why Godel's theorem makes it impossible for there to be an absolutely omniscient deity. (Which is by the way of no concern to Pandeism, which never proposes absolute omniscience anyway, but only ever proposes such relative omniscience as would be required to account for our finite Universe so far as we are able to perceive it.)