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Theologians have argued that God is simple, atleast in His form. Part of the reasoning behind this is that He takes no form given that He is taken to be immaterial.
At the same time, God is All Powerful, All knowing, and has other kinds of attributes that seem, to me atleast, undeniably complex.
Something about an eternal, all powerful entity seems very complex. Intelligence seems inherently more complex than blind processes. But is this intuition misguided?
Beginning with the latter position, Alston takes Aquinas to be one of its chief representatives. According to Aquinas, God is not dependent for his existence on anything, including his attributes. God is thought of as absolutely simple, not having any real parts distinct from God’s essence. God’s simplicity encompasses every attribute of God including his knowledge. To put it crudely, there is no difference between God, his knowledge, and the objects of God’s knowledge. So the object of God’s knowledge turns out to be God’s own essence. God’s essence contains within it the likeness of everything and God knows everything by knowing his own essence.
Alston admits that this way of knowing is very mysterious and we will never be able to adequately understand how it is that God knows everything. But he thinks we can liken God’s knowledge to our initial perceptual vision of a scene, where we have yet to extract from the scene separate facts. We have an awareness of things but the awareness is without a propositional structuring. In this initial perception, there is a unity present in which we have yet to separate subject from object, knower from things known. For humans, we do not have understanding until we begin to separate our knowledge from the things known and separate the scene into a distinct set of facts. Yet we lose and long for the underlying unity of the initial awareness. God, it may be thought, retains the unity and can have understanding without piecemeal, discursive thought present in human reasoning.
That is a rough description of what non-propositional knowledge is like, perhaps not fully illuminating, but not incoherent. If one accepts divine simplicity, one has a pretty strong argument against knowledge as propositional beliefs
Simplicity, in Solomonoff's theory of inductive inference, is based on minimum description length, i.e. the length in bits of the computer program that can produce the specified output. How long would be the computer program that could simulate God and everything God does? I don't think it would be very short. Certainly it's not "perfectly" short, because we can enumerate all the 0-byte or 1-byte computer programs in any particular language, and none of them simulate God.
Intelligence might not actually be that complex. AIXI is a relatively short computer program that also would be a full general intelligence if it only had enough computing power (which it will never get, as it takes exponential time). But the concept of God includes more than just intelligence, it also includes certain behaviors such as love, which don't seem amenable to a simple encoding as a computer program.
But perhaps some abstract version of love could be somewhat simple. Maybe a concept like, "favoring outcomes containing intelligent agents achieving their goals," could be written into the reward function of an AIXI-like computer program.
However, the probability of the God hypothesis H, given all our observations O, is written like P(H|O) = P(O|H) P(H)/P(O). The simplicity of God - the shortness of the shortest computer program simulating a being with the properties of God - affects only the P(H) term. The P(O|H) term is "how likely that we would see the exact set of observations we do see, given that the universe was created by this exact computer program." And because we have no idea what specifically such a computer program would do, because it would act as an inhuman superintelligence, P(O|H) would be very low. And that means P(H|O) wouldn't be very high either.
You need to compare it to a physics-based explanation, which would also be a fairly short program encoding simple laws of physics. But it would match only the exact physical laws we do see around us, which would give it a huge advantage in the P(O|H) term compared to God.
