Even though
I can’t even know 0.000001% of 1% of what it’s like to be God, I do get
intrigued sometimes by peculiarities understood through my limited, finite
human brain. For example, God is omniscient, omnipotent and a perfect Being –
so what does that mean in terms of some of the supposed limitations of
mathematics, logic and information? For example, we know that there cannot be a
set of all truths (especially in mathematics or logic), because Tarski proved
that truth cannot be defined within the same language in which the statements
are expressed. Suppose you try to form a set of all true sentences in a formal
system (like arithmetic). Then you would need a truth predicate that determines
whether a sentence is true – and such a truth predicate cannot be defined
within the same system - it leads to contradictions, like the liar paradox.
Ok, so, I actually don’t think that is a wholly unsolvable problem in this context, as I explained in this blog post. It says more about our own human limitations. But I do not know what a set of all truths could mean for God, because if each set of truths entails further propositions about those truths, then a set of truths is a problematic concept, even if presumably this must be contained in God’s mind somehow. This recursive, self-expanding structure creates an essential tension in the idea of omniscience when it's imagined in my limited human logic, but perhaps that’s because semantic hierarchies are also a phenomenon attached to being human. I don’t know what it means for God to know a set of all truths that entail no further propositions or any kind of semantic hierarchy. This process isn't set-like - it seems more like a dynamically unfolding, internally structured totality – at which point, we humans cannot compute it.
Maybe this means that the idea of a set of all truths is a human limitation not a Divine reality. Sets are static mathematical objects, but God must be a unified act of understanding where He intuits all relations and truths simultaneously. I suppose it’s a bit like trying to write a complete dictionary, but for every definition, you also have to include; 1) the fact that it’s a definition, 2) the implications of its use, 3) the relationships it has with every other definition, and 4) the meanings of those implications… it would loop back and extend outward endlessly. Maybe that’s what such a dictionary would be like for God, but obviously even more complex than mere words.
And, next, what about Gödel’s Incompleteness Theorem, which shows that for any sufficiently powerful, consistent formal system (like Peano Arithmetic), there are true statements about natural numbers that cannot be proven within the system. So even we try to gather all provable truths, we miss some that are true but unprovable. Therefore, even the idea of a set of all provable truths doesn’t capture all truths. Or consider Russell’s Paradox - the set of all sets that do not contain themselves, which leads to contradiction. A universal set (the set of all sets) is not allowed in standard set theory because it also leads to paradoxes. Moreover, the set of all true sentences in arithmetic is not recursively enumerable, because there’s no algorithm that can list all and only the true statements, even in principle. This again means the "set of all truths" isn't just seemingly impossible to construct, it’s not even properly definable.
With God’s omniscient mind, does He know all truths, or only all knowable truths? I assume there is nothing God doesn’t know, although His truths have to remain within the internal consistency of their own logic – so He can’t create a rock so heavy He can’t lift, because that’s just a human nonsense, just as it would be if I said, “My dog is half past three steps into next week”. For us, the set of all truths is not well-defined or not formally capturable - but again, that is presumably a human problem connected to being human (like cause and effect), not a God problem connected to being God.
Consequently, we’re left with what we kind of know already – that God's knowledge must transcend formal systems, and He must know truths that no human language or formal system can express, which means the human mind reaches the level of analysis here where it goes blank. The way I picture it is like light before it breaks into colours. In a sense that we might be able to sparsely capture for our own illustration, what we call "truths" are to God as colours are to unbroken light: distinctions that arise only when unity is filtered through the prism of human limitation, but still absolutely glorious for our having done so.
