I don't know the article, but if you know the argument for Godel's theorem, it's simple enough to reconstruct the argument that surely appears there. If you have an omniscient entity you can talk to and query in finite time, you can write the following program:
- Print's it's code into a variable R.
- Asks the omniscient entity whether the code "R" will print "hello" or "not hello"
- does the opposite.
If you make the omniscient entity a computer program, this proves Turing's theorem. If you make the omniscient entity an axiomatic system, this proves Godel's theorem. If you make the omniscient entity a divine being, this proves that either you can't get answers from the divine in finite time, or else you can't formulate step 2, "code R queries the divine entity" in any reasonable way.
The anti-omniscience sentiment can be captured in the religion of Maimonism, whose fundamental tenet is the following:
- Fundamental tenet of Maimonism: God is omniscient, but unfortunately for Maimonism, God doesn't agree with it's fundamental tenet.
There's a problem for God now, in that God can't have a consistent opinion about the fundamental tenet of Maimonism. This is the same argument, except making a gloss without the detailed construction.
The argument against omniscience is weak, because it only proves no omniscience in finite time. God is generally understood to be an asymptotic entity, only partly revealed, in most religious faiths. The omniscience is a property of the limit of infinite time, not of any finite time state. No religion that I know claims that its revealed truths are the complete word of God, rather, the revelation is gradual, as new trials reveal new acts of faith and so on.
This isn't physics, and there is a near duplicate of this on philosophy, but philosophy is disfunctional, and has little chance of improving.