Omniscience and the Incompressible Core
An Information-Theoretic Dilemma for Classical Theism
Some truths are incompressible. The bits of Chaitin's Ω are the clearest case —
necessary but algorithmically random, Turing-equivalent to the halting problem.
This paper presses the fact as a dilemma: if divine knowledge of Ω is intrinsically
constituted, God's state must compute the uncomputable, making the divine intellect
maximally complex rather than simple. The escape — locating discriminating information
outside God — is available to divine simplicity and direct-awareness accounts alike,
but it externalises knowledge of contingent reality into the creatures, sharpening
the aloneness argument and surviving the standard reply to modal collapse.
The conclusion is not that God does not exist, but that the non-representationalism
classical theism relies on is the load-bearing wall — and this argument measures the load.