The most difficult consistency problem for classical theism is the conjunction of divine omniscience and human free will. If God knows in advance every free choice a human being will make, how can that choice be genuinely free? Swinburne's response draws on the Ockhamist tradition: God's foreknowledge is not a causal condition of the human choice but a logical consequence of it. God knows what you will freely do because you will freely do it — the dependence runs from your choice to God's knowledge, not the reverse. This resolves the apparent conflict while preserving both attributes.
A related problem concerns divine eternity: if God is outside time (timelessly eternal), how can he know what is happening now? Swinburne departs from the Boethian tradition here and defends an atemporal eternity that nonetheless includes tensed knowledge — God knows what is past, present, and future from a standpoint outside temporal succession. Swinburne prefers an everlasting (sempiternal) God who exists through all time to a timeless one, on the grounds that this is more consistent with the personal agency the theist attributes to God.
Swinburne argues that God can be coherently conceived as an incorporeal personal being: a person without a body. This requires showing that mental properties (beliefs, desires, intentions) can be coherently attributed to a non-physical being, and that the personal agency implied by prayer, providence, and revelation does not require embodiment. His positive account draws on the philosophy of mind: persons are characterised by their mental properties, not their physical substrates, and there is no incoherence in positing a purely mental person whose mental properties are maximally perfect.
The Coherence of Theism is structured as a series of chapters, each examining one divine attribute. The consistency argument is cumulative: each chapter shows that the attribute in question is both internally coherent and compatible with the other attributes already defended.