For the joy of ear and eye,
For the heart and mind’s delight,
For the mystic harmony
Linking sense to sound and sight,
Lord of all, to Thee we raise,
This our hymn of grateful praise.

"Consciousness cannot be accounted for in physical terms. For consciousness is absolutely fundamental. It cannot be accounted for in terms of anything else." Thus said no less than Erwin Schrödinger. I do not think such philosophical generalities entail theism, but I think they reject reductionist materialism. Perhaps I lack imagination, but I think purely physical descriptions of the brain, however tightly they manage correlate the neural to the mental, never will satisfactorily explain how or why there is anything mental for the neural to correlate to in the first place.

I am aware of two categories of potentially satisfying accounts of this correlation. The first is the dualist appeal to a mystical enforcement of a correlation between a noetic realm and a material realm that are otherwise causally separated. The second category holds that there exist, roughly speaking, laws of consciousness that complement the laws of physics.

In the former category, the particles/waves that make up a human brain have a physical form suitable for being bound to a mind, but the brain is mindless without supernatural intervention. In the latter category, each elementary particle of the physical universe, or perhaps I should say the wavefunction of the universe, is already endowed with mental or pre-mental properties that naturally assemble into a consciousness when, for example, a human brain develops.

In the former category, the birth of a new consciousness is supernatural; in the latter category, it is quite natural. In the former category, postmortem consciousness is unsurprising: if a soul can be chained to a body, then it presumably can be unchained. In the latter category, postmortem consciousness would require a postmortem physical body or some kind of substitute "body." In the former category, whether "higher" animals have minds is a mystery; in the latter category, they very probably do. Both categories are compatible with theism and both categories are compatible with atheism.