Physicalism may be understood, roughly, as the claim that minds are not distinct from matter and hence cannot exist apart from it. There are many varieties of physicalism. They may be graded, from most “extreme” to least, as follows.

Eliminative Materialism:

On this view, there simply are no mental events, and no “inner theater.” Subjective experience is an illusion; all that is happening “in our heads” are neurochemical events in our brains.

Reductive Materialism:

This view allows that there are mental events, but holds that each mental event type is identical with a physical event type in the brain.

Supervenience Theories:

Supervenience is a relation that holds between a physical and a mental state just in case it is necessary that when that physical state obtains, so does the mental state. A supervenience theorist could hold, for example, that each instance (token) of a certain mental state type is identical to an instance of some physical state type, without holding that the two state types can be identified. For example, those who maintain that mental characteristics are functional properties often subscribe to such a view. There are those (such as Hilary Putnam) who define functional states in terms of their logical role in the execution of a computation (i.e., the formal states a computer is in when it executes a program) or those (such as David Lewis) who define them in terms of the causal role of the state.

Property Dualism:

Property dualists deny that mental properties are in any sense identical to physical properties. They may hold, however, that there are only material substances, some of which have mental properties. It is not clear in what principled way one ought to distinguish mental from physical properties. A property dualist may further hold that the instantiation of mental properties by a material thing is strongly dependent on which physical properties it has: that the relation between the instances is either one of nomological (lawlike) necessity or one of metaphysical necessity.

All but the last two positions surveyed are physicalist positions, and entail atheism. Some versions of the last two are at least arguably physicalist, and also entail atheism. Since God has mental properties, and is neither a material substance nor dependent on any material substance, his existence is incompatible with any view that makes the instantiation of mental properties strongly dependent on the states of a physical substance. So even if mental properties or substances are not physical or explainable in terms of the physical, theism will still be ruled out so long as such a dependence relation exists between the mental and the physical. That leaves open the question of how the relation might be understood (given that it is not a matter of reduction); but one might have evidence that such a relation exists, even in the absence of an understanding of its nature.