Churchland argued that mental states are brain states. He subscribes to a view known as eliminative materialism, which suggests that mental states will eventually be explained solely by physical processes in the brain.

Of or pertaining to materialism or materialists; of the nature of materialism.

It's not a law.

Materialism and atheism don't necessarily have anything to do with each other; theistic materialism exists, and the materialism part is still the same (it's incidental that there is or isn't a god involved).

See "What is Materialism?" to better understand that part.

The book Materialism was written by Jorie Graham.

Denial of materialism