Why atheism entails the possibility of God

The following partial definitions of atheism and materialism are taken from the American Atheists web pages:

Atheism may be defined as the mental attitude which unreservedly accepts the supremacy of reason and aims at establishing a life-style and ethical outlook verifiable by experience and scientific method, independent of all arbitrary assumptions of authority and creeds.

Materialism declares that the cosmos is devoid of immanent conscious purpose…

I think the partial definition of materialism quoted is a denial of the very means by which the author has constructed the definition. That, I think, is the fundamental problem of atheist materialism – it fails to account for the inherent purposiveness and creativeness that its proponents quite deliberately employ in order to formulate and express the principles of their own “mental attitude”.
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