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There are two different ways in which a non-theistic view of the world has ethical implications. One is that it is a feature of the ethics of rationality that one's outlook should be maximally evidence-based and truth-directed, thus ruling out supernaturalistic explanations or interpretations (as e.g. thinking that there must be tree spirits or Norse gods to take responsibilty for such phenomena as, respectively, the whispering sound of leaves and thunder among the clouds - but in particular ruling out god-of-the-gaps "explanations" and the legitimacy of acts of faith as justifications for belief).
The second is that people require moral and 'spiritual' resources - these jointly constituting the ethical aspect of life - and one reason for the continuation of religious belief is that the religions have successfully hijacked control of these matters. So a humanistic ethics must regain its voice on these dimensions of human life, not least by reminding people of, and promoting, the rich inheritance of thinking about such matters in the long secular tradition since classical antiquity.