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Is it possible for science to refute the "god hypothesis" beyond all reasonable doubt?
This question cannot be answered without specifying exactly what the "god hypothesis" is.
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What must such a hypothesis entail if it is to be able to be subjected to scientific enquiry (which after all is the very meaning of the term hypothesis)?
At a minimum, it must include some real world, observable consequences. In addition, if the postulated consequences are something that could occur even in the absence of god (the "good guys" beating the "bad guys" in a war, for example), there must be some way to distinguish a god-influenced outcome from a non-god-influenced outcome.
I am not of the belief that postulated miracles cannot be scientifically investigated, to a degree. To the extent that the means of creating a miracle are supernatural, the means cannot be scientifically investigated. But, to the extent that a particular observed phenomenon is attributed to a miraculous agent, I think that can be investigated. In the process of this investigation, one must be particularly careful of not simply falling for an argument from ignorance.
Those who would sacrifice an essential liberty for a temporary security will lose both, and deserve neither. -- Benjamin Franklin
We see monsters where science shows us windmills. -- Phat