Does science prove that God and human souls do not exist? Or does science simply presuppose that they do not exist?
Physicalism is the worldview which states that only physical things exist – no God, no angels, no souls, etc. And many physicalists claim that science proves their worldview to be correct. However, science cannot prove physicalism if it presupposes it. That is, one cannot prove something by using a method that presupposes what one is trying to prove. To do so is to simply argue in a circle.
Sam Harris, one of the New Atheists, acknowledges that at least one scientific discipline (i.e. neuroscience) presupposes physicalism.
A dualist who believes in the existence of immaterial souls might say that the entire field of neuroscience is beholden to the philosophy of physicalism (the view that mental events should be understood as physical events), and he would be right. The assumption that the mind is the product of the brain is integral to almost everything neuroscientists do.
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Reference
Sam Harris, The Moral Landscape: How Science Can Determine Human Values, 1st Free Press hardcover ed (New York: Free Press, 2010), 179–80.