"Where determinism fails, science fails." (Determinism and Physics, 1936, vol.18).
In Part One, Chapter V, of his 1948 Human Knowledge: Its Scope and Limits, Russell argues for a thorough-going mechanical determinism of brain processes, but he does make a rare mention of quantum uncertainty that may be based on Arthur Stanley Eddington's ideas, which in any case was the basis for David Wiggins' suggestion for an amplified quantum uncertainty. In his 1978 book Brainstorms, Daniel Dennett quoted Wiggins and called this "Russell's Hunch." Although quantum mechanical, it proves to be little more than the clinamen of Epicurus or the delicately balanced state of mind that James Clerk Maxwell (or John Eccles) was looking for, so that an infinitesimally small nudge by the mind could tip the material body one way or the other. And although Russell knows the history of philosophy better than most professional philosophers, he appears blissfully unaware of the ancient and well-known criticism of chance as the direct cause of action, which eliminates moral responsibility (except, of courses, when the agent deliberately invokes indeterminism and is prpeared to take responsibility for any outcome, as argued by Robert Kane). Russell also put forth a strong argument for denying the existence of God (Russell's Teapot") and a very weak argument claiming that any philosophical problem that is solved will be withdrawn from philosophy and added to science. We disagree with this argument, which we call "Russell's Residue."
Russell's TeapotIn 1929, Frank Ramsey made this suggestion in his book Theories. The Foundation of Mathematics (p.235 in the 1960 edition),