"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 p.288, Daniel Dennett quoted Wiggins and called this "Russell's Hunch."
It may be that, without infringing the laws of physics, intelligence could make improbable things happen, as Maxwell's demon would have defeated the second law of thermodynamics by opening the trap door to fast-moving particles and closing it to slow-moving ones... It may be maintained that one characteristic of living matter is a condition of unstable equilibrium, and that this condition is most highly developed in the brains of human beings...Perhaps in the brain the unstable equilibrium is so delicate that the difference between two possible occurrences in one atom suffices to produce macroscopic differences in the movement of muscles...we may imagine that, in a brain, the choice between possible transitions is determined by a psychological cause called "volition."Although quantum mechanical, Russell's "hunch" 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, something like Robert Kane's "self-forming actions." It is definitely not our two-stage model of free will. 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 prepared 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of God (Russell's Teapot") and a very weak argument claiming that any philosophical problem that is solved will be withdrawn from philosophy and added to science.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."Human Knowledge: Its Scope and Limits, 1948, Part One, Chapter V, pp.40-41
Russell's TeapotIn 1929, Frank Ramsey made this suggestion in his book Theories. The Foundation of Mathematics (p.235 in the 1960 edition),