Before Alan Turing made his crucial contributions to the theory of computation, he studied the question of whether quantum mechanics could throw light on the nature of free will. This article investigates the roles of quantum mechanics and computation in free will. Although quantum mechanics implies that events are intrinsically unpredictable, the `pure stochasticity’ of quantum mechanics adds only randomness to decision making processes, not freedom. By contrast, the theory of computation implies that even when our decisions arise from a completely deterministic decision-making process, the outcomes of that process can be intrinsically unpredictable, even to — especially to — ourselves. I argue that this intrinsic computational unpredictability of the decision making process is what give rise to our impression that we possess free will. Finally, I propose a `Turing test’ for free will: a decision maker who passes this test will tend to believe that he, she, or it possesses free will, whether the world is deterministic or not.
According to Lloyd “The inability of the decider to predict her decision beforehand holds whether the decision-making process is deterministic or not”.
Recursive reasoning is reasoning that can be simulated using a Turing machine, quantum or classical. If that reasoning is peformed by a system that obeys the known laws of physics, which can be simulated by a Turing machine, then it is encompassed by recursive
reasoning. We have just shown that when a decider that uses recursive reasoning to arrive at a decision then
(a) No general technique exists to determine whether or not the decider will come to a
decision at all (the halting problem).
(b) If the decider is time-limited, then any general technique for determining the decider’s
decision must sometimes take longer than the decider herself.
(c) A computationally universal decider can not answer all questions about her future
(d) A time-limited computationally universal decider takes longer to simulate her decision
making process than it takes her to perform that process directly.
So, the challenging dillema is "I make a decision? therefore I have free will?". Where does modern neuroscience stand on this question? I look forward talking to some friends who are testing this experimentally. Though, I myself tend toward the assumption that lies somewhere in between, that the "pure stochasticity" contributes to the unpredictibility in the computational domain.
See on arxiv.org