Libertarian free will and quantum indeterminism

The basic question in the long-standing debate about free will (FW) is not whether FW can be demonstrated to exist nor even whether it exists, but instead how to define it scientifically. If FW is not dismissed as an illusion nor identified with a variety of unpredictability, then logical paradoxes arise that make FW elusive to define. We resolve these paradoxes through a model of FW, in which FW is a new causal primitive empowered to override physical causality under guidance. We develop a simple mathematical realization of this model, that when applied to quantum theory, suggests that the exercise of FW corresponds to a nonlinear POVM causing deviations from the Born rule. In principle, these deviations would stand in conflict with known conservation laws and invariance principles, implying that the brain, the presumed seat of FW, may be an arena of exotic, non-standard physics. However, in practice it will be difficult to distinguish these deviations from quantum and neural noise, and statistical fluctuations. We indicate possible neurobiological and neurological tests, implications and applications of our proposed model.