  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.
