Uncomputability and free will

Abstract: The basic problem posed by free will (FW) for physics appears to be not the \textit{physical} one of whether it is compatible with the laws of physics, but the \textit{logical} one of how to consistently define it, since it incorporates the contrary notions of freedom, which suggests indeterminism, as well as control, which bespeaks determinism. We argue that it must be a fundamentally new causal primitive, in addition to determinism and indeterminism. In particular, we identify FW in a physical theory with dynamics that is uncomputable, and hence effectively indeterministic within the theory. On the other hand, it would be deterministic in a higher order theory. An important consequence for AI is that the FW aspect of cognitive systems may be fundamentally unsimulable. An implication for neuroscience is that FW will in general be experimentally undemonstrable. Apparently, it can only be subjectively experienced.