Uncomputability and free will

TL;DR

This paper explores free will as an uncomputable, fundamentally new causal primitive in physics, suggesting it is effectively indeterministic yet potentially deterministic in higher-order theories, with implications for AI and neuroscience.

Contribution

It introduces the concept of free will as an uncomputable dynamics, proposing a new causal primitive beyond determinism and indeterminism in physical theories.

Findings

Free will can be modeled as uncomputable dynamics in physics.

Artificial intelligence's free will aspect may be fundamentally unsimulable.

Free will is likely experimentally undemonstrable and subjectively experienced.

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 artificial intelligence (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.