Gödel, Tarski, Turing and the conundrum of free will (1401.1800v1)

Abstract: The problem of defining and locating free will (FW) in physics is studied. On basis of logical paradoxes, we argue that FW has a meta-theoretic character, like the concept of truth in Tarski's undefinability theorem. Free will exists relative to a base theory if there is freedom to deviate from the deterministic or indeterministic dynamics in the theory, with the deviations caused by parameters (representing will) in the meta-theory. By contrast, determinism and indeterminism do not require meta-theoretic considerations in their formalization, making FW a fundamentally new causal primitive. FW exists relative to the meta-theory if there is freedom for deviation, due to higher-order causes. Absolute free will, which corresponds to our intuitive introspective notion of free will, exists if this meta-theoretic hierarchy is infinite. We argue that this hierarchy corresponds to higher levels of uncomputability. In other words, at any finitely high order in the hierarchy, there are uncomputable deviations from the law at that order. Applied to the human condition, the hierarchy corresponds to deeper levels of the subconscious or unconscious mind. Possible ramifications of our model for physics, neuroscience and AI are briefly considered.