  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 artificial intelligence (AI) are briefly considered.
