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What is the relationship between free will and consciousness?


Even assuming elementary folk definitions of free will as the causal agency over our actions and consciousness as phenomenal awareness of environment or internal states, these two questions certainly overlap, but are distinct. A theory of consciousness seeks to explain how phenomenal experiences such as sensory experiences or thoughts arise from physical or biological components. It is essentially a theory about the instantaneous (or nearly-instantaneous) relationship between matter and experience. A theory of free will seeks to describe the relationship between physical or biological components and action regardless of whether the organism is conscious of the true causes of the action. It is essentially a theory about the dynamical (i.e. temporal) relationship between matter and action.

In some regards, free will is a simpler problem because both "matter" and "action" are operationalizable terms that could be tested empirically. Arguably, however, this makes free will progress even more challenging because of the large numbers of (psychology and increasingly neuroscience) studies that must be reconciled by a complete theory. As I argue elsewhere (here), I believe part of the reason free will science has not changed substantially is due to some dogmas that continue to dominate free will debates (including philosophical ones) that free will must only be studied in conscious agents that can make subjective reports. Accommodating these older (and arguably outdated) ideas is challenging and places limits on advances in free will investigations.

Won't a complete theory of consciousness explain free will?

While an established (i.e. empirically supported) theory of consciousness would certainly provide a good basis for thinking about free will, it does not directly address the question of action causality: i.e. what are the precursors leading to an action because many actions are not caused by conscious oversight / processes. More importantly, a theory of consciousness does not even explain how consciousnesses arises from non-conscious states. For example, a theory of consciousness would not explain where our stream of thoughts come from - only how they are represented and constructed once they are available.

What about a purely mathematical theory of free will like consciousnesses theory X, Y or Z?


The beauty of mathematical reasoning is that logical or analytical reasons can apply to all possible physical and biological universes.  The limits on mathematical reasoning are that it's not always clear if a proposed mathematical tool or model applies to the universe we live in.  Arguably, several of the mathematical based theories of consciousness might suffer from such limitations and at best we do not have the data required to eliminate them. At worst, they are theories about mathematical structures not related to the type of consciousness we wish to describe or maybe not even establishable in our empirical world. (Much has been written on unfalsifiability elsewhere).

In relation to free will, it is certainly the case that free will notions (e.g. the relationship between brain activity and action) is describable in the language of mathematics (e.g. dynamical systems).  However, it is also likely that the process involved (especially for more complex organisms) will not be captured with short equations or simple explanations.

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