Beware: This is a fragment. It was my first attempt to tackle the problem of free will; I wrote it roughly 1,5 years ago. It was only after that that I came to write the already published criticism to Sabine Hossenfelders blog and to some physical objections against free will in general. However, since I am currently writing a completely new (shortened and streamlined AND even german) piece about free will, I decided to publish this fragment as is, with all it’s flaws and fallacies…
Free will is often discussed as the conundrum of how our decisions could possibly be free on one hand while on the other hand we assume that everything in the physical world (including our brains) is determined by the laws of physics (i.e. not by „us“). Here, I shall give reasons as to why this way of posing the question of free will is largely misguided. I propose that the problem of free will should not be a debate about the special (and seemingly weird) kind of causation that might be at operation in volitional acts, but rather about the inner workings, the experience of and the interpretetation of the decision-making processes in our brains. In particular it seems that the ability to decide on the decideability of a decision is key to the „freedom“ in free will. And this in turn bears much resemblance to the halting problem in computational theory.
Fundamental aspects of these ideas have been put forward already in the 1960s by Donald Mackay and others but it was not until the 2013 paper of Seth Lloyd („A turing test for free will“) that free will has been explicitly connected to the halting problem. In this paper, Lloyd shows that regardless of the determinacy of the underlying world (i.e. regardless of the physics of our brain), a decider who is capable of self-reference can make decisions, which are fundamentally unpredictable to both, the decider and a possible outside observer of the decider.(fn) The fastest way to arrive at decisions, would therefore be to live through all the decision-making efforts it takes; generally, there is no shortcut (and no other author than the decider) to this process. Lloyd, however left out the reasoning as to why considerations about computability and predictability of computational outcomes would help to clarify the problem of free will. Here, I want to fill in some reasons, why the focus of the discussion about free will should be at least for the freedom-part on the computational routines used by the brain to exercise free will, rather than the causal nature of the brains physics.
Another gap in Lloyds argument pertains the type of unpredictability, he refers to. The algorithmic (i.e. logic) unpredictability of a deciders computations mainly precludes that another algorithm could be used to arrive faster at the final decision of the decider to predict her decissions. It does, however, not preclude the same algorithm on a faster computer from arriving earlier at the decision. You can simply think of the faster computer as the exact same brain in a slightly better condition (nutrition, temperature etc.). Such a brain could predict the outcome of its slightly less optimal doppelganger because it would (viewed as a deterministic turing machine) perform just the same operations — only a bit faster. Does the possibility of a faster doppelganger rule out free will? Are doppelgangers at all logically consistent with free will? I want to also give reasons, why the decisions of a decider would nonetheless be free in any sensible meaning of the word even if there was a doppelgangery decider.
Lastly, I want to refine the notion of free will that Seth Lloyd’s ideas point to. I hold that his ideas specify mostly the „freedom“-part, but fall short on the „will“-part. Therefore, I beg to differ from his (intentionally provocative) idea of any self-referential computer to be a bearer of free will. Since the notion of a will is tightly bound to some sort of self-awareness, I would pled to reserve the concept of free will to creatures/artifacts which can be both, free and the bearer of a will.