Richard Dawkins, Sam Harris, Daniel Dennett and Christopher Hitchens are often referred to as the ‘Four Horsemen Of Atheism’. They haven’t had too many public disagreements but perhaps the most prominent ongoing dispute, relates to free will. This is a topic that is not unrelated to religion, of course. Most of the world’s faithful are taught that the difference between eternal paradise and eternal agony, lies in how we each exercise our free will.
Sam Harris is a strong determinist and he argues that free will is an illusion. That is, since the contents of the human skull are no more immune to the laws of physics than any other matter in the universe, our behaviour is always exactly commensurate with deterministic causality. Dan Dennett agrees that science comprehensively rejects the mind-body dualism on which religious ideas of free will are based. However, as a compatibilist he also argues that free will can be reconciled with the deterministic physical laws.
As it happens, I’m convinced by the determinist argument and I find compatibilist positions to be rather slippery. The conclusion that our decisions are determined by the matter in our brains obeying the laws of physics, rather than by some ethereal mind or soul, is one that is of great import. Since the dualism on which so much of religion depends is false, explaining the implications of that would seem to be a good use of any philosopher’s time. Instead, it seems that compatibilist philosophers quite often prefer to spend their time inventing new definitions of free will, which can accommodate determinism.
I think that a better analogue for our subjective experience of volition, is found not in new definitions of free will, but rather in computational intractability. When discussing this topic, philosophers often like to return to a famous Austin thought experiment involving a golfer. If a great golfer misses a simple putt, should we consider that she could have holed it, based on some degree of freedom that she had? Alternatively, if every atom in the golfer is returned exactly as it was before the missed putt and the shot is replayed, must she miss it again, as the invariant laws of physics consistently produce the same results? Many debates around free will and determinism have considered this question (including the often heated exchanges between Harris and Dennett).
Considering the issue from the perspective of computational intractability, may allow for a different starting point. For example, if a rain cloud moved over the golf course, could we calculate which blade of grass will be first to be struck by a raindrop? Certainly, the rain cloud does not have free will, so there will be one blade of grass that will be first to get wet and that will be the result of deterministic laws of physics acting on the relevant atoms and particles. If we were able to observe which blade of grass was struck by a raindrop first, and then replace all of the atoms in the atmosphere exactly as they were before the rain started, what would happen if we then replayed the events?
Of course, since the laws of physics don’t change, the same arrangement of atoms will give rise to the same results. Quantum indeterminacy can’t deliver free will either. Even if relevant at the scale of the particles and molecules that exist in human brains and rain clouds, quantum indeterminacy would offer some randomness but no free will. However, the vast number of particles and interactions involved in rain clouds, and the even greater complexity of human brains, means that any calculation to predict either outcome would be intractable. Even if we could measure the position and momentum of every relevant atom in advance, there will be no more practical way to see where the raindrops fall, or where the putt comes to rest, than to allow the laws of physics to play out and just watch.
Trying to prove mathematically whether the brain state of the golfer will result in her sinking her putt or not, is tangentially related to Hilbert’s Entscheidungsproblem (decision problem). In our case, the decision problem asks if we can analyse the complete configuration of the golfer’s brain along with the laws of physics, and prove in advance whether her putt will be holed or not. Alonso Church and Alan Turing showed that there is no solution to the Entscheidungsproblem (a previous blog on this site discussed Turing’s 1936 paper on the topic, which introduced the Turing Machine).
For example, if we view a rain cloud as a Universal Turing Machine that is configured to calculate the interactions between all of the relevant particles, then we cannot prove in advance which blade of grass will get wet first. The only practical approach is to ‘run the program’ on the machine (the cloud) and observe which blade of grass is first struck by a raindrop.
Similarly, if we consider the golfer to be a Universal Turing Machine, then Turing’s 1936 paper on computable numbers shows that even if we could know her complete configuration in advance, we still could not prove what the outcome of the putt would be. Additionally, if the golfer actually wanted to perform the full calculation to work out what kind of putt her brain state would produce, that would take exponentially more time than just taking the putt. That is, the problem is computationally intractable not just in practice but in principle. The only way to discover the outcome is to ‘run the program’ on the machine (the golfer) and watch where the ball goes. In Programming the Universe, Seth Lloyd describes the implications of Turing’s Entscheidungsproblem proof as follows …
“… once we set a train of thought in motion, we do not know whether it will lead anywhere at all. Even if it does lead somewhere, we don’t know where that somewhere is until we get there.”
The reason why we can’t predict the actions of a human being with full confidence, is not because people have free will or an ethereal soul. It is because either under a classical deterministic universe or under a quantum probabilistic universe, the problem is computationally intractable. Free will is an illusion and our actions are fully determined by the laws of physics. The path of a golf ball rolling on an undulating green is also fully determined by the laws of physics and easily predictable. However, Turing distinguishes between some problems that are computable and others that are not. The path of a golf ball on an undulating green is an easily computable differential equation. The proof of a decision problem for the brain state of Austin’s golfer either sinking or missing a putt, is impossible in principle.
Austin’s golfer will miss the putt every time. Even if before each replay, a computer is given her complete configuration in advance, Turing shows that it will still always be impossible to prove the outcome beforehand. Each time we replace every atom in the golfer exactly as it was, we will still need to replay the putt by ‘running the program’ on the machine (Austin’s golfer) and watching her miss.
Religion says that god gave man free will, but Turing shows that it only seems like we have free will, because we’re computationally intractable and so we cannot know what we’re going to do next.