Okay. Basic idea: free will is the ability to do other than expected, where the expect-or is Laplace’s demon. Some human actions meet this condition, because the human brain is an undecidable computational system.

I had a couple of issues.

First, intuitively free will involves the possibility of any of multiple courses of action (looking in the future direction, to use the language is the article). The objection to this in the article is basically, when you’re making the choice, you’re only doing one thing. So, it doesn’t make sense to say there are multiple possibilities open to you. To the contrary, we can say that at time t1, it is possible that at time t2 I am doing A, or that I am doing B, whereas at time t2 it is only possible that I am doing 1.

But I don’t think that matters much, since the project is still interesting.

Second, key to establishing that the human brain is an undefinable computational system is the claim that the brain has infinite state spaces. This is supported by the fact that we can conceive of the natural numbers, which are infinite.

I’m not convinced that this means the human brain has infinite state spaces. We never conceive of each natural number itself. What is true is that for any of we can conceive of any of an infinite number of sets of numbers, but each of those will be of finite size. It is also true that we can think such terms “as infinite”, and various associated ideas, “1-to-1 mapping onto the natural numbers” for instance, but everything we’re ever actually thinking is finite.

Basically, it’s possible to represent some facts about infinite sets with finite information, which seems to be what we actually do.

As an additional comment, the article also contained a discussion of human decision-making being self-referential. It’s a bit long, but you may want to check out this talk by Jenann Ismael, in which she makes the self-referential aspect of decision-making key to an account of free will.