Responsibility [and free will]
It is often assumed that if there are definite underlying rules for our brains then it cannot be meaningful to say that we have any ultimate moral or legal responsibility for our actions. For traditional ideas lead to the notion that in this case all our actions must somehow be thought of as the direct result of whatever external causes (over which we have no control) are responsible for the underlying rules in our brains and the environment in which we find ourselves. But if the processes in our brains are computationally irreducible then as discussed in the main text their outcome can seem in many respects free of underlying rules, making it reasonable to view the processes themselves as what is really responsible for our actions. And since these processes are intrinsic to us, it makes sense to treat us as responsible for their effects.
Several different theories are used in practical legal systems. The theory popular from the behavioral sciences tends to assume that human actions can be understood from underlying rules for the brain, and that people should be dealt with according to the rules they have—which can perhaps be modified by some form of treatment. But computational irreducibility can make it essentially impossible to find what general behavior will arise from particular rules—making it difficult to apply this theory. The alternative pragmatic theory popular in rational philosophy and economics suggests that behavior in legal matters is determined through calculations based on laws and the deterrents they provide. But here there is the issue that computational irreducibility can make it impossible to foresee what consequences a given law will have. Western systems of law tend to be dominated by the moral theory that people should somehow get what they deserve for choices they made with free will—and my explanation now makes this consistent with the existence of definite underlying rules for the brain.
Young children, animals and the insane are typically held less responsible for their actions. And in a moral theory of law this can be understood in my approach as a consequence of the computations they do being less sophisticated—so that their outcome is less free of the environment and of their underlying rules. (In a pragmatic theory the explanation would presumably be that less sophisticated computations would not be up to the task of handling the elaborate system of incentives that laws had defined.)