This question came up a few times: how can a materialist accept the concept of free will, or how can a materialist contend the existence of non-material thoughts generated by a physical brain.
One of the arguments was that the neuro-chemical activity of the brain (which is called the mind) is purely physical, and therefore its acitivity is reducible to either deterministic physical laws, or stochastic ones. If it is reduced to deterministic laws, then it is not free in any sense of the word, if it is reduced to stochastic ones, then it is some chaotic activity, which cannot be called a desicion making process.
These arguments look quite plausible, yet they are incorrect.
Let’s look at a computer hardware. Its physical functioning is purely electronic and deterministic. If some hardware problem comes up, then its functioning will be chaotic, unpredictable. The progams, that run on the computer are just electronic impulses. Nevertheless, what the program does, is something totally different.
It is not a physical world, it is a virtual world. It is not governed by physical laws, or even mathematical or logical ones, and its working cannot be reduced to these laws. A computer program may sometimes “refuse” to add even numbers, but may willingly add up odd ones. It may sometimes say that 1 + 1 = 3. It can create a multi-dimensional world. It can suspend gravity… within its own virtual world. It can do anything.
The program is an emergent attribute, its working is not subject to any limitation, except what the programmer decided. This may seem to expose another possible line of “attack”. After all if the program is simply carrying out its instructions, then its working can be explained or reduced to the programmer’s intent.
The answer: only in some very simple cases. There are evolving, learning programs, which remember previous questions and answers. It will not answer the same question twice with the same answer. It can modify its internal structure. Its working is not predictable by anyone, not even its original programmer.
The physical activity of the brain is just a bunch of electro-chemical impulses, also reducible to physical laws. But what the mind does is not. It is also a virtual world. Its working is not determined by physical or mathematical or logical constraints.
The analogy between the computer program and the mind is very strong. Both are virtual worlds, their activity cannot be reduced to physical laws. The “only” difference is that the brain is much more complicated than the computer.
Now mind you, I have no idea how free will emerges in the mind. No one does. This is not a constructive argument, which allows to replicate the nuts and bolts of free will in a computer. It is simply an existential argument, which shows that the physical operation of the brain / computer does not predict or limit the working of the mind / software.