Supposing that every single thing that exists in our mind is due to the brain, and supposing that each and every decision we have is determined by our neurons, can there be free will? How? If everything has a physical cause, can there be free will? If that implies the existence of some sort of soul, how do we manage that?
The first thing that comes in my mind when I saw this question is the thought of Spinoza.
Spinoza thought that everything follows a rule of causality including our behaviour and our desires. With our actual knowledge, you can apply this to our neurons.
Free will is an illusion for Spinoza. The human brain have the possibility to evaluate different scenarii and that give you the sensation of will. But, taking in account your past and all the causes that bring you to this choice, you only have one thing you can do.
So that is the position of Spinoza who democratized determinism.
To go further, I found that there is a field of study dedicated to this question : https://en.wikipedia.org/wiki/Neuroscience_of_free_will It seems to lead to the conclusion that our brain send informations before we thinking about it. That could mean that everything we think about is determined.
When you have defined free will out of existence, people will still make decisions
I have never understood the insistence that if no decisions are arbitrary (read: having no explanation besides "free will"), then that is proof that people have no free will.
If I eat because I was hungry, and wanted to stop being hungry, and my body is arranged to be hungry so that I will eat and not starve, you are free to argue that nature compels me. If I plant food because I know I'll be hungry in the future, you can argue that it's still just nature's compulsion, carried to a greater level of complexity. If I build a hydroponic skyscraper in the middle of a city to grow fresh produce, and you can trace every neuron firing over the course of my life that led me to address hunger in that way, you can go on to argue that it's still nature's compulsion. So? No free will, then?
We coined the term "free will" in the first place to describe the things that people do. After piling on to that term all the ways we THOUGHT human choice worked, do we throw out the term if we discover we weren't exactly right?
Maybe. However, people will still be making choices (like whether or not to believe that we even have free will), regardless of what we refer to this process of making choices as.
Free will arguably may reduce to physical phenomena. So may the redness of the flower we are looking at. So may the idea we have that democracy is the least bad system of government. So may our scientific ideas of nature. So may our idea of the physical world.
If what I do is determined by my brain and my brain is a part of me, then what I do is determined by me. If so, conventionally, we can determine ourselves to call "free will" the ability we have to determine our own actions.
The argument the free will doesn't exist assumes a metaphysical definition of free will. Fortunately, we can without any fear of retribution to ignore the issue of metaphysical free will and the whole argument that comes with it.
It is unfortunate that human beings should feel the frivolous need to spend time and money on doing real science to prove that metaphysical free will doesn't exist. Why not prove God doesn't exist while you're at it?
I believe the most effective method for me to stay alive and feel well is to use my best judgement and pay attention to how I feel and to what I want to do. The thesis that humans have no metaphysical free will plays no part whatsoever in this process and I fail to see how it ever could.
This question has a red herring in it. It assumes neuro reductionism, and causally closed physicalism. Neuro reductionism is considered a failed project in philosophy of mind: https://plato.stanford.edu/entries/scientific-reduction/ But the problem remains whether one is a reductionist or not!
Here is the actual central issue:
If everything has a [physical] cause, can there be free will?
This is the key question. If one assumes closed causation, then the model of will that we humans have, in which willing is causative, is incompatible with a closed causation network. Willing would then be illusory, and not free.
The other part of the problem is that we all experience causative willing -- this is an immediate empirical observation, and it is nearly nonsense to question it.
The free will conflict is then between direct empiricism, and our basic theory of the world, in which everything is caused by SOMETHING -- and this conflict occurs for dualists, idealists, and materialists.
The most widely accepted solution in philosophy is to redefine willing, making it purely experiential rather than causative. An experience of willing IS compatible with a closed causal network, so one can then believe in determinism and this redefined "free will". This tactic is called Compatibilism. Daniel Dennett has written a highly praised book on compatibilist free will: https://www.amazon.com/Elbow-Room-Varieties-Worth-Wanting/dp/0262540428 In these physicalist compatibilisms, our belief in the causative power of our thinking, is a delusion.
Where souls and dualism come in -- is that if one works through the process of evolutionary tuning of consciousness, then the compatibilism of Dennett is not possible. If willing is not causative, then it could not be tuned by evolutionary processes to correlate with what we then do. But consciousness and will IS evolutionarily tuned, hence it must be INDEPENDENTLY causative:
Now if that is so, then mental powers must help animals and men in the struggle for life, for physical survival. It follows from this that mental powers must be able to exert in their turn an important influence on the physical actions of animals and men. Animals and men could not, therefore, be automata in Huxley's sense. If subjective experiences, conscious states, exist— and Huxley admitted their existence—we should, according to Darwinism, look out for their use, for their adaptive function. As they are useful for living, they must have consequences in the physical world.
Dualism of some type which can support causal independence of mind is necessary to explain why we have causitive will. Popper proposed a very strong emergence process from neurology. Soul hypotheses are an alternative. These are necessary, but not sufficient, to support the common conception of FREE will.
This is because a higher level of determinist compatibilism that included souls or emergent consciousness in the "think you are free but this is actually just a delusion" could still be constructed to encompass dualist causal willing. As noted earlier in this discussion, CAUSATION is what drives determinism, and causation is what is in conflict with conceptions of free will.
We aren't aware of many thoughts at any one time, but assuming the thoughts we are aware of are completely determined by the brain, before we give up on the reality of free will and the soul we need to find out what is causing the brain to determine those specific thoughts.
To make the example more specific suppose we are aware of a desire to eat pepperoni pizza. This is a thought. By assumption it is caused by the brain, that is, the brain makes us aware that we have this thought. But why do we want pepperoni pizza? Why not sweet potatoes with a stir fry of carrots and celery in olive oil?
Steven Gundry claims that our "holobiome", the symbiotic microbes in our gut, send chemical signals to our brains telling us what they want us to eat because that is what they want to eat. This helps explain why the brain gives us these specific thoughts about food. Our symbiotic microbes are making the choices for us.
However, the kind of microbes we have influence our longevity and health. Gundry suggests we can encourage the microbes that lead to health and discourage the ones causing illness. We can change which microbes are in symbiotic relationship with us. We make that choice by changing our diets. The new microbes give us different thoughts on what they want to eat.
Who makes that choice to change our diets? We do, if we want. This leads us full circle. The brain determines our awareness (thoughts) of what we think we want to eat. The holobiome determines the brain to tell it specifically what it wants us to want to eat. We can change our diets to modify the holobiome suggesting different food thoughts to our awareness.
That who, the ones who choose to change our diets or not, leads us right back to our freewill or the soul in spite of any belief that the brain determines our awareness of the thoughts we have at any one time.
Here is the OP's question:
If each of our thoughts is entirely determined by the brain, can there be free will or a soul?
Even if the brain determines the thoughts we are aware of at any particular moment what those thoughts actually are may still be determined by our free will or souls through some chain of causation we are only beginning to understand.
Gundry, S. The longevity paradox: how to die young at a ripe old age. 2019. Harper.