The function of a working brain is to acquire and process information in order to respond to the events of the world in manner that aids survival.
A functional brain processes information and produces results according to its own architecture and information exchange, not will.
I do not understand your tacking on the "not will" at the end. The whole point of an intelligent brain is to provide a living organism with options. Prior to intelligence, there were no options, because every behavior was instinctual, hardwired. With intelligence we gain the ability to respond creatively "to the events of the world in a manner that aids survival".
I say 'not will' because the brain does not function according to 'will' - intelligence is not willed, neural architecture is not willed, the environment that forms our physical makeup is not willed, yet it is these elements that determine who we are, how we think and act....in accordance with inner necessity, not freedom of will. Will changes nothing. Will is a part of action, action is determined by processing,
The output of a functional, deterministic brain, the actions taken, do not allow alternate actions.
That's only true of a non-intelligent organism. With intelligence, the brain continues to operate deterministically, but with an additional causal mechanism: rationality (you may recall that from Dr. Martha Farah's quote that you included earlier).
Rationality is not equivalent to free will, which is why Martha Farah said what she said. She was not supporting the notion of free will, just the opposite. It is neural architecture that enables intelligence, not free will. Artificial intelligence, for instance, is a matter processing power and function, not will.
We assume that the rational causal mechanism also operates deterministically (otherwise it would be ineffectual). So, when stepping into a new causal mechanism we are not stepping outside of determinism.
For example, addition is a deterministic rational operation: 2 plus 2 equals 4. There is no alternative within that operation.
However, choosing is also a deterministic rational operation: A or B? If A is better than B, then I will choose A, but if B is better than A, then I will choose B. With the choosing operation we always get at least two alternatives. Then we evaluate each alternative and choose the one that seems best to us. That's how it works.
Given the same identical us, facing the same issue, under the same circumstances, our choice will always be the same. That's what being a deterministic operation naturally implies. And that does not change with the rational causal mechanism. Just like 2 + 2 = 4, one choice will always be judged better than the other after evaluation.
Options are realized on the basis of criteria. Criteria is determined by needs and wants. The option taken is the one that best meets the criteria. The other options were not in the running. It may prove that option A was wrong, which changes the dynamic.
As I've pointed out a number of times, timing is the key; inputs are acquired (the senses, not will), information is transmitted, propagated and processed (by neural networks, not will), then represented in conscious form, thought, will, action (a sequence of milliseconds). Will emerges as a result of input, architecture, processing, will is not the master or director of the brain.....which, having said it a number of times, is clearly what I meant.
You continue to insist that freedom must include the absence from reliable cause and effect. This notion that determinist's carry around with them is called "freedom from causal necessity". It is an irrational notion, due to the fact that reliable causation is always required by every freedom that we have to do anything at all (including the freedom to decide for ourselves what we will do). FREEDOM REQUIRES RELIABLE CAUSE AND EFFECT.
What I have said is freedom requires regulative control, realizable, possible, alternate actions.
Determinism, by definition (forget about soft determinism) does not allow regulative control or realizable, possible, alternate actions.
Assuming responsibility requires control, and determinism does not allow regulative control or realizable, possible, alternate actions, ultimately, we are not responsible for what we do or think.
If you accept regulative control as a necessary part of free will, it seems impossible either way:
1. Free will requires that given an act A, the agent could have acted otherwise
2. Indeterminate actions happens randomly and without intent or control
3. Therefore indeterminism and free will are incompatible
4. Determinate actions are fixed and unchangeable
5. Therefore determinism is incompatible with free will