The problem here is that compatibilism is the argument that free will is compatible with determinism....and determinism is by definition a matter of inevitability, as you define it: no deviation, etc.
And we've established that there are two definitions of free will.
One free will only requires that our choice is free from coercion and undue influence, which is compatible with deterministic inevitability. Within the context of deterministic inevitability, we have scenarios where it is inevitable that we will be coerced or unduly influenced to make a choice that we would not choose for ourselves. And, also within the context of deterministic inevitability, we have scenarios where it is inevitable that we will be free of coercion and undue influence, and can decide for ourselves what we will do. This second scenario is called "a choice of our own free will" or a "freely chosen will".
The other free will is a choice that is free from cause and effect. And we both agree that there is no such thing as an event that is free from causation.
The first free will is meaningful and relevant, because it is actually used when assessing a person's responsibility for their actions.
The second free will is an irrational notion derived from the delusion that cause and effect is something that we can or need to be free of.
So Baumeister's conclusion is irrelevant to the issue at hand, where determinism does not have genuine multiple possibilities.
And here we disagree as to what constitutes a "genuine" possibility. A genuine possibility is a mental token that is part of the rational causal mechanism of logical thought. Logical thought performs many useful functions. One of these functions is making decisions.
We perform choosing whenever we are presented with two or more options, like deciding what to wear to work, or what to fix for breakfast, or what number to put in the Sudoku square or what word will give us the most points on the Scrabble board, or whether to "hold them or fold them" in poker, or which car or house to buy, or which college to attend, etc., ad infinitum.
The point is that deciding things is a heavily used mental function in human life. And it would be a shame to break it.
How could it be broken? Easy, by pretending that the single actuality is the only genuine possibility. You see, decision making requires multiple genuine possibilities. If an option is not a genuine possibility, then it cannot enter the selection pool, no matter what we are selecting (clothes, meals, Sudoku numbers, Scrabble combinations, poker moves, cars, houses, colleges, etc., ad infinitum).
It is only after we have made our choice that we can know which possibility will be the actual choice. Until then, every possibility must logically be considered genuine.
A "genuine" or "real" or "actual" possibility exists solely within the imagination. An actual/genuine/real possibility does not exist in the actual/genuine/real physical world. It exists solely within the imagination, where it allows our mind to plan, evaluate, choose, invent, create, etc. All of these are valuable human abilities. And they all employ the notion of possibilities.
We cannot drive a car across the possibility of a bridge. We can only drive across an actual bridge. But we cannot build an actual bridge without first imagining one or more possible bridges.
That is the true nature of genuine possibilities.
Your definition of determinism is pretty much the same as mine, as with other definitions that have been given.
There are some significant differences between our two views of deterministic causal necessity/inevitability. My determinism has restaurant menus with multiple genuine possibilities. My determinism has real people making real choices from those menus.
My determinism knows the difference between things that "can" happen and things that "will" happen.
My determinism creates no paradoxes.
The only difference being the addition of the compatibilist definition of free will.
The compatibilist definition of free will, a choice free of coercion and undue influence, is the only rational definition of free will. There is no such thing as "freedom from cause and effect", because every freedom we have, to do anything at all, requires us to cause some effect. We cannot be free of that which freedom itself requires.
Which is not sufficient to prove the proposition for reasons that have already been described numerous times.
I think there is a very serious disagreement as to what "the proposition" is.
My proposition is simply that, for practical purposes, we need to distinguish between the cases where a person is coerced or unduly influenced, to do something that they would not ordinarily choose to do, versus the cases where a person is free of coercion and undue influence, and chooses for themselves what they will do.
In both cases, the events are fully deterministic and part of a chain of events reliably causing subsequent events, that goes back as far as anyone cares to imagine. So, determinism is satisfied in either case.
In the specific cases where the person chooses for themselves what they will do, while free of coercion and undue influence, free will is satisfied.
Thus, determinism and free will are both satisfied.
Further issues...
Normally, "inevitability" suggests that something will happen and we cannot do anything about it. But with deterministic inevitability, the mechanism that causes us to choose the Salad instead of the Steak happens to be located within us, specifically our own brain. And it will be our own choosing that causes the Salad to be inevitable.
That contradicts your own definition and its terms by placing the brain outside of the system and giving it the ability to act independently of its evolution or development, which can have no deviations.
Nonsense. The brain needs no independence from its evolution or its development. But it does operate independently of the other objects within our universe. The planet Neptune, for example, plays no role in choosing what I will order for dinner. The choosing is all happening within my own brain, regardless of what the other objects in the universe are doing.
If the brain can make something else happen, that is a deviation, therefore we do not have determinism, instead we have autonomy and mastery over the system, and free will is not compatible with determinism, yet is the master or controller over it.
More nonsense. The universe, despite what astrologers may think, exercises no control over the operation of anyone's brain. And there is no need for me to control the universe in order to control what I will order for dinner.
The brain operates deterministically and makes happen what it deliberately chooses to make happen. The brain, as it is now, has a history of prior experiences, including its own prior choices, that are the prior causes of its current state. But it is still the brain, as it is now, that is actually doing the choosing.
Schopenhauer pointed out that ‘Man can do what he wants, but he cannot will what he wills’ - Der Mensch kann zwar tun, was er will, aber er kann nicht wollen, was er will. - Schopenhauer.
Which is essentially: “It might be true that you would have done otherwise if you had wanted, though it is determined that you did not, in fact, want otherwise.” - Robert Kane
Ah! Thanks for recalling those two quotes for me.
My point, which they both support, is that there is no difference, at all, between what we do by causal necessity/inevitability and what we ourselves want to do and what we ourselves decide that we will do.
As you can see, determinism doesn't actually change anything.