... Choice requires the possibility of taking a different option, which of course is not permitted by the terms of your definition of determinism.
The "possibility of taking a different option" does not require that we actually take that option. It is something that we can do, not something that we must do.
If a possibility were something that we must do, then we would order every item on the menu whenever we went to the restaurant!
The menu is a list of the things that we can order, not a list of things that we will order.
You are insisting that actions fixed by antecedents are a matter of choice when clearly, given how choice is defined, it is not a matter of choosing. It is entailment.
You are insisting that choosing is not fixed by antecedents, while I point to the people reading the menu and choosing what they will order. The choosing is just as entailed as the walking in, the sitting at a table, the opening of the menu, the deciding what we will order and telling our choice to the waiter.
The walking, sitting, opening,
deciding, and telling are all equally entailed by causal determinism.
If the definition is merely figurative, you can imagine it to be anything you like, add a dollop of randomness, a pint of probability, a dash of free will....gosh, make up the rules as you go along....well, why not, it's just figurative!
You've missed the point. A figurative claim is empirically false. We can compare the claim to what we observe is actually happening and immediately detect that it is not literally (actually, objectively, in reality) true.
For example, the claim that choosing is not happening in the restaurant is false. We're looking at it, as it is actually happening, and we cannot deny what we see with our own eyes.
And the claim that entailment means there is only one possible action is false. We are looking at the restaurant menu listing the many possible items we can order for dinner. The fact that only one of them will be ordered does not change the fact that any one of them can be be ordered.
How did incompatibilists get from describing things that are happening to describing things that are obviously not happening? By figurative thinking.
But we who care about the truth of things are the ones who challenge false claims.
It is probably impossible to speak without some figurative language, as many of our descriptive words are drawn from analogies. For example, I'm attempting to "rein in" figurative language to conform more to actual usage and actual meanings (as if figurative statements were a horse out of control).
''If the moon, in the act of completing its eternal way around the earth, were gifted with self-consciousness, it would feel thoroughly convinced that it was traveling its way of its own accord on the strength of a resolution taken once and for all. So would a Being, endowed with higher insight and more perfect intelligence, watching man and his doings, smile about man's illusion that he was acting according to his own free will.'' - Albert Einstein
There you have Einstein arguing figuratively by a very tenuous analogy. But the main problem is that Einstein is using "freedom from causal necessity" as his definition of free will. He is trapped in the paradox created by that definition, which leads people to say some pretty silly things. For example, Einstein also said this:
"In a sense, we can hold no one responsible. I am a determinist. As such, I do not believe in free will. ... Practically, I am, nevertheless, compelled to act as if freedom of the will existed. If I wish to live in a civilized community, I must act as if man is a responsible being."
Page 114 of "The Saturday Evening Post" article "What Life Means to Einstein" "An Interview by George Sylvester Viereck" (Oct 26, 1929)
He tells us that despite his belief that free will and responsibility cannot exist he must still act as if they did exist. It is a fine example of an "incoherent" position.
What you tend to brush over is what you call 'choosing' is also subject to the same process of necessitation as every other event within the system, that every incremental step in the decision-making process is fixed by prior states, neural architecture, inputs, memory and must lead to an inevitable conclusion: the determined thought process culminating in the inevitable action.
Nothing is "brushed over" or ignored. Every brain event, every thought and feeling, that happens within the choosing process is also causally necessary from any prior point in time.
What you are brushing over is that among these inevitable brain events you will find every possibility on the menu that the brain considered as it went about deciding what we would order for dinner. Each possibility was an inevitable mental event. And there were many possibilities that showed up for consideration in that inevitable chain of events!
That is not choosing. That is natural necessity at work, a process caused by 'actual objects and forces.'
Obviously natural necessity includes choosing as a real causal mechanism, just like it includes walking, talking, and chewing gum. So, it is false to claim that it is not choosing when it actually is choosing that is happening.
Actual objects, events and forces over which our will has no agency, being not the master but the product.
The will is an event. Like every other event, it is both an effect of prior causes and a cause of subsequent effects.
It's 5pm, time to go home, and I'm hungry. This causes me to consider how I might get my dinner tonight. Will I go out to a restaurant or will I go home and fix something myself? I have two things that I can choose to do. I decide that I will go out to a restaurant. My will to go the the restaurant has just been caused by prior events.
That will to have dinner at the restaurant now causes subsequent events. It causes me to get in my car, drive to the restaurant, walk in the door, sit at a table, open the menu, choose what I will order, tell the waiter what I will have. This dinner order then causes the waiter to take my order to the chef, who prepares my meal. The meal being ready causes the waiter to bring it to my table along with the bill I must pay on my way out.
The will is an event. Like every other event, it is both an effect of prior causes and a cause of subsequent effects.
As to who is the "master" of these events, the world would correctly have us believe that it is the person who placed the order, because that is the person to whom the waiter hands the bill for the dinner.
Hence, free will is incompatible with determinism.
The incompatibilist makes this claim based upon a false definition of "free will", a lack of understanding what a "will" actually is, and a flaky notion of what deterministic causal necessity is actually about.
Free will is not a choice free of causal necessity. It is simply a choice that is free of coercion and undue influence.
A person's will is not some free floating spirit, it is a person's intention to actually do something specific.
Deterministic causal necessity is not some puppet master that robs us of our freedom and control, it is nothing more than the assertion that our behavior is mostly reliably caused by us, according to our own goals and reasons, and by our own choices. We, like all other events, were reliably caused by prior events and will reliably cause subsequent events by our own choosing.
''How could I have a choice about anything that is an inevitable consequence of something I have no choice about? And yet ...the compatibilist must deny the No Choice Principle.” - Van Inwagen
Sorry, but I have to go with the great philosopher Bilby on this one: "the No Choice Principle is not so much a principle, as it is overly simplistic horseshit." - Bilby