Choice within a deterministic system is being claimed.
Of course. Choice within a deterministic system is as real as walking within a deterministic system, or brushing our teeth within a deterministic system, or any other event that we objectively observe to be happening. All of these events are actually happening in empirical reality.
What you describe is not choice, not as it is normally defined. The word choice is being asserted, an imposition.
We open the restaurant menu, consider the many things that we can order, and select the one thing that we will order. Selecting one thing from many is defined as "choosing". Moving forward using our legs and shifting our weight from one to the other is defined as "walking". Applying toothpaste to a toothbrush and rubbing it against the inside and outside surfaces of our teeth is defined as "brushing our teeth".
There's nothing complicated or mysterious about these simple empirical events. And, we may assume that each of them is reliably caused by prior events in the natural course of events. So, none of these events is contradicted by determinism.
Causal necessity is not a single mechanism. It is the collection of all of the causal mechanisms. We cannot pretend that choosing is not happening any more than we can pretend that walking or brushing our teeth isn't happening.
I don't pretend. I stay within the bounds of the given terms and references. It is the compatibilist who seeks to circumvent the terms and conditions by redefining the nature of freedom and choice...
Freedom is the ability to do something we want to do. Choosing is us deciding what we will do. When we choose for ourselves what we will do while free of coercion and undue influence, it is called "a freely chosen 'I will'" or simply "free will".
Like all events, the event in which we choose what we will do of our own free will is a deterministic event, fully consistent with a world of reliable causation in which all events are reliably caused by some prior events. There are prior causes of the choosing event (for example, opening the restaurant menu), the process itself proceeds deterministically (I consider the juicy Steak, recall that I had bacon and eggs for breakfast and a double cheeseburger for lunch, and select the Salad instead), and becomes the prior cause of the next event (telling the waiter, "I will have the Salad, please", which causes the waiter to tell the chef, which causes the chef to prepare the Salad, etc. ad infinitum).
And that is determinism. Each state of the universe and its events are the necessary result of its prior state and prior events. ("Events" change the state of things.) Determinism means that events will proceed naturally (as if "fixed as a matter of natural law") and reliably ("without deviation"). All of these events,
including my choices, were causally necessary from any prior point in time. And they all proceeded without deviation from the Big Bang to this moment.
So, choosing not only happens in empirical reality, it also happens by deterministic causal necessity. The restaurant will inevitably have a menu, we will inevitably consider the selections on the menu, and we will inevitably select what we will order, according to our own inevitable goals and our own inevitable reasons, inevitably of our own free will.
Waiter: "What will you have for dinner tonight?"
Diner: "I don't know. What are my possibilities?"
Waiter: "Due to determinism, there is only one possibility and thus only one thing that you can order."
Diner: "Oh! Then what is the one thing that I can order?"
Waiter: "I have no clue. But, since it is the same thing as what you will order, if you tell me first what you will order, then I can tell you what you can order".
Diner: "How can I tell you what I will order if I don't know first what I can order?"
You have never been able to solve this paradox which your own words have created.
There is no paradox to solve.
The paradox is that it is impossible to choose if there is only one thing that we "can" do. There must always be many things that we "can" do whenever choosing happens. It is the natural, deterministic unfolding of events (fig.), such as the event in which we unfold the menu (lit.), that inevitably brings us to a point where we must make a choice.
Whatever the waiter and Diner ruminate over has no bearing on the underlying processes that brought about the thoughts and actions.
The Waiter's thoughts and the Diner's thoughts are part of the underlying process that causally necessitate the behavior. For example, the Waiter, being a hard determinist who takes himself literally, supposes that "can" and "will" are the same word, and thus will not tell the Diner what he "can" order without first knowing what the Diner "will" order. The Waiter thinks these two words mean the same thing.
You could say, look I have free will and choice because in precisely one second, I shall choose to lift my right arm'' - which of course ignores the initial prompt, the driver and the underlying process that brought about your inevitable response.....where you as a conscious entity being generated by a brain had no idea until the related and inevitable thoughts popped into consciousness, Libet, Haynes, Hallett, Haggard, et al.
Nothing is being ignored. However, not every fact makes a relevant difference. We assume that the brain's activity includes both unconscious and conscious processes. We cannot see or experience the unconscious processes other than through their results, which is our conscious experience. I was conscious of the desire to order the Steak. I was conscious of considering what I had for breakfast and what I had for lunch. I was conscious of deciding that the Salad would be better for dinner.
Our normal (compatibilist) waiter does not know any of my conscious experiences. All the waiter knows is that I said, "I will have the Salad, please". So, the waiter brings me the Salad and the bill. I am responsible for the bill because I deliberately chose to order the Salad, "of my own free will".
In other words, compatibilists habitually ignore inner necessity and the fixed causal progression of deterministic events
Have you not been paying attention? Or, are you deliberately lying? Or, is there some other explanation for that statement?
Saying 'will be' in reference to a deterministic system is equivalent to 'must necessarily be' and 'cannot be otherwise' or 'fixed by antecedents.'
Saying "will be" is never the same as saying "can be".
Saying "will not be otherwise" is never the same as saying "cannot be otherwise".
Saying "would not do otherwise" is never the same as saying "could not do otherwise".
The words "can" and "will" have two distinct meanings. "Can you take this woman to be your wife" is very different than "Will you take this woman to be your wife". "Can" asks whether you have the "ability" to marry. For example, are you already married, are you old enough to marry, etc. "Will" asks whether it is going to happen or not, and if you answer "Yes" it actually happens right then and there.
Those who compile and publish dictionaries don't concern themselves with the debate over the nature of determinism and free will.
Unfortunately, the definition of "free will" now includes the paradoxical definition as well as the operational definition in general purpose dictionaries.
Yet there is an ongoing debate that has spanned decades. Which now includes neuroscience and the law, instead of merely referring to common perception and word use, taking into consideration the nature of cognition and action and moving away from the simplistic. notion of free will.
Which only demonstrates the extent of the damage that is possible as more and more people become trapped in the paradox. The notion of causal necessity as a causal agent that removes our ability to choose for ourselves what we will do, is a superstitious notion, spread pretty much as any other religion, through false but believable suggestion. It is concocted by metaphors and similes that lead the mind to false conclusions.
The purpose of Philosophy should be to help us to think more clearly, not trap us in silly paradoxes.