Yes, that's right.
This next series of comments center around the "can" versus "will" problem:
No moment in time has special properties over the one before or the one after.
(Actually, the key properties of "a moment in time" is where everything is and what everything is doing, at that moment. In the next moment, the interaction of things in the previous moment will causally determine where they will be and what they will be doing in this new moment. But that's another topic).
What you can't do one moment but can the next is not a matter of the ability of your will or its freedom, just information interacting within a deterministic web of events.
Let's put that a little differently. Within the context of deterministic certainty, what you
won't do one moment but
will the next is not a matter of "ability", it is a matter of "necessity".
There are no exemptions, no special clauses, no play on words that elevates Will over any other action.
Correct. What events will happen is always a matter of necessity. Every event is the reliable result of prior events.
One of the reliable causal
mechanisms that
necessitates what we will do is the choosing operation. Choosing employs the notions of "ability", "can", "might", "possibility", "alternative", "option", and other concepts that we have evolved specifically to deal with matters of uncertainty, such as our uncertainty about what we should do next. So, we consider things that we actually "can" do, and from them we select the thing that we actually "will" do.
The concept of what we "can" do is distinct from the concept of what we "will" do. There are multiple things that we actually "can" do, but only one thing that we actually "will" do.
An "ability" is something that you "can" do. To say you are able to do something never implies that you actually "will" do it. It simply means that you "could" do it if you chose to.
So, your brain was indeed "able" to make the decision, even though it did not make that decision this time around.
The fact that you "can" do something never implies that you "will" do it. The fact that you "did not" do it, never implies that you were "not able" to do it.
It literally means that in that instance in time that you were physically unable to.
Causal necessity cannot "mean" anything regarding "ability". The context of causal necessity is certainty. If we know that you will choose A and not B, then we simply say "you will choose A". We do not say "you are only able to choose A", because "able" only has meaning in a context of uncertainty, such as the context of choosing.
The context of "ability" is uncertainty. If we do not know what you will choose, then we say, "you are able to choose A" and "you are able to choose B".
And, at the end of choosing, we will still say "You were able to choose A and you were able to choose B, but you decided to choose A, even though you
could have chosen B".
The brain in that instance in time does not have the necessary information to make that decision in that moment in time. It may have a moment later if the necessary information is introduced and acts upon the brain, enabling it to make a decision that literally it could not a moment ago.
This second issue popped up and I failed to deal with it correctly. The issue regarded a new possibility, something that did not occur to us when we made our original choice. But, due to new information, we thought of it later. Was this new "option C" something we were "able" to choose or not? Well, if we did not think of this option C, then surely we could not have chosen it.
But could we have chosen it if we
did think of it? Yes, we certainly could have. On the other hand, option A might have been better than Option C as well as better than Option B. So, the fact that under certain circumstances we
could have chosen Option C, remains true even though it was always the case that we
would choose Option A.
Some compatibilists want it both ways, that you could have done otherwise, and that all is necessary is absence of coercion;
''
According to this view, humans (but not other animals) can freely decide what to do regardless of the past or present state of the universe. The human will is seen as the only force that can set in motion a new causal chain, with itself being uncaused. This type of free will is radical and godlike; it creates something out of nothing; it does not have to answer to prior causes. Alas, this conception of free will is certainly false, impossible, and logically incoherent. No one (correct me if I’m wrong) has demonstrated that or how this type of will can triumph over the old soldiers of necessity and chance. Radically free will does not exist because it cannot exist.
Those who believe that responsibility and punishment (and praise) can be apportioned to acting humans only if the existence of a radically free will is assumed must hang on to this idea lest their moral judgments become groundless. Not being able to pass moral judgment seems abhorrent if not terrifying to them. Hence, the doctrine of the radically free will is moralistic and religious at its core. That’s why Nietzsche and the Hyperboreans objected to it.''
Some aspiring compatibilists maintain that only humans are judged morally because only they could have acted differently. Those who try this argument must realize that they are not compatibilists at all; they are libertarians. The acceptance of determinism is a defining element of compatibilism. It forbids us to say that evil-doers could have done good if only they wanted to. Well yes, if they wanted to, but they were determined to not want to.''
Dr. Krueger's (the author of the article cited) argument suggests that a compatibilist must believe in "radical free will". But that's nonsense. Free will is nothing more than a person deciding for themselves what they will do, while free of coercion and other forms of undue influence. This is the operational meaning of free will, the one used when assessing a person's moral or legal responsibility for their actions. It requires nothing supernatural. It makes no claim to being uncaused. It simply works.
So, PhD or not, I cannot consider Krueger competent to provide an accurate or fair presentation of compatibilism. But, he does raise the modern issue of how the notion of free will supposedly affects our notion of justice. So, let's address that now.
Ironically, praise and reward, as well as blame and punishment, are
deterministic tools of behavior modification. No one is ever punished for having free will. They are only punished because they have harmed someone else. It is the harm that justifies our intervention. It is the harm that justifies the penalty.
But what kind of penalty is justified? What is the offender's "just desserts", that is, what does the offender justly deserve to be done? This is not a question of free will, but rather a question of justice. So, what is a justice system all about?
We have agreed to respect and protect a set of specific rights for each other. And we have have created laws that prohibit specific behavior that violates those rights. So, our justice system is about protecting everyone's rights. What then should a just penalty include?
A just penalty should seek to (a) repair the harm to the victim if possible, (b) correct the offender's future behavior if corrigible, (c) secure the offender to protect others from harm until the offender is corrected, and (d) do no more harm to the offender and his rights than is reasonably required to accomplish (a), (b), and (c).
Justice comes with a natural limit upon the penalties that can be imposed. Not only does society and the victim have rights, but so does the criminal offender. Any harm to the offender that falls beyond what is needed to repair the victim, correct the behavior, and protect society, is itself an unnecessary and unjustified harm to the offender, a violation of his rights.
So, don't attack free will and responsibility to insure fair penalties, attack instead the misguided notions that would substitute vengeance or retribution for justice. If we seek vengeance and retribution, we are unlikely to find justice.
nondeterministic programming before. It is a concept from computer science that is relevant to this discussion (as opposed to Jahryn's earlier reference to "perceptron" 
), because the label "nondeterministic" is used in roughly the same way by programmers. That is, it is a program with a set of predetermined "if-then" branches, but the decision of which branch to take cannot be predetermined. So the program needs to choose which branch to take at the time the program is running, not before. It can only do that by going down each branch with a set of predetermined goals and priorities that may or may not cause a branch to fail, and those decisions lead to the success or failure of different branches every time that the program runs. 
I'm going to play Devil's Advocate for a moment. I don't disagree with your conclusion, but I challenge your methodology to reach that conclusion. I'm also playing Devil's Advocate, because I suspect that my view with respect to a deterministic existence will be sufficiently covered by my 'quantitative' argument.