There is no possibility of having taken the alternative shot, not because the action is impossible per se, but because your mental state in that moment in time did not permit the action to happen. X then Y.
What happens in the restaurant also holds true in the pool room. Instead of reading a "menu", I will be "reading the table". Given the current position of the balls on the table, I see several shots that are physically possible. Impossible shots are excluded from consideration, because we don't want to waste time or energy considering the impossible. So, before we spend any time considering our options, it must be the case that we believe these options to be possible to choose and possible to carry out.
I see that the 5 ball in the corner pocket as not only possible, but very easy. Unfortunately, it leaves the cue ball in a position that gives my opponent an equally easy shot. So, I consider the 3 ball in the side pocket. This shot is harder, but it is not impossible. And, even if I miss, the cue ball will be in a bad position for my opponent, leaving her without any easy shots.
I could have chosen the 5 ball in the corner pocket. But I chose the 3 ball in the side pocket. Both were real possibilities.
The series of mental events were X then Y,
all the way through. And each mental event was
"fixed" by the prior events. And this included reading the table, to find the several shots that I could take, then considering the consequences of each shot, and deciding that the 3 ball in the side pocket would be the shot I
would take, even though I
could take the 5 ball in the corner pocket.
All of these events, that took place solely within my imagination, constitute the
inner necessity that made my choice inevitable.
Your own definition of determinism tells you that actions are fixed, that no alternate actions may happen.
No alternate actions
will happen. I will perceive, by simply reading the table, that the 5 ball in the corner is a real possibility. And I will also see that the 3 ball in the side pocket is a real possibility too. Both
can be chosen, and both are physically
possible to carry out. Each is a
realizable alternative. Once I have established two or more real possibilities, I will
consider the likely consequences of each choice, and I decide to attempt the 3 ball in the side pocket.
If there were only one shot that was physically possible, then I would have no choice but to take that shot. But there were two possibilities, not just one. There were two shots that I might choose, even though there was only one shot that I would choose.
All of that is X then Y, with no deviation or alternative to that specific series of events. Within those "fixed" events we have two possibilities that were seriously considered, two pool shots that I
could take. One of them, the 5 ball in the corner pocket, became the thing that I
would not choose, even though I
could have. The other, the 3 ball in the side pocket, became the thing that I inevitably
would choose.
It's just the English language.
If your brain state had been different, you could have taken the shot....but of course, given determinism, your brain was not different, it cannot be different, hence what you imagine you 'could have done' had things been different is merely a construct of imagination.
The imagination is the "room where it happens". It is where choosing happens and it is where all possibilities reside and are explored. My opponent will not allow me to take practice shots on the pool table during the game. I have to imagine the likely outcome of my shots and then select the shot most likely to produce the best outcome.
It is the key component of that
inner necessity that you keep referencing, while you continue to deny its causal role in the chain of events.
“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
I love that quote. It pithily explains why causal determinism is never experienced as a meaningful or relevant constraint. You are never being forced to do anything that you don't want to do. Thus, it is neither coercion nor an undue influence. It presents no challenge to free will. It is just you being you, doing what you wanted to do. It is basically "what you would have done anyway".
Or, as I like to say, determinism doesn't actually change anything.