(IFF) "rational thought" is logical (AND) logic is predetermined by initial conditions (THEN) "rational thought" is incompatible with choice
Can you prove that rational thought can result in only one outcome? I contend that rational thought provides the option of more than one possible outcome in some cases. I can't prove either proposition so where does that leave us? And please don't say that an outcome that didn't happen could not have existed because only one outcome does exist.
I like where you're going with this.
Think of a game of chess.
Do you always (logically) have a "best move"?
A chess Grandmaster actually has less choice than a novice.
The Grandmaster's nearly comprehensive knowledge of the game allows them to logically deduce the best possible move.
To a novice, they have tons of choices, they might even believe (imagine) they have choices that actually violate the rules of the game.
The novice is unable to logically deduce the best move and therefore they have many apparent choices.
The Grandmaster is able to logically deduce the best move and therefore they have very few choices.
In some cases, the Grandmaster may be presented with two (or more) moves that have, at least apparently, an equal chance of attaining their goal.
In such cases, the Grandmaster is unable to adequately distinguish the pros and cons of the choices at the moment, and the outcomes may actually be nearly identical (absolutely incidental and utterly meaningless). However, they might find themselves reflecting after the match, and realize that one of the moves they neglected could have had some distinguishable advantage over the move they chose.
The point is that in such a model, a "free-will" decision is only free if the decision is apparently incidental.
If you have logically processed all of the pertinent data, and the data itself is inconclusive, only then do you have "free-will".
In such a case, this perfectly incidental decision would not be based on logic, because your data is inadequate.
In such a case, this perfectly incidental decision would be the equivalent of a mental coin flip.
In such a case, "free-will" = ignorance. The more ignorance you have, the more "free-will" you have.