I’d like to dispute your usage of “predetermined” there: like “fated”, it implies an establishment in advance, rather than by events. A game of Agricola is predetermined to last 14 turns, even in a nondeterministic universe, because no change to gameplay at any point during the game will cause it to terminate before or after the 14th turn. The rules say 14, and that’s fixed in advance. (Factors outside the game may cause mistakes to be made or the game not to finish, but those are both different from the game lasting 13 or 15 turns.) On the opposite side, an arbitrary game of chess is not predetermined to last (as that one did) 24 turns, even in a deterministic universe, because a (counterfactual) change to gameplay could easily cause it to last fewer or more.
If one may determine without knowing Alice’s actions what dish she will be served (e.g. if the eggplant is spoiled), then she may be doomed to get that dish, but in that case the (deterministic or nondeterministic) causal chain leading to her dish does not pass through her decision. And that makes the difference.
I’m not sure that I sufficiently understand you. “Fated” implies that no matter what one do, one will end up as fate dictates, right? In other words: in all counterfactual universes one’s fate is same. Predetermination I speak of is different. It is a property of deterministic universe: all events are determined by initial conditions only.
When Alice decides what she will order she can construct in her mind bunch of different universes, and predetermination doesn’t mean that in all those constructed universes she will get fettucini, predetermination means that only one constructed universe will be factual. As I proved in previous post Alice cannot know in advance which constructed universe is factual. Alice cannot know that she’s in universe A where she’s predetermined to eat fettucini, or that she’s in universe B where she’s to eat eggplant. And her decision process is integral part of each of these universes.
Without her decision universe A cannot be universe A.
I’d like to dispute your usage of “predetermined” there: like “fated”, it implies an establishment in advance, rather than by events. A game of Agricola is predetermined to last 14 turns, even in a nondeterministic universe, because no change to gameplay at any point during the game will cause it to terminate before or after the 14th turn. The rules say 14, and that’s fixed in advance. (Factors outside the game may cause mistakes to be made or the game not to finish, but those are both different from the game lasting 13 or 15 turns.) On the opposite side, an arbitrary game of chess is not predetermined to last (as that one did) 24 turns, even in a deterministic universe, because a (counterfactual) change to gameplay could easily cause it to last fewer or more.
If one may determine without knowing Alice’s actions what dish she will be served (e.g. if the eggplant is spoiled), then she may be doomed to get that dish, but in that case the (deterministic or nondeterministic) causal chain leading to her dish does not pass through her decision. And that makes the difference.
I’m not sure that I sufficiently understand you. “Fated” implies that no matter what one do, one will end up as fate dictates, right? In other words: in all counterfactual universes one’s fate is same. Predetermination I speak of is different. It is a property of deterministic universe: all events are determined by initial conditions only.
When Alice decides what she will order she can construct in her mind bunch of different universes, and predetermination doesn’t mean that in all those constructed universes she will get fettucini, predetermination means that only one constructed universe will be factual. As I proved in previous post Alice cannot know in advance which constructed universe is factual. Alice cannot know that she’s in universe A where she’s predetermined to eat fettucini, or that she’s in universe B where she’s to eat eggplant. And her decision process is integral part of each of these universes.
Without her decision universe A cannot be universe A.
So her decision is crucial part of causal chain.
Did I answer your question?
Edit: spellcheck.
I don’t like the connotations, but sure—that’s a mathematically consistent definition.