Your reasoning treats the event as simple precognition, like learning the outcome of a baseball game before it happens. You have to remember: Louise sees a future event in which she is told about information she conveyed in her immediate present that could not have been learned from that immediate present. The future moment cannot occur without the precognition, unlike that earlier baseball game which will occur regardless of the precognition.matrixschmatrix wrote:v I would say that, given that she is able to defuse that plot element only by using highly specific future knowledge that she could have gotten at in no way other than precognition, it is clear at least that the existence of pregognition has therefore changed things. Therefore, the idea of a locked timeline- as her going forward with have a child might imply- cannot hold
Why is this crucial? Because your argument rests on assumptions about causality and ontology that do not hold. Your argument is based on the idea that the present causes the future (hence you can talk about whether or not people in the present can change the future). But it cannot work if the future causes the present. In Arrival, the future causes the present.
The real argument here is not one of fate vs free will, because this is not about individual will (not yet). This is about ontology, the nature of being: how is something existing, and what is the nature of that existence.
In Arrival, we have a closed system, a loop, with two key causal moments: 1. the phone call relaying secret information (a); 2. the meeting where a is discussed (b). Now, a causes b (a --> b) because there's no meeting without the first phone call; but b also causes a (b --> a) because there's no phone call without the information from the meeting. So they're mutually dependent, a if and only if b (a ≡ b). So if the information that causes the future could only have come from the future it's supposed to've caused, then the information is ontologically prior to itself (possible, despite what Aquinas says). And if information from the future is the only way for the present to cause the future, then the future is ontologically prior to itself. Same with the past: it must be prior to itself, too, since it must precede the future that causes it.
So you see the problem: in a loop, things exist before they happen temporally. Ontology and temporality are split. The future and the present depend on each other for their existence; without the one, there cannot be the other. Hence both must happen, because they are each other's cause. If one ceases to exist, the other has no cause, and therefore must fall into non-existence. Meaning, therefore, that the present both can and cannot change the future, and the future both can and cannot change the present. On top of that, certain objects (including ideas) are self-existing, ie. they bring themselves into existence. It is a paradox, and only solvable if you agree it's a dialetheism and that contradictions can be true.
The idea of whether free will exists within co-dependent systems is, I don't know, kind of beside the point. But it still falls into an ontological paradox in this instance: if you change the future, you must negate the present, meaning you did not change the future, so the present exists for you to change the future, so you negate the present, meaning you did not change the future... And on and on.