I want to start by clarifying some terminology. Any time travel story where the act of time travel changes the past is based on the assumption that what we perceive as time comes from a dynamic and changing present, and that the future does not exist. The idea that parallel universes are generated as a result is just one theory about the possible consequences of such changes.
Time travel stories in which the act of time travel does not change the past are based on the idea that the past, present and future all exist simultaneously and are all essentially the same. We perceive time passing because we can only see a changing, three dimensional cross section of this four dimensional universe, but our perception that the universe itself is changing is an illusion.
J.M.E. McTaggart referred to these as the A-Theory and B-Theory of time, respectively, and I will use these terms as I find referring to A-Theory as the multiverse theory rather limited, and the term Predestination Paradox to be a little misleading.
That said, I see four ways to interpret the first two Terminator movies.
1: It's all A-Theory. The problem is that the story of the first movie falls apart under this assumption. In addition to plot details like Kyle being John's father, and the John giving him a picture of Sarah that we see get taken later, there is also the very narrative structure of the film. At the beginning, we're shown a Sarah Connor that is disorganized, unassertive and completely unlike the person Kyle describes. Over the course of the film, we see her become that person, and just when we see her transformation completed, then we are given proof of the nature of the story in the form of seeing the picture actually get taken, thus leaving us with a sense of inevitability as the movie ends. Trying to convert this into an A-Theory story requires creating reams of unconvincing fan fiction to try to explain what happened in the previous timelines.
2: It's all B-Theory. The original ending of T2 definitively proves that Cameron intended for his heroes to have changed the future. This wouldn't be possible in a B-Theory universe. But even without it there are other elements, such as Dyson being killed before creating the chipset that would've become Skynet that can only be explained away with more unconvincing fan fiction.
3: Cameron wrote T1 as a B-Theory story, then changed his mind and wrote T2 as an A-Theory story. The problem with this idea is that if Cameron intended for T2 to be an A-Theory story, then why would he incorporate strong B-Theory elements like the fact that Skynet would never have existed in the first place without being reverse engineered from the first Terminator's chip? Cameron chose to emphasize this fact by having Dyson say that the chip gave them ideas that they would never have come up with on their own. He also introduced John Connor as being no longer in a position to be trained by Sarah for the war, because John thought his mom was crazy. This was only resolved by the time travellers, which is clearly a B-Theory conceit. It does not appear as though Cameron changed his basic concept from the first movie.
4: Cameron took the idea that the time travellers were always part of the past, but grafted it onto a world view in which the future is not fixed. The idea the the future already exists and is therefore fixed and unchangeable seems to be a prerequisite for the idea that time travellers from the future have always existed in the past. However, some people tend to approach time travel theory as nothing more than arbitrary rules, like the ripple effect in Back to the Future, without considering the underlying theories about the nature of time that generate these rules. B-Theory tells us that their is no objective "present"in which events are occurring, but even so, we still have to experience these events at some point. When we do, we make decisions about how to respond to these events. Cameron is assuming that instead of our choices being predetermined and forced on us, we are free to make our own choices. Sometimes our decisions might change the future. This is why the phrase, "No Fate but what we make," is given as an explanation for Sarah's decision to try and kill Dyson. Later Sarah says that the future, always so clear to her before, is now like a dark road at night. Before the future was clear because she was following the predestined course of events described by Reese, but now she doesn't know what the future will bring.
There are also indications in the first movie that Cameron saw the future as changeable. He had Reese say at one point that he didn't come from the future, but rather from one possible future. It's easy to dismiss this as a red herring, especially since Reese himself immediately says that he doesn't understand it, but consider the implications. In an A-Theory universe, the presence of the Terminator and Kyle Reese would have changed the future. This means that Reese would have been wrong in saying that his future was still possible. Furthermore, in an entirely deterministic universe there would only be one possible future. According to A-Theory it would be a different future, in B-Theory it would be the same one, but multiple futures could only be generated by a non-deterministic universe, not by time travel. This fits our conception of a pre-destination paradox with a fixed past, but an indeterminate future perfectly. Reese also passes on a message about how Sarah has to be brave and this would arguably be unnecessary if her future was fixed so that she couldn't possibly not be brave. Plus there is also a deleted scene in which Reese uses the phrase, "No Fate."
None of these are definitive proof, but they all indicate that Cameron may have already been thinking of the future as changeable even when he wrote the first movie. Our only problem is in trying to reconcile the idea that time travellers from the future have always existed in the past with the idea that other possible futures also exist.
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