TERMINATOR 2 time paradox here!

two ways to resolve paradox via two different world models.

1) Novikov's Self-Consistency principle.
Stated simply, the Novikov self-consistency principle asserts that if an event exists that would give rise to a paradox, or to any "change" to the past whatsoever, then the probability of that event is zero. In short, it says that it's impossible to create time paradoxes.

The Final Countdown is an excellent film holding to the "no-paradox" theory of timetravel. Basically, if you go back in time from 1980 to 1941, whatever you do in 1941 HAPPENED in 1941 and therefore has already happened in 1941 from the perspective of 1980.
Take the famous Grandfather Paradox. You go back in time to kill your grandfather. The very fact you exist is proof that you failed. perhaps the man you thought was your grandfather wasn't, or your grandmother was having a secret affair, perhaps you took the trip back and discovered something that changed your mind. whatever the reason, the FACT remains that you exist therefore you did NOT kill your grandfather.

In the Final countdown, two F-14 Tomcats from USS Nimitz shoot down two Japanese Zeros the day before the attack on Pearl. People complain that this would cause an alteration (via butterfly effect) in the future time because now those pilots won't participate in the attack and the alterations ripple out from there. Novikov's Self Consistency principle says not so fast there bub... Those planes were shot down on Dec 6th 1941. Nimitz was in 1941 even if from a day before in 1980 they had not yet gone back in time. So those aircraft never did take part in the raid on Pearl. Close examination of the Japanese records would reveal two Zeros being used as scouts failing to return for unknown reasons. Enemy (US) activity was ruled out as we were not alerted, therefore it must have been navigational error til they ran out of gas. Only we, from the perspective of the film now know that it was Tomcats that shot them down.


2) Multiverse theory.
While simpler and IMHO much more realistic and if timetravel were to ever be a reality, the No-paradox model would be the reality as well, It makes for pretty boring sci-fi. Good timetravel shows exploit the very paradoxes and time alterations that the Self consistency principle rules out as impossibilities.
So comes the multiverse theory to exploit the time alterations without getting caught in paradox. This would be the case with Terminator. Every decision, every action, that every person and everything makes... branches off a new timestream. There is an INFINITE number of timestream because of this. Every action creates a new stream. Even if that action is caused by a timetravelling terminator. So in one instance, the original timeline goes on as before with no terminator parts left behind, and another in which it is.


I joined the Navy to see the world, only to discover the world is 2/3 water!

The bootstrap paradox is no more paradoxical than the existence of the universe. If the universe does not need an ontological cause and can exist "self-sustainingly" in timespace, then why not the terminator technology or the andromeda? They simply exist uncaused in a closed time loop. On the other hand if the universe has a non-physical cause above/outside time, then so can the terminator or the andromeda.

In a storytelling perspective, it's a metaphor about how, as humans, we keep making the same mistakes over and over even when we should know how to avoid them.

It's also a metaphor about how we don't consider the long-term ramifications of our actions -- and that we may face those ramifications sooner than we think.

As far as this film is concerned, they don't destroy Andromeda, there's a last secret vile stored in a locker on the space station at the end of the film, the president also refuses to stop vent mining during the funeral scene. The number in the message from the future is the locket number on the space station

What happened happened and will happen again regardless