While watching the two Terminator movies, one might notice a few time paradoxes. If you don't want to read the spoiler, stop right here!!

1. Kyle Reese is John Connor's dad. He is from the future. Picture this:
   1. War happens.
   2. John saves humanity.
   3. John finds out a Terminator has gone back to wipe out his mother.
   4. John sends Kyle back to save Sarah.
   Now hold on! In order for Kyle to get back to 1984, John needs to send him. In order for John to exist, Kyle must have already gone back to the past.
2. At the end of Terminator 2, it is revealed that Cyberdyne's design of Skynet came from the remnants of the first Terminator. These pieces are destroyed at the end of the movie, which means Skynet will never be created. First, this never could have happened because if the pieces didn't exist in the first place, Cyberdyne could not have designed Skynet. Ever. No war, no nuclear holocaust. Second, this means that Skynet will never create the Terminators. So there's never a reason to send Kyle back in the first place. So John is never born.

Thank goodness they're just movies!

I think the whole point of the Terminator films is those paradoxes. Unlike in the Back to the Future films, where temporal changes are immediately resolved, the Terminator films are based around the twin facts that the good and bad guys both rely on time paradoxes to exist.

Both were created as a result of a war in the future which they come back to stop from ever happening, thus meaning they would never exist...... To stop the war which would therefore happen and they'd be... etc.

All a bit weird I know, but I think it's pretty obviously deliberate that these issues aren't addressed.

It's actually possible to solve for the second paradox mentioned above. Although Schwartzenegger's T-800 character does destroy the chip and bionic arm kept at Cyberdyne, there is one additional detail:

About five minutes previous to that scene, Arnold's arm gets ripped up and torn off his body in between two gears!

Now, assuming that John and Sarah don't catch this on the way out (ya figure that defeating a liquid-metal badguy from the future would wear you down a bit), couldn't that arm be used to recreate Skynet?