In Terminator 2: Judgement Day Sarah Conner gets information from a T-800, learning that Cyberdyne Systems used parts from the previously destroyed T-800 to design SkyNet. She then uses that information to destroy Cyberdyne Systems sufficiently to eliminate the possibility that they might provide the hardware solution needed to deploy SkyNet in 1997. As noted last time, though, if Cyberdyne is destroyed, SkyNet is created by the Air Force at a slightly later date using a software solution, and all knowledge of Cyberdyne's solution is erased from history. No one will ever have known of Cyberdyne's importance, and so no one will be able to tell Sarah Conner that Cyberdyne is the villain, and Cyberdyne will never be destroyed. That, though, means that Cyberdyne will develop the SkyNet hardware, putting the system online at the early date and itself back in the history, which leads to Sarah destroying it and eliminating all knowledge of its involvement. We have a classic grandfather paradox, an infinity loop.
Fortunately it does not eliminate all knowledge of Cyberdyne's involvement, and in this the series has its salvation. John Conner knows that acting on information from a T-800 that he sent back to protect himself Sarah destroyed Cyberdyne. He also knows that the destruction of Cyberdyne delayed judgement day about seven years. It is evident that Cyberdyne was knocked out of the development, but also that the world would have been the worse with it involved. Thus it must be that John lies to his mother, programming the T-800 with a history of a world he knew only from the reports he heard as a boy. If he does this, then Sarah will not know that she is merely delaying SkyNet, or that her attack on Cyberdyne is already part of the future history that leads to the presence of machines from the future trying to kill or protect her and her child. She does what she believes will change the future--and it will, but not as she expects. In the CD history, it changes the world from what it would have been in the AB history to what it became in the CD history. That is, it confirms the change already made, instead of reverting to the original history.
This is a very improbable outcome. After all, when Sarah delays judgment day from 1997 to 2004, she also changes the information she would have received previously from Kyle Reese. Kyle, though, is young--too young to have been born in 1997, and if he is sixteen in 2018 (the year of Terminator Salvation), he is two in 2004, and will remember little or nothing of it. He may be repeating what John Conner told him as well, bringing back to the past the information he honestly but incorrectly believes is true about his own history, a history that was changed by his own actions. It is not impossible that John Conner is aware enough to cover this; it is doubtful that most of his warriors care about past dates and places--they care about winning now.
The other problem is that a setback to SkyNet is also a setback to the Terminator project; the killer robots will not be as sophisticated as early. However, there are too many variables we do not know. We do know that the first time travel machine will only accommodate a machine encased in flesh, and therefore it cannot send a terminator back until it has developed the T-800, whenever it does so. We also know that its information about John Conner was sufficiently limited initially that it attacked several women named Sarah Conner, and that does not appear likely to change. The only significant question is how old Kyle Reese will be when he is sent, and a few years one way or the other is probably not too severe a difference.
So history is saved by the lie, and we can get through the first two movies in a way that delivers us to the beginning of the third without necessarily destroying time--if we are very lucky.
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