A Note on Time Travel in 12 Monkeys
The built-in circularity in the Time Travel that occurs in 12 Monkeys is a welcome departure from radical-change-to-be-effected that so often characterises Time Travel in science fiction movies. And this enhances the film as a whole.
It has been said (by tallman above) "They are there only to observe, and to bring back information that will help in the future." With this carefully designed mission for Cole, the writers try to eliminate paradox entirely. However, they ran into problems that could have been avoided when Cole had to report back to his team. See Time Travel and the Knowledge Paradox for details of how this paradox can generally be avoided.
Unfortunately the mode of message-leaving is such that his team in the future have to know about the messages before they send him off to the past - i.e. graffiti and a telephone message that were not taken into account when Cole is first sent back in time. Hence, they have the information, but just hadn't worked out what it meant until after they had sent Cole back twice. This is clearly neither neat nor convincing - surely they would have carefully reviewed all evidence before sending him back?
Clearly, Cole cannot return to the future with his observations about the events of the past, as he has to die where he (temporally) is, as he recalled in his childhood memory at the airport. But, he could have communicated them in some unsuccessful way, or, "Bill & Ted"-style, gone back to do the things that he had already done (ahem). This latter suggestion would not be so fruitful for the narrative in this particular instance though, as Cole would have not been overjoyed at the prospect of knowingly heading towards his death. Of course, with enough omitted information it could still have been a great movie, if a rather different, paradox-avoiding one.
Master Villain says: "There is a way to leave phone messages for the future - if they give him a number selected at random before he leaves and then go and check it they get the message without knowing the message was there." Great thought - but the only reason the characters could give for this is that it would deliberately avoid the paradoxes of time travel!
Why should we bother analysing this in such depth - isn't it just a movie? Philosopher Andrew Harrison claims that intrinsic to any work of fiction is its fictional frame - science fiction gives the clearest example of this. This means that there are laws which are broken (e.g. time travel is impossible), and laws which are not (e.g. humans are mortal). It seems that the makers of 12 Monkeys are trying to preserve our time-travel paradoxes as paradoxes. This is why Cole's death is necessarily in his own time line. So, unless they are trying to shift the fictional frame deliberately for stylistic reasons (From Dusk till Dawn is a good example of this), this no-paradoxes rule should be observed if the film is to properly satisfy its audience.
Thanks to tallman for the correction!
Andrew Harrison's material is found in his Philosophy and the Arts (Thoemmes Press, Bristol, 1997), Chapter four, although I heard it from him in undergraduate lectures in Aesthetics at the University of Bristol, 2003.