12 Monkeys is like a visit to an eye doctor with a world-bending phoropter. The doctor swaps out a lens, and the bottom row is as clear as Ryan Gosling's sex appeal. He turns a nob, and suddenly the whole world feels like it's been censored for daytime television.
Our characters face a similar problem—only it isn't an understanding of six random letters that's at stake, but their understanding of reality.
The imagery of lenses is found throughout the film. The Scientists, for example, are associated with all types of lenses. Many of them wear either glasses or loupes, and their study is littered with microscopes, telescopes, and magnifying glasses. When first interviewing Cole, the Astrophysicist inspects him through a huge magnifying glass to examine him. At a later meeting, the audience spies her through the same magnifying glass, resulting in a massive distortion of her face.
Another example is found when Cole and Railly drive into Philadelphia. Rather than seeing the city from an aerial shot, the camera points toward the windows of the skyscrapers, and we see the city through the twisted view of a fun-house mirror.
These and other lenses symbolize how easily human perception can be manipulated, twisted, and shaped by the world around us. These lenses shape our physical view of the world, but we can easily see how this extends to our worldview.
Cole tries to convince people that he is from the future, while later he tries to convince himself that he's crazy. As a counterpoint, Dr. Railly has no questions that Cole is mentally ill, until she does. And the Army of the 12 Monkeys is absolutely responsible for the release of the virus…until we learn it isn't.
But the film extends this idea beyond the characters and asks you, the viewer, to select which reality you prefer. Do you prefer reality one…or reality two? Is James Cole a time-traveling savior of humanity or just a real crazy dude?