Twelve Monkeys

A deadly virus wipes out almost all of humanity in 1996, forcing remaining survivors to live underground. A mysterious group known as the Army of the Twelve Monkeys is believed to be behind the virus. In 2035, James Cole (Willis) is a prisoner living in a subterranean shelter beneath the ruins of Philadelphia. Cole is selected for a mission, where he is trained and sent back in time to collect information on the virus in order to help scientists develop a cure.[3] Meanwhile, Cole is troubled by recurring dreams involving a foot chase and an airport shooting.
Cole arrives in Baltimore in 1990, not 1996 as planned. He is arrested, then hospitalized in a mental institution on the diagnosis of Dr. Kathryn Railly (Stowe). There he encounters Jeffrey Goines (Pitt), a fellow mental patient with fanatical views. After an escape attempt, Cole is locked in a cell, but soon disappears, returning to the future. Back in his own time, Cole is interviewed by the scientists, who play a distorted voicemail message which discloses the location of the Army of the Twelve Monkeys and asserts their association with the virus. He is also shown photos of numerous people suspected of being involved, including Goines. He is given a second chance to go back in time, but another error results in him arriving at a battlefield of World War I. He is wounded in the leg and then suddenly sent to 1996.
In 1996, Railly gives a lecture about the Cassandra complex to a group of scientists. At the post-lecture book signing, Dr. Peters (Morse) questions her about mankind's sustainability on earth and points out that humanity's gradual destruction of the environment may be the real lunacy. Cole arrives at the venue after seeing flyers publicizing it, and when Railly departs, he kidnaps her and forces her to take him to Philadelphia. They learn that Goines is the founder of the Army of the Twelve Monkeys, and set out in search of him. When they confront him, however, Goines denies any involvement with the virus and says that wiping out humanity was Cole's idea at the asylum in 1990.
Cole convinces himself that he is insane, but Railly confronts him with evidence of his time travel. They decide to spend their remaining time together in the Florida Keys before the onset of the plague. On their way to the airport, they learn that the Army of the Twelve Monkeys was not the source of the epidemic; the group's major act of protest is releasing animals from a zoo and placing Goines' Nobel Prize winning virologist father (Plummer) in an animal cage.
At the airport, Cole leaves a last message telling the scientists that in following the Army of the Twelve Monkeys they are on the wrong track, and that he will not return. He is soon confronted by Jose (Seda), an acquaintance from his own time, who gives Cole a handgun and ambiguously instructs him to follow orders. At the same time, Railly spots Dr. Peters, and recognizes him from a newspaper photograph as an assistant at Goines' father's virology lab. Peters is about to embark on a tour of several cities that match the locations and sequence of the viral outbreaks.
Cole forces his way through a security checkpoint in pursuit of Peters. After drawing the gun he was given, Cole is fatally shot by police. As Cole lies dying in Railly's arms, she makes eye contact with a small boyâthe young James Cole witnessing the scene of his own death, which will replay in his dreams for years to come. Peters, aboard the plane with the virus, sits down next to Jones (Florence), one of the scientists from the future.

Question: Who convinces him himself that he is insane?
Answer: Cole