Here's the breakdown of his twisted logic:
* People have become complacent and unappreciative of life: Jigsaw believes modern society has lost its sense of survival and takes life for granted. He sees himself as a catalyst for change, forcing people to fight for their lives and rediscover their will to survive.
* "Games" as a test of character: He sees his traps and puzzles as tests of character, designed to reveal the true nature of his victims. If they survive, they prove their worth and learn to appreciate life. If they fail, they've already shown a lack of will to live.
* Punishing those he sees as "unworthy": Jigsaw targets individuals he sees as having wasted their lives or made bad choices. He feels justified in punishing them for their lack of responsibility.
* A twisted form of redemption: He sees his "games" as offering his victims a chance to redeem themselves. By overcoming the challenges, they can learn to value life and become better people.
Important to note: Jigsaw's methods are extremely brutal and cruel. While he might have good intentions, his actions are undeniably wrong and have tragic consequences. His philosophy is deeply flawed, and his methods are ultimately a form of torture and murder.