There is obviously no rational argument or evidence by which we can establish that Meursault should be acquitted of murder. There are no mitigating factors, and I believe this is the way Camus intended the scenario to be.
The question becomes not one of guilt or innocence but rather the meaning of Meursault's very real guilt within the context of the story. Throughout literary history we can identify similar scenarios in which deliberate killings are emblematic of some deeper problem or mystery at the heart of human actions. Why does Macbeth kill? Why does Raskolnikov kill in Dostoevsky's Crime and Punishment? Why does the title character in Cela's The Family of Pascual Duarte kill? Why does Cross Damon kill in Wright's The Outsider?
There is no absolutely clear answer in any of these instances—or in that of Meursault. In Raskolnikov's case, it's evidently an assertion of his will, a defiance of what he perceives as the injustice of the cosmos that causes him to murder the woman...
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