One of the things I kept returning to while reading Crime and Punishment was that Raskolnikov's motive for murdering the pawnbroker was never really explained. While we get a great deal of insight into Raskolnikov's state of mind just prior and in the period after the murder, we still don't get an explicit reason for why he committed such a brutal crime (I don't trust Raskolnikov's after the fact explanations). The only reason we do get, is the visitation of an unexplainable urge upon Raskolnikov, a dark passenger which drives him to kill. This may not seem like much, but I do believe there is a reason that the motive lies mostly unexplained.
Throughout the novel, Raskolnikov disparages the rational egoism and "progressive thinking" of men like Luzhin. These men are suppoesd to carry the banner for an enlightened age, moving past the romanticism and backward thinking of the past. Raskolnikov's motive for murder is the exact opposite of this. It is a primordial urge, savage and animalistic, that contains no elements of rationalism or reasoned thought. Someone mentioned in class that they thought Raskolnikov killed because he felt oppressed by poverty. While I think poverty played a role in Raskolnikov's fragile mental state, his urge to murder came from somewhere deeper. I think the murder was Raskolnikov, himself formerly a student of an "enlightened" university, rebelling against these new philosophies. He cast aside his rational self in favor of the savage, sadistic animal that lay within him, and which he had always been taught to suppress. The motive lies unexplained because, ultimately, the element of Raskolnikov that drove him to kill cannot be explained, it simply exists. Neither the narrator, nor Raskolnikov, nor the reader is capable of understanding it, and so, unexplained, it hangs over the entire story.
In Notes from Underground the narrator dedicates the whole first section towards a critique of rationalism, and juxtaposes a romantic view of life as preferable to it. If this idea carries over to Crime and Punishment, then Dostoyevsky is, in a way, praising the murder as a justifiable reaction to rational egoism. This confused me. I never thought, while reading, that Dostoyevsky was calling the murder justified, and the disintegration of Raskolnikov's life seems to support this. Yet, once I thought through my other line of thinking, it led me to this point. I'm really not sure what to do with this contradiction, and perhaps this is a final paradox Dostoyevsky intends us to leave with.