As the previous answer provides a good overview of both characters, this answer will focus primarily on Raskolnikov.
The very name “Raskolnikov” comes from the Russian root “raskol,” meaning “schism” or “split,” which speaks to the duality of Raskolnikov’s character. One of the clearest illustrations of this double nature is in his quest to prove himself “extraordinary.” Perhaps Raskolnikov’s greatest inner conflict comes from the fact that he does not know whether he is a great man. Indeed, it is this very obsession that pushes him to murder the old pawnbroker.
Early on, Raskolnikov’s erratic behavior makes his motivations for murder difficult to understand. It appears as though he murders the pawnbroker to steal her money, however, he goes on to bury the goods he stole, rendering them useless. Only when we learn about Raskolnikov’s old article does it become clear that the murders were motivated by his utilitarian theory...
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of the “extraordinary man.” In the article, Raskolnikov suggests that such an individual may have the moral right to transgress society’s laws and norms to fulfill some greater purpose or to increase overall good. A great man (which Raskolnikov imagines himself to be) would be able to commit and/ or get away with murder easily because his superior rationality would let him know that his actions are not, in fact, a crime.
Of course, in the actual commission of the murder, Raskolnikov’s utilitarian justification completely breaks down. He is utterly terrified and, in his panic, kills the innocent Lizaveta, proving that he could not be further from the cool, rational “Napoleon” that he imagines himself to be. Eventually, Raskolnikov reveals a second, alternate motive that is purely selfish, rather than utilitarian.
It wasn't to help my mother I did the murder—that's nonsense—I didn't do the murder to gain wealth and power and to become a benefactor of mankind. Nonsense! I simply did it; I did the murder for myself, for myself alone, and whether I became a benefactor to others, or spent my life like a spider catching men in my web and sucking the life out of men, I couldn't have cared at that moment. (Chapter IV)
Desperate to prove his superiority to the society he feels so estranged from, Raskolnikov murders simply to see if he is powerful enough to do it. Raskolnikov’s deteriorating mental state following the murders reflects the dissonance between his dual motivations for murder. He fails to recognize the inevitable dichotomy between the inherent altruism of utilitarianism and the ability to murder fellow human beings without guilt or remorse. In his quest to prove himself “extraordinary,” Raskolnikov ultimately proves his worst fear—that he isn’t a “great” man in any sense of the word.
Svidrigailov can be considered “dual” in that he acts as a foil to Raskolnikov; in some ways, he actually personifies Raskolnikov’s ideal of the “extraordinary man.” Unchecked by the morals or laws of society, Svidrigailov acts only to gratify himself and, as a result, commits terrible crimes, including the rape of a young girl. Unlike Raskolnikov, Svidrigailov has no dual motivation; he does things purely because he feels powerful enough to do them. He does not care for humanity or the greater good and, therefore, feels no remorse or guilt for his actions. Svidrigailov’s character shows us that Raskolnikov’s split nature, while having led to his mental devastation, is also what protects him from becoming wholly corrupted. Svidrigailov’s obvious moral decay serves as a glimpse into Raskolnikov’s future should he choose not to pursue spiritual and moral rehabilitation.