To determine whether Raskolnikov in Fyodor Dostoevsky's Crime and Punishment is a tragic hero, we first have to review the characteristics of a tragic hero and then see if Raskolnikov fits those.
According to Aristotle, a tragic hero is a virtuous but flawed person who suffers some kind of reversal of fortune, moving from good to bad and, in the end, either dying or experiencing great suffering that is more than the hero probably deserved. However, as the years passed, this definition has shifted a little bit. While the tragic hero must still be sympathetic to readers and come to some sort of ruin by the end of the play, the qualification of virtue has sometimes been abandoned, although usually a tragic hero must still make some kind of effort to do the right thing or to have good intentions.
Now let's think about whether Raskolnikov is a tragic hero. Raskolnikov is a poor law student who murders Alonya Ivanovna and her sister without even knowing entirely why. He tells Sonia that he wants to see if he can get past the revulsion that murder would cause in a person committing that act, but he also wants to experiment with whether he can have full power over someone else and push against or even step over the limits of evil.
It is clear that Raskolnikov is a highly troubled person. He murders out of what he thinks is logic, and he is cold and emotionless about it. Afterward, he is puzzled and filled with doubts. He is split between his intellect and his emotions. As the novel progresses, Raskolnikov eventually confesses to his crime and ends up in Siberia, shattered in body and mind but still proud and distant from the rest of humanity.
Does Raskolnikov fit the characteristics of a tragic hero then? He is certainly not virtuous in most ways. He does come to ruin in Siberia, but he does not really have good intentions in any particular way other than confessing to the murder. He seems to be in a rather bad state from the beginning to the end of the novel although we could argue that his act of murder has scarred him in many ways. We might say that Raskolnikov is just at the edge of being a tragic hero and that he might be better labeled as an antihero due to his overall lack of repentance for his act and because his morality is highly compromised.
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