In Crime and Punishment by Fyodor Dostoevsky, one of the primary themes of the story as a whole becomes the question of what motivated Raskolnikov to kill Aliona Ivanovna. This question arises many times in the novel, not only by the other characters but by Raskolnikov as well. Many potential reasons for the "crime" (which Raskolnikov considers to be a misnomer) are introduced throughout, which complicates the already tentative reasoning behind his actions and causes his motives to become even more unclear.
The supposition that primarily arises is that he murdered the pawnbroker as a means to increase the wealth of his poverty-stricken family; however, Raskolnikov himself has an internal debate as to whether this was in fact the reason, but comes to the eventual conclusion that it was not.
A more probable explanation for the murder is ironically introduced not by Raskolnikov but by Peter Petrovich Luzhin during his first meeting with Raskolnikov, when he explains his revolutionary concept of "loving himself above all else," that "in acquiring weatlth solely and exclusively for myself [Luzhin], I am acquiring, so to speak, for everyone, and helping to get my neighbor a little more than a torn coat..." (p. 145). This theory is intriguing because it expands upon an idea that Raskolnikov had previously overheard from a conversation between two gentlemen in a tavern playing pool, when one of them hypothetically stated, "'Kill her [Aliona Ivanovna], take her money and with the help of it devote yourself service of humanity and the common good'" (p. 66). It can be safely assumed that Raskolnikov abided by a similar philosophy, for during his meeting with Peter Petrovich he ignores Razumikhin's protests and points out that "if you carry out logically the theory you [Luzhin] were advocating just now, it follows that people may be killed..." (p. 147), which startles Petrovich. All this makes it likely that Raskolnikov did in fact kill the woman for the good of society, but the entire idea is rendered futile when he fails to utilize her items and none of her wealth ends up being used for the common good in spite of his efforts.
Raskolnikov's philosophy of ordinary v. extraordinary individuals in society seems to most closely reflect his motives for killing the pawnbroker; he believes that those who transcend the law are extraordinary and are essential to the recreation of the human race, whereas those who abide by the law (or falsely assume they are extraordinary) are merely ordinary. However, he does not know which class he belongs to in this scenario, and actually is troubled by this uncertainty throughout the remainder of the novel. It is notable that during his second interview with Porfiry Petrovich, Porfiry describes the determining characteristics of a a guilty man who suffers from agony and guilt; in doing so he describes perfectly the condition that Raskolnikov is currently in, and it is likely that Porfiry himself is very much aware of it: "'Why, they are all sick, nervous, irritable! . . . And then how angry they all are!'" (p. 324), followed by a paranoia-inspired outburst on Raskolnikov's part. From this it can be theorized that Raskolnikov belongs merely to the "ordinary" class since his state of mind was so predictable at this point and because it was so easy for Porfiry to "play cat and mouse" with him.
Additionally, Raskolnikov had no trouble in thoroughly explaining his article's message to Porfiry, but had great difficulty in reasoning his murder to Sofia Semionovna. He gave a number of explanations, but his best defense was that "'whoever is strong in mind and spirit will have power over them. Anyone who is very daring is right in their eyes. He who despises most things will be a lawgiver among them and he who dares most of all will be most in the right'" (p. 396). Raskolnikov says this, and yet he was not daring; yes, he murdered the pawnbroker, but was extremely hesitant and tentative in doing so.
In actuality, he had no revolutionary cause to kill the woman. "'I . . . I wanted to have the daring . . . and I killed her. I only wanted to have the daring, Sonia! That was the whole cause of it!'" (p. 397). Raskolnikov's true intention in murdering Aliona Ivanovna was presumably, therefore, to determine whether he belonged to the ordinary or extraordinary class established by his article, the result being that he was ordinary because he only did it "to have the daring" that characterized the extraordinary group and thereby attempt to become extraordinary. In the end, even when he is in prison, Raskolnikov refuses to see the murder as a crime because he proclaims it was needed for the common good, yet no actual benefit came of it; thus, his motives for it become almost irrelevant.