The theory of the extraordinary man, set out in an article by Raskolnikov, divides people into ordinary ones, who must live in obedience and have no right to transgress the law, and extraordinary ones, who may allow their own conscience to overstep certain obstacles when the execution of one of their ideas requires it.
Raskolnikov corrects the brutal summary that Porfiry gives of the article: it is not an official right, but the right of the extraordinary man to "allow his conscience to overstep" certain obstacles, and only when his idea, "sometimes saving, perhaps, for all humanity," requires it. Kepler and Newton would have the right to eliminate ten or a hundred men so that their discovery could reach humanity; lawgivers such as Lycurgus, Solon, Muhammad, and Napoleon violated the old law in founding the new one. The core is the division into two groups: "The first group is always master of the present, the second, master of the future."
The theory is put to the test in Porfiry's own house. Razumikhin, who knows nothing of the crime, reaches the objection by himself: "you allow blood according to conscience." Porfiry confirms that it is "more terrible." Asked whether he himself would overstep the obstacle, Raskolnikov replies: "If I had overstepped it, of course I wouldn't tell you so."
The book does not topple the theory with a counterargument. Alone and feverish, Raskolnikov says: "The principle, that I killed, but I did not overstep, I stayed on this side." Svidrigailov calls it "a theory like any other," and in the Epilogue Raskolnikov himself still defends it, acknowledging guilt only for not having endured the crime and for having given himself up. What undoes it, for the novel, is what the body and other people do to him after the act.