What does Leo Tolstoy’s The Death of Ivan Ilyich suggest about how Peter Ivanovich reacts in emotional situations?

Despite knowing Ivan Illyich for his entire life, Peter shows little or no emotion at his rapidly deteriorating condition. As his old acquaintance prepares to meet his maker, all that Peter can think about is the opportunities for advancement that Ivan's imminent death will open up.
Peter's selfishness represents the shallow, materialistic society that Tolstoy is so eager to critique in the story. In this heartless, vacuous world, relationships between human beings are instrumental; people see each other as nothing more than a means to an end, rather than as ends in themselves. In such a world, there is no place for compassion or for a true understanding of death. Death, like the illness that precedes it, is something that happens to other people.
Nonetheless, Peter does display a greater degree of sensitivity towards Ivan's plight than anyone else. It's just that he can't quite make that final leap of faith to a true understanding of the significance of Ivan's death. At least not yet. Peter's patronymic, Ivanovich, means "son of Ivan," and this would appear to suggest that, in due course, Peter will eventually develop the kind of understanding of life and death that Ivan himself had shown in his final hours upon this earth.