Ivan isn’t in a private room, as he claimed, but at a place by the window that’s separated by screens. Alexei knows that Ivan doesn’t like taverns, so he must have shown up to meet with Dmitri, who isn’t there. Ivan offers to order fish soup for Alexei, who accepts. He remembers how much Alexei liked cherry preserve when he was little, so he orders that, too.
It isn’t clear why Ivan would identify this as a room—perhaps to feel as though he’s enjoying an exclusive privilege, given his propensity for pretension. His attention to Alexei’s food preferences is an attempt to show that he has some knowledge of his brother.
Ivan says that he wants to live and “love with [his] insides.” He plans to move to Europe. Alexei expresses joy at his brother’s desire to love life, and believes that people should in order to understand its meaning. Ivan asks if it’s true that he’s leaving the monastery. Alexei says he will because Zosima is “sending [him] into the world.”
Ivan seems to want to become less cerebral and to adopt a closer connection with life’s pleasures and with other people, without falling into the kind of dissipated lifestyle that corrupted both his brother and his father.
Alexei wonders how things will end between Dmitri and their father, causing Ivan to snap and to feel as though he’s being turned into his brother’s keeper. He repeats that he’s finished his affairs and will be leaving. He says that “Dmitri is only a strain” and that, one day, Katerina Ivanovna will realize that she doesn’t love him at all but loves Ivan. Then again, maybe she’ll never realize it.
Ivan’s comment about not being his brother’s keeper echoes that of Smerdyakov (and again quotes the Biblical Cain, who killed his brother). Neither is interested, at this point, in protecting Dmitri from his worst impulses. In fact, Smerdyakov will exploit them and Ivan will ignore them to focus on his own interests.
Ivan asks how Katerina Ivanovna is doing. Alexei tells him about her hysterics. Ivan admits that he decided to dine at the tavern to avoid eating with their father. He then tells his brother not to worry so much about his leaving, for they’ll have all of eternity to talk, though that doesn’t really matter. He insists that they should talk only about “the eternal questions” that preoccupy all of “young Russia”: questions about God, immortality, socialism and anarchism, and the transformation of humanity “to a new order.”
Ivan doesn’t seem to like his father very much, though Fyodor expresses an appreciation for Ivan due to his intellectual abilities. In that regard, Ivan is very eager to talk to Alexei about Russia’s future. The “eternal questions” concern not only the fate of the nation but also that of humanity.
Ivan insists that he won’t fixate on “all the modern axioms,” which come from Europe anyway. Ivan explains what he believes in and hopes for. He accepts God “pure and simple.” He believes that God created Earth in accordance with Euclidean geometry and that he, too, has “a Euclidean mind” that cannot understand things that aren’t of this world. He accepts that God’s wisdom and purpose are unknown to mortals. Ivan believes “in order, in the meaning of life,” and “in eternal harmony.” It isn’t God that he doesn’t accept but the world that he’s created, with all of its suffering. During “the world’s finale,” he thinks that something precious will be revealed and that it will “redeem all human villainy” and make forgiveness possible. Alexei asks Ivan why he doesn’t accept the world. Ivan, suggesting that he’d like to be healed by Alexei, proceeds to explain.
The “modern axioms” would probably be Enlightenment ideas that were exported to Russia during the reigns of Peter the Great and Catherine the Great. Ivan’s notion of an ordered and geometric world reflects the ideas of the Deists, who believed that God created the world, ensured its proper function, and then abandoned it. The Deists, like Ivan, never claimed to know why God did this. Unlike the Deists, Ivan dislikes the world as it is, equating it with a cesspool for evil. He appeals to Alexei to disabuse him of this notion.