In his journal, Dostoevsky wrote against the notion that societies were formed from the mere "need to live together": "This is not true; rather, it always happened as a result of a great idea" (source). The Brothers Karamazov is an extended dialogue about what exactly this "great idea" is and ought to be. Some characters advocate a society based on secular, liberal humanistic values and socialism. But the novel questions the wisdom of these ideals, criticizing them as Western European imports and thus alien to the true spirit of the Russian people. As the elder Zosima, the moral core of the novel, points out, these ideals exclude the Russian Orthodox faith. Without religion, these ideals have no moral core and thus are easily corrupting, leading to a society based on tyranny and injustice. Individuals such as Ivan Karamazov who are skeptical of religion are torn apart by doubt. The novel can be read as an attempt to offer up an idea or an "image" of a just society grounded in Russian Orthodoxy.
Dostoevsky's Brothers Karamazov is ironic toward intellectual characters who over-estimate the power of reason to create an ideal or just society.
In its melding of religious values and literary realism, Dostoevsky's Brothers Karamazov aspires to offer a vision of human nature and human society that is both ideal and realistic at the same time.