More about his theology: I understand very few, if anyone, would consider Dostoevsky to be a theologian; however, his philosophy has a tremendous impact on existential theology.
In Fyodor Dostoevsky’s The Brothers Karamazov, a story of four brothers in Russia is a grim description of the reality of what the world would look like if God were not to exist. One brother, Ivan, an atheist, tells another brother that there are no objective truths, specifically that there are no moral absolutes. Ivan’s brother then kills his father, an act that obtains no condemnation if God does not exist.
This can be understood as ☐(~Eg ⊃ ∀ϕ~Wϕ), also known as Karamazov’s Theorem. It is necessarily true that if God does not exist then any action cannot be wrong. It may also be true if a conjunct of rightness is inserted into the theorem. This ultimately leads to moral nihilism—a nonexistence of value. Without God, everything is permitted. Nothing can be praised and nothing can be condemned. This world, as Dostoevsky understands it, is a world of nothingness.
Dostoevsky, like Camus, Nietzsche, and Sartre, acknowledges the absurdity that arises. Every man must face the anxiety an absurdity that obtains in a world without God. Dostoevsky’s response is that every man must face this reality and overcome this absurdity by trusting in and putting his faith in Christ. Christ is the only one who can overcome the absurdities and relieve man’s anxiety.
Dostoevsky is Christianity’s Nietzsche. Dostoevsky realizes the despair, guilt, anxiety, and absolute absurdity of a life without God, like Nietzsche; however, he does not self-construct his own teleology. There is no higher state of being in a world of absurdity. There would be no incentive to attain any state of being. There could not be any differentiation between a higher and lower state of being since one would need an objective referent to make such a determination. The only rational act a man could make in an unreasonable world would be to trust in the reconciling ability of God. There would be no hope for any reconciliation in a closed system of absurdity—from absurdity only comes absurdity.
 Let Eg represent the existence of God, ϕ for any action, and W for wrong.