Is Dostoyevski making a socially consequential statement--or warning--about a society that turns its back on God? If so, did Russia, his homeland, pay any attention to him?
"If God does not exist, anything is permissible" was uttered by Ivan in 'Brothers Karamazov'.
Dostoyevsky is a controversial author, and he saw western Europe as a civilization of nihilism, atheism and spiritual death (Oswald Spengler largely agreed with this, and he discusses Dostoyevsky quite a lot in his masterpiece 'Decline of the West'), and Ivan Karamazov is a typical European intellectual.
"did Russia, his homeland, pay any attention to him?". Yes they did, and as you know he is extremely influential in the west as well as in Russia. In 19th century Russia, there was a big philosophical argument between "zapadniki" (pro westerners, and Ivan Karamazov is also in this camp) and "slavophiles" (proponents of the idea that Russia is a unique civilization distinct from the west), and Dostoyevsky was in the latter camp.
No Dostoevsky's character said that. Nor did they say "If there is no God, then everything is permitted", which is Sartre's surmise of Karamazov Brothers that became a meme, see Zizek and Cortesi. What Dmitri asks Rakitin in Brothers Karamazov is:"without God and immortal life? All things are permitted then, they can do what they like?" Arguably, the quip describes the sentiment of Dmitry's "immoral" brother Ivan, who does utter:"If there is no immortality, there is no virtue". While attempting to live by the implication, Ivan admits to Alyosha that he does believe in God after all, and accepts the price of his transgressions.
The idea is that without a promise of ultimate reward, or fear of ultimate retribution, without God as the law-giver and sin-punisher, men are released from any motivation to observe their moral obligations, or even to justify those obligations in the first place. Such is Ivan's initial logic, anyway. The message, as interpreted by moral conservatives, like the Russian philosopher Berdyayev, was that Godlessness is inhumane and destructive, and they saw Dostoevsky as forewarning the atrocities of communism that eventually triumphed in Russia, see Kiskaddon, Dostoyevsky and the Problem of God. This is the message that continues to make the quip so popular among conservatives criticizing the moral corruption of modern societies.
However, as both Berdyaev and Zizek noted, Dostoevsky's message is far more nuanced than exposing Ivan's philosophy as self-destructive (although he is more definitive when depicting another all-permitter, Stavrogin, in Demons):
"Furthermore, when Dostoyevsky proposes a line of thought, along the lines of "If there is no God, then everything is permitted," he is in no way simply warning against limitless freedom - that is, evoking God as the agency of a transcendent prohibition which limits human freedom: in a society run by the Inquisition, everything is definitely not permitted, since God is here operative as a higher power constraining our freedom, not as the source of freedom. The whole point of the parable of the Great Inquisitor is precisely that such a society obliterates the very message of Christ: if Christ were to return to this society, he would have been burned as a deadly threat to public order and happiness, since he brought to the people the gift (which turns out to be a heavy burden) of freedom and responsibility."
For Sartre, his interpretation of Ivan's realization was the entry point to existentialism. Morality grounded in rewards or fear is a false morality unworthy of men (in this, existentialists agree with the "slave morality"'s nemesis, Nietzsche). The men must instead seize their freedom, forge their own morality and take the responsibility for it. Here is from Sartre's Existentialism Is a Humanism:
"The existentialist... finds it extremely embarrassing that God does not exist, for there disappears with Him all possibility of finding values in an intelligible heaven. There can no longer be any good a priori, since there is no infinite and perfect consciousness to think it. It is nowhere written that “the good” exists, that one must be honest or must not lie, since we are now upon the plane where there are only men.
Dostoevsky once wrote: ‘If God did not exist, everything would be permitted’; and that, for existentialism, is the starting point. Everything is indeed permitted if God does not exist, and man is in consequence forlorn, for he cannot find anything to depend upon either within or outside himself. [...] Nor, on the other hand, if God does not exist, are we provided with any values or commands that could legitimise our behaviour. Thus we have neither behind us, nor before us in a luminous realm of values, any means of justification or excuse. – We are left alone, without excuse. That is what I mean when I say that man is condemned to be free."
What did Dostoyevski mean with his character saying "Without God and the afterlife, all things are allowed"?
He is saying that the only reason people behave morally and follow the Ten Commandments is based on a simple reward/punishment system. Obey God and be rewarded. Disobey God and you will be punished. Without this incentive, people will do whatever they want.
Any system that provides this incentive can enforce moral behavior whether the incentive is supernatural or secular.
There is a higher essence than just asimple reward and punishment system (ala Steve Saban). It is the noble, essential virtue called accountability. With a laissez faire approach to moral conduct sans accountability, there is a void, not just of a sense of justice, but justice itself. This is perhaps what Dostoyevsky wanted to portray in his character, a character who is being held accountable for his actions.
Without the "after life" (and pending accountability) injustice reigns the universe. And that is unthinkable, unbearable, unconscionable. Even Benjamin Franklin, an old fashioned Deist, acknowledged an afterlife wherein each man would be judged according to his deeds, and spent the later of his life doing as many "public works" as possible (See his autobiography and learn of his establishing a post office, hospital, sewer works, library, etc.)
Did the Russian people take full advantage of Dostoyevsky's warning? What has the history of modern Europe revealed? What philosophies have dominated academia as far as this topic is concerned? What has been the result(s) of European society's response?
I don't think that all written here is relevant to Dostoevsky, it looks like no here one didn't read him. And all proofs are same. Zizek, Sartre, that woman... About the problem to live without faith in immortal "soul" and "God" Dostoevsky minding in several several works, atleast in "Подросток", "Братья Карамазовы", "Бесы". But to understand what did Dostoevsky you should to understand main distinction Between Orthodox and the West( Catholic, Protestant) ethic.
What happened in "BK"**, main question is: who killed old immoral father Feodor Karamazov, who is the murderer? Dmitriy have a motive to kill, he need money to realize his passion to Grushenka; Ivan was close to atheistic thoughts, he haven't any moral, he is ammoral and he is smart, he hate the father, because he was not fathering to sons, Feodor is just biological father to his sons, he didn't care about anyone, except maybe Alesha, and Ivan looks at his father as totally useless, harmful and bad human. Also Ivan said to Alesha, that he murdered FK; or a murderer is the bastard son Smerdyakov(the son from townie-mad woman, but "all" thought that his fathe is Feodor, his name translate the "stinky/stinkiest") - he is rasty and ugly character, which causes nothing but disgust, is any reader who saddened his suicides? nope, no one. he looked ugly and silly, but he is slippery, tricky. Nakamura said that Smerdyakov hasn't self mind. Smerdyakov told with Ivan, imbibed with his thoughts and he could to murder. But the result he killed-self. no one love him during life, all looks at him as on dirty Karamazov's pet. Why he killed self? because his master dead or because he got awareness of his ugly role? was his self-murdering unconscious or conscious action? He was nothing, he has nothing, can he killed for ..pleasure?.. Strange things...; or maybe it was Alesha? why not? he played the role of peacemaker, but maybe he had murdered? most postmodern detective stories can have this plot. Why no one thought(in the story) that Alesha wasn't?
Or no one of sons didn't?
Your brain try to find solid earth to thought. If you have a killed man, you want to find the killer, that make your mind troubled. You should to find it? why? for punish the man that will be proved/judged as a murderer? Or to make sense that you didn't it, that it is not you sin? Or You should to blamed the other, to not blame yourself?
Every one like to be owner of goods, but does any one wanted/wished/willed to be the owner of sin? So who is the sins owner? You can find the killer, but who is a murderer? Not You? Why? You don't believe in God, You don't believe at nothing except rational, except logic, except moral judge, except that punish the other is rightfully. Why you are judging the other, if only God can? But if no God, all is allowed. Not things, all thoughts, all theories, even autophagy of alive humans can be reasonable.
Who is the crime action author? When the sin is start? Action is the end only but infraction was before, in thoughts, whose thoughts? You are looking always at the result, always missing an infraction body...
Did Russia pay any attention to Dostoevsky? I donno, his story "Преступление и наказание"(wrong translation on wiki "Crime and punishment", because in Rus it is a wordplay means also "infraction and retaliation", this story not about "Crime". Any crime have a reason, motive, Rodya hadn't any motive, he had theory) read at school. Some others too, "BK" is more difficulty for teens, but many Rus people read Dostoevsky. But Dostoevsky is not for attention actions, it is not instruction how to do right/wrong, even how to think right or wrong. Nope. He didn't answered own questions, he only present the problem, without any solving, and all solves(like Sartre did, or else) are not work. Still not work.
** BK main characters:
Feodor Karamazov - the father, surname Kara-mazov mean Sin-painted.
Dmitry - violently passion, Ivan - rational brain, Alesha - faith, and bastard Smerdyakov - are his sons and also Karamazovy - sin containing. FK character had all this "sins" - he was smart, he was violently passion, he was ugly for others, and he had no doubts = he had totally faith in self-right.