Barry Arrington at Uncommon Descent offers a succinct discussion on the topic of the possibility ethics without God. I've edited his argument slightly:
In an earlier post I lamented the apparent extinction of what I called "Nietzsche atheists," by which I meant atheists with the courage and honesty to accept the bleak conclusions logically compelled by their premises. Some of our atheist friends seemed to not know what bleak conclusions I was referring to. Here is a comment that sums it up nicely. This post is adapted from a comment to that earlier post.
Make two assumptions:
(1) That atheistic naturalism is true.
(2) One can't infer an "ought" from an "is" [i.e. because things are a certain way doesn't mean that they ought to be that way].
Richard Dawkins and many other atheists should grant both of these assumptions.
Given our second assumption, there is nothing in the natural world from which we can infer an "ought." And given our first assumption, there is nothing that exists over and above the natural world; the natural world is all that there is. It follows logically that, for any action you care to pick, there's nothing in the natural world from which we can infer that one ought to refrain from performing that action.
Add a further uncontroversial assumption: an action is permissible if and only if it's not the case that one ought to refrain from performing that action. This ..... [all simply conforms] to standard principles and rules of logic and we've started out with assumptions that atheists have conceded.
And yet we reach the [following] absurd conclusion:
...therefore, for any action you care to pick, it's permissible to perform that action.
If you'd like, you can take this as the meat behind the slogan "if atheism is true, all things are permitted." For example if atheism is true, every action Hitler performed was permissible. Many atheists don't like this consequence of their worldview, but they cannot escape it and insist that they are being logical at the same time.
So here's the predicament that the atheist finds him or herself in:
If there is no God then there are no morally impermissible acts. But most atheists want to argue that there are morally impermissible acts, thus they are driven to the conclusion by modus tollens that there is a God.
To avoid this conclusion they must either agree that there are no morally impermissible acts and stop irritating the rest of us by indulging their silly penchant for passing baseless moral judgments or they need to show how, in the absence of a transcendent moral authority, there can still be something which is morally impermissible.
Unfortunately for atheists' self-image as paragons of rationality, few of them are willing to do the first and none of them is able to do the second.RLC