Let’s review what you need in your worldview in order to have a rationally grounded system of morality.

You need 5 things:

1) Objective moral values

There needs to be a way to distinguish what is good from what is bad. For example, the moral standard might specify that being kind to children is good, but torturing them for fun is bad. If the standard is purely subjective, then people could believe anything and each person would be justified in doing right in their own eyes. Even a “social contract” is just based on people’s opinions. So we need a standard that applies regardless of what people’s individual and collective opinions are.

2) Objective moral duties

Moral duties (moral obligations) refer to the actions that are obligatory based on the moral values defined in 1). Suppose we spot you 1) as an atheist. Why are you obligated to do the good thing, rather than the bad thing? To whom is this obligation owed? Why is rational for you to limit your actions based upon this obligation when it is against your self-interest? Why let other people’s expectations decide what is good for you, especially if you can avoid the consequences of their disapproval?

3) Moral accountability

Suppose we spot you 1) and 2) as an atheist. What difference does it make to you if you just go ahead and disregard your moral obligations to whomever? Is there any reward or punishment for your choice to do right or do wrong? What’s in it for you?

4) Free will

In order for agents to make free moral choices, they must be able to act or abstain from acting by exercising their free will. If there is no free will, then moral choices are impossible. If there are no moral choices, then no one can be held responsible for anything they do. If there is no moral responsibility, then there can be no praise and blame. But then it becomes impossible to praise any action as good or evil.

5) Ultimate significance

Finally, beyond the concept of reward and punishment in 3), we can also ask the question “what does it matter?”. Suppose you do live a good life and you get a reward: 1000 chocolate sundaes. And when you’ve finished eating them, you die for real and that’s the end. In other words, the reward is satisfying, but not really meaningful, ultimately. It’s hard to see how moral actions can be meaningful, ultimately, unless their consequences last on into the future.

Theism rationally grounds all 5 of these. Atheism cannot ground any of them.

Let’s take a look at #4: free will and see how atheism deals with that.

Atheism and free will?

Here’s prominent atheist Jerry Coyne’s editorial in USA Today to explain why atheists can’t ground free will.

Excerpt:

And that’s what neurobiology is telling us: Our brains are simply meat computers that, like real computers, are programmed by our genes and experiences to convert an array of inputs into a predetermined output. Recent experiments involving brain scans show that when a subject “decides” to push a button on the left or right side of a computer, the choice can be predicted by brain activity at least seven seconds before the subject is consciously aware of having made it. (These studies use crude imaging techniques based on blood flow, and I suspect that future understanding of the brain will allow us to predict many of our decisions far earlier than seven seconds in advance.) “Decisions” made like that aren’t conscious ones. And if our choices are unconscious, with some determined well before the moment we think we’ve made them, then we don’t have free will in any meaningful sense.

If you don’t have free will, then you can’t make moral choices, and you can’t be held morally responsible. No free will means no morality.

Here are some more atheists to explain how atheists view morality.

William Provine says atheists have no free will, no moral accountability and no moral significance:

Let me summarize my views on what modern evolutionary biology tells us loud and clear — and these are basically Darwin’s views. There are no gods, no purposes, and no goal-directed forces of any kind. There is no life after death. When I die, I am absolutely certain that I am going to be dead. That’s the end of me. There is no ultimate foundation for ethics, no ultimate meaning in life, and no free will for humans, either.

Richard Dawkins says atheists have no objective moral standards:

In a universe of blind physical forces and genetic replication, some people are going to get hurt, other people are going to get lucky, and you won’t find any rhyme or reason in it, or any justice. The universe that we observe has precisely the properties we should expect if there is, at bottom, no design, no purpose, no evil and no good, nothing but blind, pitiless indifference… DNA neither knows nor cares. DNA just is. And we dance to its music. (Richard Dawkins, River Out of Eden: A Darwinian View of Life (1995))

When village atheists talk about how they can be moral without God, it’s important to ask them to justify the minimum requirements for rational morality. Atheists may act inconsistently with their worldview, believing in free will, expecting praise and blame for complying with the arbitrary standards of their peer group, etc. But there is nothing more to morality on atheism that imitating the herd – at least when the herd is around to watch them. And when the herd loses its Judeo-Christian foundation – watch out. That’s when the real atheism comes out, and you can see it on display in the Planned Parenthood videos. When God disappears from a society, anything is permissible.