No, it is not.
Let's break down the equation:
» Believe no God = No belief in God
» (Yes) Believe No God = (No) Belief God
» (Yes) Belief = (No) Belief
» Yes = No
Obviously, it is illogical. One can't dismiss this as "purely semantics". It is actually indicating a subtle, yet critical issue.
The difference is the level of assertion.
Not having a belief is not accepting a claim as true. If one actively believed there was no god, that would be accepting a claim as true. One who lacks a belief is waiting to find out what's actually true.
It is the difference between Innocent, Not Guilty and Guilty.
It is the difference between Positive, Neutral and Negative.
It is the difference between Confirmed, Pending and Falsified.
Many atheists are "neutral", in that they are not necessarily accepting that a god absolutely does not exist, but rather are waiting for theists to demonstrate their claims, using the scientific method, preferably.
Colloquially, most people think of this position as "agnostic", but in fact, it is both. In short, agnosticism deals with what is knowable, and atheism deals with what's believed. Most self-described atheists describe themselves as "agnostic atheist".
- Isn't "believing that God doesn't exist" the same thing as "not believing in God"?
- Do you only believe in what you can see, touch, feel, etc?
- Why do you ignore all the evidence around you for a god?
- Where does morality come from, if not God?
- Why do atheists support gays so much?
- Do atheists believe in nothing?
- Are you afraid of going to hell?
- If it wasn't God, who created the universe?
- Why are you so closed minded?
- What is the point of living without an afterlife or god?
- What if you are wrong?
- Can you prove that God doesn't exist?
- Will you admit that there is a possibility of a god?
- Do atheists have faith?
- Where does the meaning, and purpose of life come from?
- If there is no god, how do you explain _______?
- Why do atheists have faith in science?
- Are atheists empty, unhappy people?
- What bad experience made you hate god?
- Where to do you go when you die?
- Do you believe all this came about by random chance or by accident?
- What would it take to prove to you that a god exists?
- Why don't you just sit down and shut up, and let others have their beliefs?
- Why are atheists so angry?
- Isn't it arrogant to say that science has all the answers?
- Wouldn't it be safer to just believe than risk going to hell?
- Aren't you just rebelling against God because you want to sin?
- What is faith?
- Have you tried to believe in God?
- Doesn't you being so against God prove he exists?
- Why did you choose to be an atheist?
- Where do you think rights come from, if not God?
- Is atheism a religion?
- Do atheists want to take religious freedom from Christians?
- Don't atheists believe there is no god?
- What is in it for me to be an atheist?
- Do you believe in a soul or spirit?
- How do you know you are right?
- What is an agnostic?
- If you don't worship God, do you worship yourselves?
- What is the difference between an agnostic and an atheist?
- Don't you have to be skeptical about skepticism?
- Don't you know that you're just supposed to have faith?
- What do you base your beliefs from?
- What is an atheist?
- Why do you ignore god?