Most atheists these days say that they don't believe that God exists. Religious people, however, are prone to assuming that this means the atheists believe that God doesn't exist.
It does mean that in ordinary language. If I say that "I don't believe in global warming", most people would interpret that as my denial that global warming is happening. If I say that "I don't believe in right and wrong", most people would interpret that as me denying the reality and applicability to me of these ethical values.
And the religious people would seem to me to be (roughly speaking) correct about atheists.
Atheists typically entertain a whole collection of additional beliefs
besides "We lack the belief that God exists". They include:
1. 'God exists' is F, ~(God exists) is T. In other words, I think that most atheists believe exactly the belief that you insist religious people falsely attribute to them.
2. (As atheists typically use the word) God seems to exclusively refer to the "Abrahamic" God, perceived in a particular way, seemingly derived from fundamentalist Protestantism. Atheists love to respond to philosophy of religion arguments with Biblical (dis)-proof texts, using their Bibles and Bible quotations precisely as fundies do, except in reverse. The Bible is still the uniquely revealed Word of a God that the atheist no longer believes in. This completely ignores the possibility that maybe some sort of God exists in the sense of the universe's ultimate Source and Explanation, something that might even conceivably give some sort of big-picture meaning to the seemingly random and pointless events of human life, but the Bible is nevertheless an ancient book-of-myths that has no more to do with it than Homer's Odyssey. (It's a little telling that theoretical physics often seems to want to intrude into natural theology's turf, into the role of revealing the fundamental mysteries.)
3. Atheists will typically insist that there is no evidence for the existence of God. Which is obviously a propositional assertion that goes beyond simply saying "I don't currently believe in God". It's also factually false, since there's no end of what religious believers take to be evidence. Religious experience, miracles, arguably even the existence of reality and the seeming "laws of nature". We should be saying that
There's no evidence that I'm willing to accept as being good or convincing evidence. There may be sound and convincing reasons for the atheist taking that position, but it nevertheless is a position and it does need argument. Argument that can't be evaded by the familiar atheist "I'm not asserting anything and have no burden of proof!" evasions.
4. Atheists will typically insist that belief in God or adherence to religion is somehow 'ignorant'. The idea that if somebody was suitably intelligent, educated and knowledgeable, then he or she would naturally reject religion. There's some radical enlightenment inspired idea that atheism is more 'progressive'. Atheism is supposedly what all the smart people believe. There's a widespread tendency for atheists to picture themselves as champions of "reason" (while they simultaneously argue that they have no need to present an intellectual case for their atheistic position). We see it in how atheists often make analogies between belief in God and belief in spaghetti monsters, pink unicorns or fairies. Beliefs that the atheist believes are ridiculous.
5. There's often a highly emotional edge to atheism. Many atheists viscerally dislike religion and they react to it with anger. (We see plenty of that right here on Sciforums.) Atheists will often insist that belief in God is morally reprehensible. Not only is there the implication that one shouldn't (in some moral sense) believe in 'ignorant' ideas or hold unfounded beliefs, there's a style of atheist historiography that interprets religion as the historical cause of most war and much of man's inhumanity to man. Religion was supposedly invented by evil priests to strengthen their hold over the innocent masses, so the story often goes. There's the familiar "conflict thesis" that (falsely) interprets the history of science as science's valiant battle against the cold grip of ignorant and obscurantist religion which has always tried to suppress the flowering of "reason".
In case a theist (i.e. God believer) reading this is having trouble following the analogy, here's a brief summary of how this applies to your God belief:
When an atheist says she doesn't believe in your God, that usually doesn't mean she believes your God doesn't exist. Rather, it means exactly what it appears to mean on its face: that the atheist doesn't share your God belief - no more and no less.
That's collapsing atheism together with agnosticism. As an agnostic, I welcome atheists moving over to what I consider a far stronger intellectual position. But I oppose atheists claiming agnosticism's turf as their own while still clinging to their atheist beliefs (beliefs that they deny even having).
If an atheist wants to become an agnostic, then lose the equation of "religion" with Protestant Christianity. Lose the conviction that there's no evidence and replace it with "I haven't seen any evidence yet that convinces me". Lose the visceral anger and hostility towards religion and religiosity. Lose the simplistic philosophy and historiography.
To put it another way, the atheist who says she doesn't believe in your God is not "in denial" about the existence of your God. She isn't denying that your God exists; she is telling you that she doesn't believe your God exists.
When an atheist acknowledges that your God must logically either exist or not exist, that is not equivalent to the atheist implicitly agreeing with your belief that your God exists.
You're still arguing against Jan Ardena's peculiar arguments, aren't you? (
Where is Jan??)
There is a valid point there that if we are arguing about the existence or non-existence of 'X', we need to have some shared concept of what 'X' means, what it refers to (assuming it actually refers). So in order to be an atheist, an atheist seemingly must have some familiarity with the concept of 'God', at least in one of its countless variants. So Jan would be right to the limited extent that 'God' must exist as an idea, in order for atheists to exist.
The problem there is that the word 'God' has been understood in many different ways. There's the big blustering Jewish guy on top of Mt. Sinai, the voices Mohammed heard in his head in a cave outside Mecca, and the lithe blue guy in India who was always seducing milkmaids. Then there's the austere and abstract metaphysical first-cause and designer proposed by Aristotle and the natural theologians.
Where Jan went off the rails is in his/her conviction that there is one single correct definition of 'God' that is found in all 'scriptures' and upon which all 'scriptures' agree. (Whatever 'scriptures' are.)
If you can't adequately explain to atheists how you know your God exists, then you probably don't have a good reason to claim that you know that your God exists.
If one can't explain the objective nature of mathematics and explain how human beings know about things like logical necessity and logical implication (necessary not only for mathematical proofs, but for reasoning in general), then theoretical physics would seem to be just another aspect of life based primarily on intuition.
Ancient scriptures tell you that ancient people thought a God existed. They are unlikely to be regarded by atheists as convincing evidence that your God exists.
I certainly agree with that.
Your gut feeling that your God exists is unlikely to convince an atheist that your God exists.
That's certainly true. But the problem doesn't just apply to religion.
Your gut feeling that some things are morally right and other things are morally wrong is unlikely to convince somebody who holds different moral views. The point being that ethics exists on ground that's probably just as shaky as the ground beneath religion.
Agnostics (in Thomas Huxley's original sense) are inclined to think that most of the things we believe are on shaky ground, if we just poke deeply enough.