Everyone lives their life without god, though some convince themselves otherwise. As an Atheist I cannot say gods do not exist, all I can point out the complete lack of evidence that any gods do exist so that accepting their existence as real is not rational. My conclusion is that they do not. That conclusion is PROVISIONALLY TRUE, and it is not a belief. The provision being conditional on no valid evidence being found for their existence. I also don't spend a lot of time considering the existence of Unicorns for exactly the same reason.
I (kinda) agree with Grumpy on that.
My tendency is to distinguish atheism and agnosticism this way: Atheism is a belief about God's existence, typically the belief that God doesn't exist. And agnosticism is a belief about whether we have (or can have) knowledge about God. Agnostics argue that we don't/can't.
So there seem to be four basic permutations of these views:
1. Atheist/gnostic - Somebody who believes that they know that God doesn't exist.
2. Atheist/agnostic - Somebody who doesn't believe that humans can know about things like gods, so there isn't any reason to believe in the existence of such things. Apparently both Grumpy and myself would plant ourselves here.
3. Theist/gnostic - The typical theist position in which people claim to know that God exists.
4. Theist/agnostic - A very interesting position, often embraced by religious mystics, where it is believed both that God exists and that God is cognitively unknowable, exceeding and transcending all human words and concepts. In these kind of theologies (the technical term for them is 'apophatic') one ascends to God by a process of meditation/contemplation, in which all of one's thoughts and cognitive contents are gradually eliminated, leaving (it is argued) pure consciousness of the divine. We see it in Hindu yoga and in the Christian contemplative traditions.
And there is a lot of loose use of words in this discussion. Faith and belief are not rational.
This where Grumpy and I disagree.
Faith basically just means 'trust' or 'confidence'. And belief is simply a mental state, with a proposition as its content, in which the truth of the proposition is affirmed. While many of our beliefs are tentative and probabilistic, sometimes little more than hypothetical shots in the dark (we might not even call them 'beliefs' in that case), we do typically have faith in the ones that we feel have higher probability. In other words, we are willing to act on those beliefs, and perhaps even to take risks on the assumption that they are true.
Faith and belief, at least as philosophers use those words, can be and often are rational. Whether a particular belief or item of faith is or isn't rational is a function of the reasons why people have that faith or belief in the first place, and of the quality of the justifications that can be marshalled in its support.
It is a misuse of the word faith to say one must have faith(acceptance without evidence)that the sun will rise in the East. Faith is not required, there is evidence that leads us to KNOW that the sun will rise in the East. And that the sun will rise in the East is not a belief, it is a fact, whether you are aware of the evidence or not. All of this is PROVISIONALLY TRUE, as is everything we call knowledge.
I'm inclined to be one of those (the tradition goes back at least as far as Plato) who would define 'knowledge' as 'justified, true belief'. If we believe that some proposition about X is true, then in order for our belief to qualify as knowledge, whatever we believe about X must really be the case, it must be a fact. And what's more, in order for a belief X to qualify as knowledge, we usually need to have some good sound reason why we believe X. Knowledge of X can't just be the result of a guess, even if the guess happens by chance to be true.