Words have shifted a bit. In the strictest possible senses, "It's not possible to know for sure" is an agnostic position and the atheistic position would be either "I believe there is no god, whatever the evidence" or "I believe there is no god, here is the evidence". These strict uses sometimes confuse more typical uses, where "probably not, because I haven't seen sufficient evidence to make 'there is any sort of a god' more likely than other options" is called "atheist" and "shrug I dunno" falls under "agnostic".

There are lots of atheism and agnostic variations. Actually an agnostic can be also an atheist (or a theist, by the way). But here you have a nice explanation: http://atheism.wikia.com/wiki/Atheist_vs_Agnostic

As explained in the link, there are two kind of atheists: gnostic-atheists (strong-atheists) and agnostic-atheists (weak-atheists)

In my opinion, since proving the existence/non-existence of gods (and spaghetti monsters, and pink unicorns) is impossible, gnostic-atheism is untenable (in the same sense that gnostic-theism is untenable).

But, and I think this what matters for an atheist to identify as such, the fact that the non-existence of god can not be proved does not make it an important subject. It is just one of those things that can not be proved or disproved (by construction), and has no more relevance that the orbiting of a tea pot around the sun.

EDIT: actually, I stand corrected by this very interesting article and I will stick to the Sagan Plausability Scale for these discussions: http://www.skepticink.com/incredulous/2013/08/20/why-the-fam...

I want to be clear that I don't think it is in any way unreasonable to use "atheist" to mean "I don't think God is any more likely than Russell's teapot", just that this isn't always what it is used to mean and the two meanings are sometimes confused/conflated.

It is not unreasonable to think that "God is less likely than Russell's teapot", but it is definitely unreasonable to say "I am sure god does not exist" since, by definition, god is untestable.

I guess that what I am trying to say is that a "strong atheist" (with judgements based on reason), can not really assert with 100% confidence that god does not exist. He can, nevertheless, be convinced that the likelihood of its existence is for all practical purposes 0.

It is not that he "believes that god does not exist", it is more that he thinks along the lines of "why should I care about this particular teapot?"

It is that he believes that God does not exist, in that he asserts that the probability of God is substantially less than the probability of no God. In the same way that he believes that, having looked both ways and seen no car, he won't be hit by a car when he's crossing the street (though I'm not asserting any relationship between the magnitude of the respective likelihoods). There's the possibility he's wrong, and that'd be unfortunate, but it's what he believes in that it's what his understanding of the world says and it's what determines his actions. Using the word "atheist" for such people seems entirely reasonable. Most of them will agree that they are, in some senses, strictly agnostic as well - the categories needn't be mutually exclusive.

> So yes, you can accept science and religion, but accepting the later can not be based on reason (because there is no logical method to disprove the existence of god)

Reason doesn't rely on falsifiability (science does, but science is a subset of reason, not the same thing as reason.)