Atheism is lack of belief in gods. Some atheists will go as far as claim in some form that there are no gods, others won't. On atheist sites I frequented, the terms "strong atheist" and "weak atheist" were adopted for distinction when the philosophical battles raged.
Agnosticism is the opinion that the existence of gods is unknowable. There are differences regarding whether it is practically or theoretically unknowable, and what "to know" means. (The way you defined it, with "knowledge", implies a rather extreme form I rarely encountered.) Non-agnostics usually also reject agnosticism on the basis of one or another different concept of "to know" and "proof".
Theists, weak atheists, and strong atheists each can be either agnostic or non-agnostic. I met with ardent proponents of all six variants. But all six encompass a number of very different views. To just take non-agnostic strong atheists who'd seem a single strang to many: some think science disproves theism, others that the very definition of "god" is nonsensical, others are convinced of a general theory of the cultural genesis of religions, still others argue that a statement is false by default unless its maker presents proof (which in the case of gods didn't happen), yet again others make the Moral Argument (God is supposed to be moral + the world is immoral => God doesn't exist), still others argue with internal contradictions.
Myself, I am a non-agnostic weak atheist. (I won't detail my rejection of the various forms of strong atheism, as well as of agnosticism, but false dichotomies and special pleading to save what would be trivialisms would feature prominently.)
Actually, even the above classification doesn't encompass 'em all. Some atheists argue that belief is not the issue (the Sun is a god in some religions but we others still believe the Sun exists), worship is. *Lunatic*, n. One whose delusions are out of fashion.
Weak atheist: you don't believe in god, but don't say there isn't one non-agnostic: it's possible to know whether god exists.
How can you both know and not know if god exists? In the long run, we're all dead. John Maynard Keynes
I don't believe in unicorns, but I accept it's possible someone could produce one. I don't not believe in unicorns, not do I believe it's impossible to prove they exist.
I'm not being entirely frivolous here: there are possible positive proofs that something god-like could exist - depending on your definition of god.
you don't believe in god, don't know if there is one of not, but are willing to be convinced either way if a good proof comes along.
That's me as well, then. What were we arguing about, exactly, throughout the day? In the long run, we're all dead. John Maynard Keynes
whistle, whistle,
has the teacher gone, Colman?
Here take that, and you DoDO, buh, argh, uff, autsch
with regards to Jerome,
wouldn't know - don't feel competend to comment
...
hehe, another funny comment, as if that had ever stopped me...
Making a decision.
I am a weak atheist who even has time for the religious gnostic argument, that you can know the truth of a religion by faith. Only: as all kinds of religions have believers who think faith was a route to Truth for them, which one to try first?
Similarly, as long as none of them seems more well-founded than a couple of others, you don't need to pose 'absolute' standards of proof for various gods and religions.
A further issue is whether you see the knowability of the existence of gods as a question different from say the knowability of the existence of Saturn or giant squids or fairies or toothbrushes (and that would lead to a whole discussion about the meaning of "to know"). *Lunatic*, n. One whose delusions are out of fashion.
Oh, sorry about that, I haven't even noticed (and put it better the second time without even realising I used a different word :-)) - it was sloppiness on my part. (On the other hand, in my experience, those emphasizing their agnosticism tend to call atheism a belief and vice versa - while some of both call their own views a knowledge which is an even stronger claim.) *Lunatic*, n. One whose delusions are out of fashion.