From PhilPapers forum PhilPapers Surveys:

2009-12-13
Theism, Atheism, Agnosticism?
Reply to Noam Zohar
Theism can safely be taken to be the belief that God, as traditionally conceived by Jews, Christians and Muslims, exists. Atheism is the belief that theism is false. Indeed, some dictionaries go this way and in contexts like the survey the terms are unlikely to mislead.

But it is much harder to know what position ‘agnosticism’ denotes. It is often defined as the view that we cannot know whether theism or atheism is correct. Suppose I believe that theism is false, because I think all the evil and trouble in the world make theism’s truth so unlikely that disbelief is warranted. So I’m an atheist. But suppose I also believe that I cannot positively know that theism is false–I hold that we cannot positively know such things one way or the other. (There are, surely, things I'm entitled to believe that I don't know, e.g. that I won't be run over by a bus today.)
Then I’m also an agnostic, which seems wrong. Atheism and agnosticism are supposed to exclude one another.

I believe this problem led Russell to say that he was an agnostic, while cautioning that his version of agnosticism would strike many people as atheism.

Or suppose that I have no opinion one way or another about these matters, but I don’t believe that we cannot know whether theism is true or false. Perhaps there are arguments in books somewhere that positively prove theism or perhaps prove atheism. Further, I can imagine events that, if they happened, would decide the matter. For example, suppose tomorrow morning the trumpet blows, the dead rise, and so on. That would settle things as far as I’m concerned. Then I am not an agnostic, even though I have no opinion one way or the other about theism, because I don’t believe that we cannot know that theism is true or false.

So it’s pretty unclear what agnosticism amounts to. One wants it to exclude theism and atheism, but on the standard definition, it doesn’t. Nor does it necessarily include people who have no opinion one way or another about religious matters.