Agnostic = "Without knowledge"

So such a person would claim to have no knowledge, yet still for some (to me, inexplicable, hence the thread) reason, still believes one way or the other anyway?

What is the motivation or point of believing something without basing it on anything you even personally think is knowledge? That just seems deeply internally contradictory to me.

Several categories make perfect sense from where I sit, but not the classic four. I see no issue with:

• Agnosticism, period (rendering theism irrelevant due to no basis for belief if already claimed no knowledge)

• Gnostic theism

• Gnostic atheism

• "SEMIgnostic" atheism/theism would also both make sense: "I see SOME things as knowable evidence for or against a god, other things I don't know, but the some are enough for me to commit." Although if you forced me to use only the traditional terms, I would have to classify these as "gnostic" since "some knowledge" clearly fits much better with the category "those claiming knowledge" than "those claiming no knowledge" and it's logically what most people generally mean by "gnostic" already anyway, unless they're claiming to be omniscient...

But not "agnostic theism" or "agnostic atheism". If you're agnostic, you cannot, by definition, have any of those some things upon which to base a probability or estimate. The concept of probabilities or likelihoods is simply undefined/nonsensical in the absence of any evidence at all.

I know several people have flairs that combine what I see here as mutually exclusive things. Please explain?

Edit: Have been convinced by argument that atheism is just "Not(theism)" rather than "Anti-theism" and therefore also includes lack of belief either way. Thanks!

Edit 2: Apparently the above is actually in dispute. Okay, sure. Feel free to argue other points if desired, under the supposition it does mean "anti-theism" if you like, and I will still be interested.