Agnosticism is at its base an admission of the inability to know of the existence of God. It's saying I don't have the information or the faith to make that leap or decision.
It is not the tautology you describe above, because, as you so cogently point out, that would mean an a priori acknowledgement of God's existence. Agnostics, in whose number I currently count myself, as a rule don't seem to have that much information that they feel comfortable in making such an assertion. You will, of course, find some who do, just as you will find Jews for Jesus. But philosophically it would be a difficult position to justify. It doesn't play by the linguistic rules of the philosophy game.
There is perhaps a similar problem with atheists.
But one must wonder to what extent these folks have had the chance to name themselves, and to what extent they may have been named by others who had unkind feelings toward them. These are at any rate the names that have come down to us. Skeptics have been trying to figure out what to call themselves for years now, without much luck, since being a skeptic and having a skeptical attitude should not be tied to thought about religion, but may usefully be applied to, say, politics as well, and matters of budget, and the gathering of data in general.
Being skeptical out to be a decent thing, not something seen as an assault on religion or on God; but there you have it, another word bent out of shape, and people don't know how to bend it back.
With your response to my post, I am almost entirely in agreement.
But even the empiricism assumed by science was never derived empirically, but was and is taken as first principle, on faith. I think we've discussed that before though.
I believe we have discussed this before. I believe I'm trying to make a different point here. I'm drawing an analogy between the various types of mathematics and the various types of philosophical systems. I am saying that each starts out with a set of givens or presuppositions upon which the system is built, and that the system derives from those presuppositions. In Geometry, Euclid designed a system that meant that parallel lines never met. That was a supposition, even a theorem of the system. In Riemann's Geometry, parallel lines do meet. There are also base ten mathematics and base two mathematics.
None of these things are wrong, they are simply different ways of looking at the same set of information. They start from different presuppositions and are often used for different things. How people arrive at the presuppositions doesn't particularly matter, as long as they describe actual data of one sort or another, and bring some order to it that others can understand and duplicate and use.
This is why it is not necessary for empiricism to be empirically derived. It is necessary for it only to be usefully formulated, to supply useful and reproducible data that others can understand and duplicate and use. In the case of empiricism, it has an added advantage of helping to build a view of the world that makes the world more understandable.
Its limitation is that nobody has thought to do research on matters of the soul and spirit, and that many who do empirical research — not believing in these concepts — tend to be hostile to the concept of such research. It's certainly a potential career killer. And the more religious folks are ambivalent about such research anyway. For all sorts of reasons both rational and not.
Anyway, this is probably more of a response than you were looking for, but here it is anyway.
My best to you and your family,