Is it logical for a Theological Noncognitivist to identify as an atheist?

[Pyrrho]

Atheism can also be defined as "lacking a belief in gods". By that definition, we are certainly atheists.

That is not a definition an igtheist would accept. According to igtheism, that has an undefined term in the definition, and is therefore meaningless.

Think about it. You are not going to say you don't believe in Säugetieren if you don't know what "Säugetieren" means, are you?

The prefix a- means without, or lacking, right? It's not an active position (as I see it) it's the lack of another active position. Of course it can optionally be made into an active position.

That's how I see it, anyhow. But as Pyrrho says, it comes down to exactly how you define words. Probably 75% of people in the world, including many atheists, don't even understand what atheist means anyway. (Atheists denying they are atheists, for one thing.) So I wouldn't worry too much, atheist is a good enough description for almost any conversation. Only when your discussion partners show a detailed understanding of the subject will it become necessary to clarify.

It only matters if one wishes to communicate one's exact position to others. Otherwise, one need not know what term(s) most accurately describe one. But if one does wish to communicate one's exact position with others, then having the right terms is extremely useful. Or is if the other person understands the terms. Otherwise, it will require explanation.