(Sorry for the long delay)

Ah, I see why you're arguing now.

(And an idea that works for central examples but fails for edge cases is an idea that fails.)

Ironically, this is not a universal criteria for the success of ideas. Sometimes its a very useful criteria (think mathematical proofs). Other times, its not a very useful idea (think 'choosing friends' or 'mathematical intuitions').

For example the idea of 'cat' fails for edge cases. Is this a cat? Sort of. Sort of not. But 'cat' is still a useful concept.

Concepts are clusters in thing space, and the concept that I am pointing at is also a cluster.

Isn't this kind of like the Aumann agreement theorem?

Are there any humans who meet that lofty standard?

There are certainly people who meet it better than others.