Doubting that there are any examples of P is not, so to speak, Carol’s job. The claim is that E is an example of P. The only reason Carol has for thinking that there are examples of P (excepting cases where P is something well-known, of which there are obviously many examples) is that Dave has described E to the reader. Once E is disqualified, Carol is back to having no particular reason to believe that there are any examples of P.
It seems to me that there’s likely to be enough cases where there are differences in opinion about whether P is well-known enough that examples aren’t needed, or whether P isn’t well-known but whether the reader upon hearing a definition could think of examples themselves, that it’s useful to have norms whereby we clarify whether or not we doubt that there examples of P.
All of the cases I am thinking of are those where P is a new concept, which the author is defining / describing / “crystallizing” for the first time. As such, it seems unlikely that this sort of edge case would apply.
It seems to me that there’s likely to be enough cases where there are differences in opinion about whether P is well-known enough that examples aren’t needed, or whether P isn’t well-known but whether the reader upon hearing a definition could think of examples themselves, that it’s useful to have norms whereby we clarify whether or not we doubt that there examples of P.
All of the cases I am thinking of are those where P is a new concept, which the author is defining / describing / “crystallizing” for the first time. As such, it seems unlikely that this sort of edge case would apply.