I'm looking for an adjective which suggests that the noun it modifies can't support or justify itself, thinking mainly in terms of an argument. There is "self-defeating", but this isn't the sense I'm looking for. I don't want to suggest that the argument has proved itself wrong, but rather it has failed to prove itself right.
E.g.
A.J. Ayer's verification principle is [failing to support itself] because the statement "Only verifiable statements are meaningful" is not itself verifiable."