Error theory is a cognitivist form of moral nihilism. It is the view that ethical statements can be propositions, but that all ethical propositions are false (or cannot be true) — that we are generally in error when we make any moral statement.
There are generally two forms of error theory, which depend on the semantic reason for our error in making ethical statements. Global falsity holds that all ethical statements are false propositions.
Presupposition failure alternatively holds that the statements are not explicitly false, but are certainly not true because the statements themselves make false presuppositions about morality (namely, that morality exists). Similarly one may state that “the aliens on the moon have purple hats”, which is logically a proposition but suffers from a presupposition failure, by assuming that there are aliens on the moon, which is false¹. On some accounts, this presents the statement from being false.
¹ I hope.