Which immunity to error?

A self-ascription is a thought or sentence in which a predicate is self-consciously ascribed to oneself. Self-ascriptions are best expressed using the first-person pronoun. Mental self-ascriptions are ascriptions to oneself of mental predicates (predicates that designate mental properties), non-mental self-ascriptions are ascriptions to oneself of non-mental predicates (predicates that designate non-mental properties). It is often claimed that there is a range of self-ascriptions that are immune to error through misidentification relative to the first-person pronoun (IEM for short). What this means, and exactly which self-ascriptions are properly classed as IEM, is a topic hotly disputed. Some claim that only mental self-ascriptions are IEM, others claim that some non-mental self-ascriptions are IEM. Before this question can be decided, it needs to be judged exactly what it means to say that a self-ascription is IEM. And here we stumble across the fact that there are, at least, two non-equivalent ways of defining the phenomenon1. I will be claiming that one of these definitions should be rejected.