Johnathan Harrison has argued that "incorrigible" may be the wrong term, since it seems to imply (by the dictionary definition) a sense that the beliefs cannot be changed, which isn't actually true. In Harrison's view, the incorrigibility of a proposition actually implies something about the nature of believing---for example, that one must exist in order to believe---rather than the nature of the proposition itself.
For illustration, consider Descartes': I think, therefore I exist. Stated in incorrigible form, this could be: "That I believe that I exist implies that my belief is true." Harrison argues that a belief being true is really only incidental to the matter, that really what the cogito proves is that belief implies existence. One could equally well say, "That I believe God exists implies that I exist," or "That I believe I do not exist implies that my belief is false."---and these would have the same essential meaning as the cogito.
Charles Raff draws a distinction between three types of incorrigibility:
It should be noted that type-2 and type-3 incorrigibility are logical converses, and therefore logically independent. Charles Raff argues that introspection is not type-1 incorrigible, but is in fact type-2 and type-3 incorrigible.