Directly and conclusively verified, not subject to any further tests. A class of so-called basic statements or propositions that are descriptive of present contents of experience (for example, “I have a headache”) are generally regarded as incorrigible in so far as they express nothing about which one could be uncertain or mistaken.
Such statements may, however, be false, even when the claim is sincere, not because experience itself can be in any way fallible but because it might be misidentified or incorrectly formulated in words.
(from A Dictionary of Philosophy, Rev. 2nd ed., ed. Antony Flew, 166-167)
Another common example of an incorrigible belief is Descartes’s “cogito ergo sum”: I think, therefore I am.