In his book The Enterprise of Knowledge, Isaac Levi makes a distinction between infallibility and incorrigibility and remarks that many authors, among them Peirce, do not seem to be aware of the difference. Levi's distinction is made in the context of his discussion of fully justified belief, or “knowledge as a standard for serious possibility.”

To be (epistemologically) infallible about a piece of knowledge is to ascribe maximum certainty to it, in the sense that anything inconsistent with it will not be regarded as a serious possibility. According to Levi, we are entitled to claim infallibilism for a certain corpus of knowledge that extends beyond logical, analytical, mathematical, and other a priori truths.

To claim incorrigibility for a piece of knowledge is to claim that we will never change our mind about it, that it will still belong to our corpus of knowledge no matter what new evidence will come across. It is permanent, rather than maximum certainty.

Levi's standpoint is that although we are entitled to disregard certain possibilities as not being serious (and hence to claim epistemological infallibility about their negations), we must still allow the possibility that we will change our mind in the future, that is, we must not claim incorrigibility.

In the latter respect, he agrees with common morality, which, at least in scientific contexts, is to be prudent about one's conclusions and to admit the possibility of being mistaken and therefore to admit corrigibility about anything that is not a priori.