On al-Jāḥiẓ’s account, falsehood in its stipulated sense requires both a report’s disagreement with reality and the speaker’s belief that it disagrees. Hence a factually mistaken statement made in sincere conviction falls outside this narrow definition of falsehood.
Suppose ʿAmr is not at the market, but the speaker believes that he is and asserts “ʿAmr is at the market.” The majority will call it false. For al-Jāḥiẓ, it lacks the belief condition of his complete falsehood category, opening the possibility of a third classification.