Philosophy
Authors can rationally believe their book is both entirely checked and definitely wrong
Book prefaces often thank reviewers while admitting 'any errors that remain are my own.' Philosopher David Makinson noticed an author can rationally believe every single claim in their carefully checked book, while also believing, from experience, that some claim in it is false. That's two directly contradictory beliefs, both held reasonably at the same time.
— D. C. Makinson, The Paradox of the Preface — Analysis, 1965