The Preface Paradox
Many authors introduce their books with a caution: it is inevitable that somewhere in this book there is an error. This is a common claim in prefaces. But do the authors that write these claims believe them or not?
If the author is asked of each specific claim in the book Is this an error? then he will say No. For each individual claim that the author makes, he believes that it is true.
If the author believes that each claim is true, though, then mustn’t he believe that every claim is true? A collection of claims, none of which is an error, contains no errors. The author believes that his book is a collection of such claims; he believes that it contains no errors.
Yet the author also believes that somewhere in the book he will have made a mistake. Aware of his fallibility, he believes that not every claim in the book is true, that somewhere in the book there is an error.
What is really odd about this is not that authors have inconsistent beliefs, it is that the author is being perfectly rational in believing both that his book does and does not contain errors.