Preface paradox

The preface paradox, or the paradox of the preface, was introduced by David Makinson in 1965. Similar to the lottery paradox, it presents an argument according to which it can be rational to accept mutually incompatible beliefs. While the preface paradox nullifies a claim contrary to one's belief, it is opposite to Moore's paradox which asserts a claim contrary to one's belief.

Overview

The argument runs along these lines:

It is customary for authors of academic books to include in the preface of their books statements such as "any errors that remain are my sole responsibility." Occasionally they go further and actually claim there are errors in the books, with statements such as "the errors that are found herein are mine alone."

(1) Such an author has written a book that contains many assertions, and has factually checked each one carefully, submitted it to reviewers for comment, etc. Thus, they have reason to believe that each assertion they have made is true.

(2) However, they know, having learned from experience, that, despite their best efforts, there are very likely undetected errors in their book. So they also have good reason to believe that there is at least one assertion in their book that is not true.

Thus, they have good reason, from (1), to rationally believe that each statement in their book is true, while at the same time they have good reason, from (2), to rationally believe that the book contains at least one error. Thus they can rationally believe that the book both does and does not contain at least one error.

Attempted solutions

In classical deductive logic, a set of statements is inconsistent if it contains a contradiction.