Preface paradox
Encyclopedia
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.
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, he has reason to believe that each assertion he has made is true.
(2) However, he knows, having learned from experience, that, in spite of his best efforts, there are very likely undetected errors in his book. So he also has good reason to believe that there is at least one assertion in his book that is not true.
Thus, he has good reason, from (1), to rationally believe that each statement in his book is true, while at the same time he has good reason, from (2), to rationally believe that the book contains at least one error. Thus he can rationally believe that the book both does and does not contain at least one error.
David Makinson
David Clement Makinson, D.Phil, , is an Australian mathematical logician living in London, England.- Career :Makinson began his studies at Sydney University in 1958 and was an associate of the Libertarian Society and Sydney Push...
in 1965. Similar to the lottery paradox
Lottery paradox
Henry E. Kyburg, Jr.'s lottery paradox arises from considering a fair 1000 ticket lottery that has exactly one winning ticket. If this much is known about the execution of the lottery it is therefore rational to accept that some ticket will win. Suppose that an event is very likely only if the...
, 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
Moore's paradox
Moore's paradox concerns the putative absurdity involved in asserting a first-person present-tense sentence such as 'It's raining but I don't believe that it is raining' or 'It's raining but I believe that it is not raining'. The first author to note this apparent absurdity was G.E. Moore...
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, he has reason to believe that each assertion he has made is true.
(2) However, he knows, having learned from experience, that, in spite of his best efforts, there are very likely undetected errors in his book. So he also has good reason to believe that there is at least one assertion in his book that is not true.
Thus, he has good reason, from (1), to rationally believe that each statement in his book is true, while at the same time he has good reason, from (2), to rationally believe that the book contains at least one error. Thus he can rationally believe that the book both does and does not contain at least one error.