In Moralia, the Greek biographer and philosopher Plutarch states "Chrysippus says that the number of compound propositions that can be made from only ten simple propositions exceeds a million. (Hipparchus, to be sure, refuted this by showing that on the affirmative side there are 103049 compound statements, and on the negative side 310952.)" These numbers are known as the Plutarch numbers. 103049 can be interpreted as the number s_10 of bracketings on ten letters . Similarly, Plutarch's second number is given by (s_10 + s_11)/2 = 310954 .