  In pages 15–59, a little more than half of the 82 pages in MAL, Boole focused on a slight generalization of Aristotelian logic, namely augmenting its four types of categorical propositions by permitting the subject and/or predicate to be of the form not-\(X\). In the chapter on conversions, such as Conversion by Limitation—All \(X\) is \(Y\), therefore Some \(Y\) is \(X\)—Boole found the Aristotelian classification defective in that it did not treat contraries, such as not-\(X\), on the same footing as the named classes \(X, Y, Z\), etc. For example, he converted No \(X\) is \(Y\) into All \(Y\) is not-\(X\), and All X is Y into All not-Y is not-X. 