 Jevons, who had studied with De Morgan, was the first to offer an alternative to Boole’s system. In 1863 he wrote to Boole that surely Boole’s operation of addition should be replaced by the more natural ‘inclusive or’ (or ‘union’), leading to the law \(X + X = X\). Boole completely rejected this suggestion (it would have destroyed his system based on ordinary algebra) and broke off the correspondence. Jevons published his system in his 1864 book, Pure Logic (reprinted in Jevons 1890). By ‘pure’ he meant that he was casting off any dependence on the algebra of numbers—instead of classes, which are associated with quantity, he would use predicates, which are associated with quality, and his laws would be derived directly from the (total) fundamental operations of inclusive disjunction and conjunction. But he kept Boole’s use of equations as the fundamental form of statements in his algebra of logic.