 The key (but not original) observation that Boole used was simply that one can convert secondary propositions into primary propositions. In MAL he adopted the convention found in Whately (1826), that given a propositional symbol \(X\), the symbol \(x\) will denote the cases in which \(X\) is true, whereas in LT Boole let \(x\) denote the times for which \(X\) is true. With this the secondary proposition If \(X\) is true or \(Y\) is true then \(Z\) is true is expressed by All \(x\) or \(y\) is \(z\). The equation \(x = 1\) is the equational translation of \(X\) is true (in all cases, or for all times), and \(x = 0\) says \(X\) is false (in all cases, or for all times). The concepts of all cases and all times depend on the choice of the universe of discourse. 