  Secondary propositions were Boole’s version of the propositions that one encounters in the study of hypothetical syllogisms in Aristotelian logic, statements like If \(X\) is true or \(Y\) is true then \(Z\) is true. The symbols \(X, Y, Z\), etc. referred to primary propositions. In keeping with the incomplete nature of the Aristotelian treatment of hypothetical propositions, Boole did not give a precise description of possible forms for his secondary propositions.