 The answer is simple: the law \(x + x = x\) would have destroyed his ability to use ordinary algebra: from \(x + x = x\) one has, by ordinary algebra, \(x = 0\). This would force every class symbol to denote the empty class. Jevons’s proposed law \(x + x = x\) was simply not true if one was committed to constructing the algebra of logic on top of the laws and inference rules of ordinary algebra. (Boolean rings satisfy all the laws of ordinary algebra, but not all of the inferences, for example, \(2x = 0\) implies \(x = 0\) does not hold in Boolean rings.) It seems quite possible that Boole found the simplest way to construct a model—whose  domain was classes contained in the universe of discourse—for an algebra of logic that allowed one to use all the equations and equational arguments that were valid for numbers. 