 Note that this algebra restricted the values of the variables to 0 and 1, but placed no such restriction on the values of terms. There was no assertion that this was to be a two-element algebra. Burris and Sankappanavar (2013)  viewed the quote as saying that this algebra was just the ordinary  algebra of numbers modified by restricting the variables to the values 0 and 1  to determine the validity of an argument. They called this  Boole’s Rule of 0 and 1,  and said he used this Rule to justify three of his main theorems  (Expansion, Reduction, Elimination). These main theorems  along with the Solution Theorem yielded Boole’s General Method for discovering the strongest possible consequences of propositional premises under certain desired constraints (such as eliminating some of the variables). Further comments on this  Rule are below in Section 5.2. 