These laws or properties differ from the properties of binary operations in arithmetic. It will be noted, however, multiplication (homologous to meet) is idempotent for two numbers: 0 * 0 = 0 and 1 * 1 = 1, and addition (homologous to join) is idempotent for one of them: 0 + 0 = 0, but 1 + 1 > 1. (The significance of numbers 0,1 is soon noted.).

In statement logic (homologous to "Boolean algebra"), these idempotent laws apply to disjunction, conjunction of statements. This logic is Chrysippian or bivalent in arguing that any statement is exclusively either TRUE or FALSE -- values representable, respectively, as 1, 0 -- the only numbers brought into this subject. Since TRUE disjuncted with TRUE cannot be twice as TRUE, the deviation from arithmetic addition must follow.

The property of idempotency follows from application of the commutative, associative, absorption laws. Since the first two laws are homologous to arithmetic ones, this singles out absorption as the most significant property of this mathematical field, compared to arithmetic.