Let us make up a logic in which there are three truth-values, T, F, and M, instead of the two truth-values T and F. And, instead of the usual rules, let us adopt the following:

1. (a) If either component in a disjunction is true (T), the disjunction is true; if both components are false, the disjunction is false (F); and in all other cases (both components middle, or one component middle and one false) the disjunction is middle (M).

2. (b) If either component in a conjunction is false (F), the conjunction is false; if both components are true, the conjunction is true (T); and in all other cases (both components middle, or one component middle and one true) the conjunction is middle (M).

3. (c) A conditional with true antecedent has the same truth-value as its consequent; one with false consequent has the same truth-value as the denial of its antecedent; one with true consequent or false antecedent is true; and one with both components middle (M) is true.

4. (d) The denial of a true statement is false; of a false one true; of a middle one middle.

These rules are consistent with all the usual rules with respect to the values T and F. But someone who accepts three truth values, and who accepts a notion of tautology based on a system of truth-rules like that just outlined, will end up with a different stock of tautologies than someone who reckons with just two truth values.