or implication, n. (Logic) 1. the binary truth-functional sentential connective that assigns the value false to a compound sentence only when its first argument (the antecedent) is true and the second (the consequent) is false, and the value true otherwise, without consideration of relevance etc.; its truth-table is The closest approximation in natural language is if... then.... See material conditional. 2. a compound sentence formed with this connective, written `P → Q' or `P ⊃ Q', where P is the antecedent and Q the consequent; a conditional statement. 3. the relationship that holds between an ordered pair of sentences when there are no circumstances in which the first is true and the second false. 4. paradoxes of material implication. a number of inferential patterns that follow immediately from the definition: a falsehood materially implies any statement whatever, and anything whatever materially implies a truth. Compare strict implication.