correspondence theory of truth See TRUTH. corresponding conditional (of a given argument), any conditional whose antecedent is a (logical) conjunction of all of the premises of the argument and whose consequent is the conclusion. The two conditionals, ‘if Abe is Ben and Ben is wise, then Abe is wise’ and ‘if Ben is wise and Abe is Ben, then Abe is wise’, are the two corresponding conditionals of the argument whose premises are ‘Abe is Ben’ and ‘Ben is wise’ and whose conclusion is ‘Abe is wise’. For a one-premise argument, the corresponding conditional is the conditional whose antecedent is the premise and whose consequent is the conclusion. The limiting cases of the empty and infinite premise sets are treated in different ways by different logicians; one simple treatment considers such arguments as lacking corresponding conditionals. The principle of corresponding conditionals is that in order for an argument to be valid it is necessary and sufficient for all its corresponding conditionals to be tautological. The commonly used expression ‘the corresponding conditional of an argument’ is also used when two further stipulations are in force: first, that an argument is construed as having an (ordered) sequence of premises rather than an (unordered) set of premises; second, that conjunction is construed as a polyadic operation that produces in a unique way a single premise from a sequence of premises rather than as a dyadic operation that combines premises two by two. Under these stipulations the principle of the corresponding conditional is that in order for an argument to be valid it is necessary and sufficient for its corresponding conditional to be valid. These principles are closely related to modus ponens, to conditional proof, and to the so-called deduction theorem. See also ARGUMENT, CONDITIONAL , CON- DITIONAL PROOF, LIMITING CASE , MODUS PONENS , PROPOSITION , TAUTOLOGY. J.Cor.