Again, of arguments, some are true, and some are false. Those are true which deduce a conclusion from true premisses, as, for instance, “If virtue profits, then vice injures.” And those are false which have some falsehood in their premisses, or which are inconclusive; as, for instance, “If it is day, it is light; but it is day, therefore, Dion is alive.”
There are also arguments which are possible, and others which are impossible; some likewise which are necessary, and others which are not necessary. There are too, some which are not demonstrated from their not standing in need of demonstration, and these are laid down differently by different people; but Chrysippus enumerates five kinds, which serve as the foundation for every kind of argument; and which are assumed in conclusive arguments properly so called, and in syllogisms, and in modes.
The first kind that is not demonstrated, is that in which the whole argument consists of a conjunctive and an antecedent; and in which the first term repeats itself so as to form a sort of conjunctive proposition, and to bring forward as the conclusion the last term. As, for instance, “If the first be true, so is the second; but the first is true, therefore, so is the second.” The second kind that is not demonstrated, is that which, by means of the conjunctive and the opposite of the conclusion, has a conclusion opposite to the first premiss. As, for instance, “If it be day, it is light; but it is night, therefore it is not day.” For here the assumption arises from the opposite of the conclusion, and the conclusion from the opposite of the first term. The third kind that is not demonstrative, is that which, by a negative combination, and by one of the terms in the proposition, produces the contradictory of the remainder; as, for instance, “Plato is not dead and alive at the same time but Plato is dead; therefore, Plato is not alive.” The fourth kind that is not demonstrative, is that which, by means of a disjunctive, and one of those terms which are in the disjunctive, has a conclusion opposite to what remains; as, for instance, “It is either the first, or the second; but it is the first; therefore, it is not the second.” The fifth kind that is not demonstrative, is that in which the whole argument consists of a disjunctive proposition, and the opposite of one of the terms, and then one makes the conclusion identical with the remainder; as, for instance, “It is either day or night; but it is not night; therefore it is day.”