Lives of Eminent Philosophers VII.79-81

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Further, arguments may be divided into true and false. The former draw their conclusions by means of true premisses; e.g. If virtue does good, vice does harm; but virtue does good, therefore vice does harm. Those are false which have error in the premisses or are inconclusive; e.g. If it is day, it is light; but it is day, therefore Dion is alive. Arguments may also be divided into possible and impossible, necessary and not necessary. Further, there are statements which are indemonstrable because they do not need demonstration; they are employed in the construction of every argument. As to the number of these, authorities differ; Chrysippus makes them five. These are assumed alike in reasoning specifically conclusive and in syllogisms both categorical and hypothetical.

Referencing norms: FiveIndemonstrablesExhaustive, Inference, Proposition, conclusion_requested, licensed_conclusion, major_premise, minor_premise

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The first kind of indemonstrable statement is that in which the whole argument is constructed of a hypothetical proposition and the clause with which the hypothetical proposition begins, while the final clause is the conclusion; as e.g. If the first, then the second; but the first is, therefore the second is. The second is that which employs a hypothetical proposition and the contradictory of the consequent, while the conclusion is the contradictory of the antecedent; e.g. If it is day, it is light; but it is night, therefore it is not day. Here the minor premiss is the contradictory of the consequent; the conclusion the contradictory of the antecedent. The third kind of indemonstrable employs a conjunction of negative propositions for major premiss and one of the conjoined propositions for minor premiss, concluding thence the contradictory of the remaining proposition; e.g. It is not the case that Plato is both dead and alive; but he is dead, therefore Plato is not alive.

Referencing norms: FirstIndemonstrable, FiveIndemonstrablesExhaustive, SecondIndemonstrable, ThirdIndemonstrable, is_conditional, is_conjunction, is_negation_of

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The fourth kind employs a disjunctive proposition and one of the two alternatives in the disjunction as premisses, and its conclusion is the contradictory of the other alternative; e.g. Either A or B; but A is, therefore B is not. The fifth kind is that in which the argument as a whole is constructed of a disjunctive proposition and the contradictory of one of the alternatives in the disjunction, its conclusion being the other alternative; e.g. Either it is day or it is night; but it is not night, therefore it is day. From a truth a truth follows, according to the Stoics, as e.g. It is light from It is day; and from a falsehood a falsehood, as It is dark from It is night, if this latter be untrue. Also a truth may follow from a falsehood; e.g. from The earth flies will follow The earth exists; whereas from a truth no falsehood will follow, for from the existence of the earth it does not follow that the earth flies aloft.

Referencing norms: DiogenesFifthReading, FifthIndemonstrableDiogenes, FiveIndemonstrablesExhaustive, FourthIndemonstrable, is_exclusive_disjunction