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 premise 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 the major premise and one of the conjoined propositions for the minor premise, 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."
The fourth kind employs a disjunctive proposition and one of the two alternatives in the disjunction as premises, 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.
—Diogenes Laërtius, 7.80-81
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