Lives and Opinions of Eminent Philosophers

​A logotropos (argument-mood) is that which is compounded of both, for example: "If Plato lives, Plato breathes; but indeed the first; therefore the second." The logotropos was introduced in order that in longer compositions of arguments one might no longer state the additional premise (minor premise), being long, and the conclusion, but concisely conclude: "And the first; therefore the second." Of arguments, some are non-conclusive, while others are conclusive. Non-conclusive are those in which the contradictory of the conclusion does not conflict with the conjunction formed by the premises, such as the following: "If it is day, there is light; and it is day; therefore Dion walks."

​Of conclusive arguments, some are called conclusive homonymously with the genus, while others are syllogistic. Syllogistic arguments, then, are those which are either indemonstrable or reducible to the indemonstrables according to one or more of the logical themes (rules), such as the following: "If Dion walks, Dion moves; but indeed Dion walks; therefore Dion moves." And specifically conclusive arguments are those which draw a conclusion non-syllogistically, such as the following: "It is false that it is day and it is night; and it is day; therefore it is not night." And asyllogistic arguments are those which plausibly resemble the syllogistic ones, but do not validly conclude, for example: "If Dion is a horse, Dion is an animal; but indeed Dion is not a horse; therefore Dion is not an animal."

​Furthermore, of arguments some are true, others false. True arguments, then, are those that conclude through true premises, for example: "If virtue is beneficial, vice is harmful; but indeed virtue is beneficial; therefore vice is harmful." False arguments are those that have some falsehood among the premises or are non-conclusive, for example: "If it is day, there is light; and it is day; therefore Dion lives." Arguments are also possible, impossible, necessary, and not necessary. Some are also called indemonstrable, through not needing demonstration; different writers reckon different numbers of them, but Chrysippus recognizes five, through which every argument is woven; and these are employed in the case of conclusive arguments, syllogisms, and categorical/mood forms.

​The first indemonstrable is that in which the entire argument is composed of a conditional and the antecedent with which the conditional begins, and infers the consequent as conclusion, for example: "If the first, the second; but indeed the first; therefore the second." The second indemonstrable is that which, by means of a conditional and the contradictory of the consequent, has the contradictory of the antecedent as its conclusion, for example: "If it is day, there is light; but indeed it is night; therefore it is not day;" for the additional premise comes from the contradictory of the consequent, and the conclusion from the contradictory of the antecedent. The third indemonstrable is that which, by means of a negative conjunction and one of the conjuncts in the conjunction, infers the contradictory of the remainder, for example: "Not: Plato has died and Plato lives; but indeed Plato has died; therefore Plato does not live."

​The fourth indemonstrable is that which, by means of a disjunctive proposition and one of the disjuncts in the disjunction, has the contradictory of the remainder as its conclusion, for example: "Either the first or the second; but indeed the first; therefore not the second." The fifth indemonstrable is that in which the entire argument is composed of a disjunctive proposition and one of the opposing terms in the disjunction, and infers the remainder, for example: "Either it is day or it is night; but it is not night; therefore it is day." According to the Stoics, truth follows upon truth, as upon "It is day" follows "There is light;" and upon falsehood follows falsehood, as upon the false proposition "It is night" follows "There is darkness;" and upon falsehood follows truth, as upon "The earth flies" follows "The earth exists." Upon truth, however, falsehood does not follow; for upon "The earth exists," "The earth flies" does not follow.