Greek Texts & Translations

Of conclusive some are denoted by the common name of the whole class, "conclusive proper," others are called syllogistic. The syllogistic are such as either do not admit of, or are reducible to such as do not admit of, immediate proof in respect of one or more of the premisses ; e.g. "If Dion walks, then Dion is in motion ; but Dion is walking, therefore Dion is in motion." Conclusive specifically are those which draw conclusions, but not by syllogism ; e.g. the statement "It is both day and night" is false : "now it is day ; therefore it is not night." Arguments not syllogistic are those which plausibly resemble syllogistic arguments, but are not cogent proof ; e.g. "If Dion is a horse, he is an animal ; but Dion is not a horse, therefore he is not an animal."

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." ^note 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. 7.1.80 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." ^note 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." 7.1.81 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.

There are also certain insoluble arguments ^note: the Veiled Men, the Concealed, Sorites, Horned Folk, the Nobodies. The Veiled is as follows ^note : . . . "It cannot be that if two is few, three is not so likewise, nor that if two or three are few, four is not so ; and so on up to ten. But two is few, therefore so also is ten." . . . The Nobody argument is an argument whose major premiss consists of an indefinite and a definite clause, followed by a minor premiss and conclusion ; for example, "If anyone is here, he is not in Rhodes ; but there is some one here, therefore there is not anyone in Rhodes." . . .

Such, then, is the logic of the Stoics, by which they seek to establish their point that the wise man is the true dialectician. For all things, they say, are discerned by means of logical study, including whatever falls within the province of Physics, and again whatever belongs to that of Ethics. For else, say they, as regards statement and reasoning Physics and Ethics could not tell how to express themselves, or again concerning the proper use of terms, how the laws have defined various actions. ^note

Moreover, of the two kinds of common-sense inquiry included under Virtue one considers the nature of each particular thing, the other asks what it is called. Thus much for their logic.