A false judgment is a proposition, which, while it has at the same time the appearance of a real judgment, loses this character by the addition, and under the influence of, some particle, as for instance:
The Parthenon at least is beautiful.
How like the herdsman is to Priam’s sons.
There is also the dubitative proposition, which differs from the judgment, inasmuch as it is always uttered in the form of a doubt; as for instance:—
Are not, then, grief and life two kindred states?[87]
But questions, and interrogations, and things like these, are neither true nor false, while judgments and propositions are necessarily one or the other.
Now of axioms, some are simple, and others are not simple; as Chrysippus, and Archedemus, and Athenodorus, and Antipater, and Crinis, agree in dividing them. Those are simple, which consist of an axiom or proposition, which is not ambiguous, (or of several axioms, or propositions of the same character,) as for instance the sentence, “It is day.” And those are not simple, which consist of an axiom or proposition which is ambiguous, or of several axioms or propositions of that character. Of an axiom, or proposition, which is ambiguous, as “If it is day;” of several axioms, or propositions of that character, as, “If it is day, it is light.”
And simple propositions are divided into the affirmative, the negative, the privative, the categorical, the definite, and the indefinite; those which are not simple, are divided into the combined, and the adjunctive, the connected and the disjunctive, and the causal and the augmentative, and the diminutive. That is an affirmative proposition, “It is not day.” And the species of this is doubly affirmative. That again is doubly affirmative, which is affirmative of an affirmative, as for instance, “It is not not day;” for this amounts to, “It is day.” That is a negative proposition, which consists of a negative particle and a categorem, as for instance, “No one is walking.” That is a privative proposition which consists of a privative particle and an axiom according to power, as “This man is inhuman.” That is a categorical proposition, which consists of a nominative case and a categorem, as for instance, “Dion is walking.” That is a definite proposition, which consists of a demonstrative nominative case and a categorem, as for instance, “This man is walking.” That is an indefinite one which consists of an indefinite particle, or of indefinite particles, as for instance, “Somebody is walking,” “He is moving.”
Of propositions which are not simple, the combined proposition is, as Chrysippus states, in his Dialectics, and Diogenes, too, in his Dialectic Art; that which is held together by the copulative conjunction “if.” And this conjunction professes that the second member of the sentence follows the first, as for instance, “If it is day, it is light.” That which is adjunctive is, as Crinis states in his Dialectic Art, an axiom which is made to depend on the conjunction “since” (ἐπεὶ), beginning with an axiom and ending in an axiom, as for instance, “Since it is day, it is light.” And this conjunction professes both that the second portion of the proposition follows the first, and the first is true. That is a connected proposition which is connected by some copulative conjunctions, as for instance, “It both is day, and it is light.” That is a disjunctive proposition which is disconnected by the disjunctive conjunction, “or” (ἤτοι), as for instance, “It is either day or night.” And this proposition professes that one or other of these propositions is false. That is a causal proposition which is connected by the word, “because;” as for instance, “Because it is day, it is light.” For the first is, as it were, the cause of the second. That is an augmentative proposition, which explains the greater, which is construed with an augmentative particle, and which is placed between the two members of the proposition, as for instance, “It is rather day than night.” The diminutive proposition is, in every respect, the exact contrary of the preceding one; as for instance, “It is less night than day.” Again, at times, axioms or propositions are opposed to one another in respect of their truth and falsehood, when one is an express denial of the other; as for instance, “It is day,” and, “It is not day.”
Again, a conjunctive proposition is correct, when it is such that the opposite of the conclusion is contradictory of the premiss; as for instance, the proposition, “If it is day, it is light,” is true; for, “It is not light,” which is the opposite to the conclusion expressed, is contradictory to the premiss, “It is day.” And a conjunctive proposition is incorrect, when it is such that the opposite of the conclusion is not inconsistent with the premiss, as for instance, “If it is day, Dion is walking.” For the fact that Dion is not walking, is not contradictory of the premiss, “It is day.”