The Lives and Opinions of Eminent Philosophers Diogenes Laërtius (first ebook reader .TXT) 📖

through a rock.”⁠ ⁠… And of categorems, some are direct, some indirect, and some neither one nor the other. Now those are correct which are construed with one of the oblique cases, in such a manner as to produce a categorem, as for instance, “He hears, he sees, he converses.” And those are indirect which are construed with the passive voice, as for instance, “I am heard, I am seen.” And those which are neither one nor the other are those which are construed in a neutral kind of manner, as for instance, “To think, to walk.” And those are reciprocal which are among the indirect ones without being indirect themselves. Those are effects, ἐνεργήματα, which are such words as “He is shaved;” for then, the man who is shaved, implies himself.

The oblique cases are the genitive, the dative, and the accusative.

An axiom is that thing which is true, or false, or perfect in itself, being asserted or denied positively, as far as depends upon itself; as Chrysippus explains it in his Dialectic Definitions; as for instance, “It is day,” “Dion is walking.” And it has received the name of axiom, ἀξίωμα, because it is either maintained, ἀξιοῦται, or repudiated. For the man who says, “It is day,” appears to maintain the fact of its being day. If then it is day, the axiom put before one is true; but if it is not day, the axiom is false. And an axiom, a question, and an interrogation, differ from one another, and so does an imperative proposition from one which is adjurative, or imprecatory, or hypothetical, or appellative, or false. For that is an axiom which we utter, when we affirm anything positively, which is either true or false. And a question is a thing complete in itself, as also is an axiom, but which requires an answer, as for instance “Is it day?” Now this is neither true nor false; but, as “It is day” is an axiom; so is “Is it day?” a question. But an interrogation, πύσμα, is a thing to which it is not possible to make an answer symbolically, as in the case of a question, ἐρώτημα, saying merely “Yes,” but we must reply, “He does live in this place.”

The imperative proposition is a thing which we utter when we give an order, as for instance this:

Do you now go to the sweet stream of Inachus.85
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The appellative proposition is one which is used in the case in which when a man says anything, he must address somebody, as for instance:

Atrides, glorious king of men,
Most mighty Agamemnon.86

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