Greek Texts & Translations

A denial contains a negative part or particle and a predication : such as this, "No one is walking." A privative proposition is one that contains a privative particle reversing the effect of a judgement, as, for example, "This man is unkind." An affirmative or assertory proposition is one that consists of a noun in the nominative case and a predicate, as "Dion is walking." A definitive proposition is one that consists of a demonstrative in the nominative case and a predicate, as "This man is walking." An indefinitive proposition is one that consists of an indefinite word or words and a predicate, e.g. "Some one is walking," or "There's some one walking"; "He is in motion."

Of propositions that are not simple the hypothetical, according to Chrysippus in his Dialectics and Diogenes in his Art of Dialectic, is one that is formed by means of the conditional conjunction "If." Now this conjunction promises that the second of two things follows consequentially upon the first, as, for instance, "If it is day, it is light." An inferential proposition according to Crinis in his Art of Dialectic is one which is introduced by the conjunction "Since" and consists of an initial proposition and a conclusion ; for example, "Since it is day-time, it is light." This conjunction guarantees both that the second thing follows from the first and that the first is really a fact. 7.1.72 A coupled proposition is one which is put together by certain coupling conjunctions, e.g. "It is day-time and it is light." A disjunctive proposition is one which is constituted such by the disjunctive conjunction "Either," as e.g. "Either it is day or it is night." This conjunction guarantees that one or other of the alternatives is false. A causal proposition is constructed by means of the conjunction "Because," e.g. "Because it is day, it is light." For the first clause is, as it were, the cause of the second. A proposition which indicates more or less is one that is formed by the word signifying "rather" and the word "than" in between the clauses, as, for example, "It is rather day-time than night." 7.1.73 Opposite in character to the foregoing is a proposition which declares what is less the fact, as e.g. "It is less or not so much night as day." Further, among propositions there are some which in respect of truth and falsehood stand opposed to one another, of which the one is the negative of the other, as e.g. the propositions "It is day" and "It is not day." A hypothetical proposition is therefore true, if the contradictory of its conclusion is incompatible with its premiss, e.g. "If it is day, it is light." This is true. For the statement "It is not light," contradicting the conclusion, is incompatible with the premiss "It is day." On the other hand, a hypothetical proposition is false, if the contradictory of its conclusion does not conflict with the premiss, e.g. "If it is day, Dion is walking." For the statement "Dion is not walking" does not conflict with the premiss "It is day."

An inferential proposition is true if starting from a true premiss it also has a consequent conclusion, as e.g. "Since it is day, the sun is above the horizon." But it is false if it starts from a false premiss or has an inconsequent conclusion, as e.g. "Since it is night, Dion is walking," if this be said in day-time. A causal proposition is true if its conclusion really follows from a premiss itself true, though the premiss does not follow conversely from the conclusion, as e.g. "Because it is day, it is light," where from the "it is day" the "it is light" duly follows, though from the statement "it is light" it would not follow that "it is day." But a causal proposition is false if it either starts from a false premiss or has an inconsequent conclusion or has a premiss that does not correspond with the conclusion, as e.g. "Because it is night, Dion is walking." 7.1.75 A probable judgement is one which induces to assent, e.g. "Whoever gave birth to anything, is that thing's mother." This, however, is not necessarily true ; for the hen is not mother of an egg.

Again, some things are possible, others impossible ; and some things are necessary, others are not necessary. A proposition is possible which admits of being true, there being nothing in external circumstances to prevent it being true, e.g. "Diocles is alive." Impossible is one which does not admit of being true, as e.g. "The earth flies." That is necessary which besides being true does not admit of being false or, while it may admit of being false, is prevented from being false by circumstances external to itself, as "Virtue is beneficial." Not necessary is that which, while true, yet is capable of being false if there are no external conditions to prevent, e.g. "Dion is walking."