“In every affirmative proposition the predicate is taken particularly,” and it is not also required that it be true.
2. “In a negative proposition the predicate is taken universally” or is distributed, for a negation is understood to be false if any part of the predicate may be truly affirmed of the subject.
3. The quantity of subjects is understood from the signs prefixed [to them]. Hence in A, the subject is universal, and the predicate is particular. In E, both are universal. In I, both are particular. In O, the subject is particular, and the predicate is universal.
Only those propositions are said to be universal in which the subject is distributed, and a predicate is affirmed or denied of the individual things which are covered by the common word. This is not the case when the predicate is [made up] of several [things] collectively: thus, All men are mortal is universal, but not the following: All men form one state; all the apostles were twelve.
Propositions about kinds of individuals are in a certain sense universal; e.g., Every animal was in Noah’s ark, or, the Gospel has been preached to men of all nations.
Here it is said that certain individuals of each kind were in the ark or have heard the Gospel, but these things are not predicated separately of every individual or of each individual in the kinds.
CHAPTER 4
These are the axioms about universals:
1. “Whatever is affirmed of a distributed subject (that is, [of a subject] universally taken) may be affirmed of all the inferiors which are contained in its extension.”
2. “Whatever is denied of a distributed subject can equally be denied of all its inferiors.” These two in combination are the dictum de omni et nullo; on this depend both subalternation and the force of the syllogism, which we shall discuss later.5
CHAPTER 5
Some propositions are simple, others complex; simple [propositions] “denote one single judgment”; complex [propositions] “denote more than one judgment.”
Among complex propositions, the modal propositions are preeminent [which are] “when something is both predicated and the mode of its connection with the subject is made clear.” There are four modes: the necessary, the impossible, the possible, and the contingent.6 But generally modal [propositions] are simple [propositions], or signify a single judgment of a speaker. For they are ambiguous. Sometimes they merely affirm or deny the statement itself more emphatically, as in saying, “God most certainly exists” or “Certainly no man is immortal.” Sometimes the proposition itself, which is called the statement, is the subject, and the mode is predicated of it, as in saying, “the Divine existence is necessary,” or “God is, is a necessary proposition”; and similarly with the other modals.
In the same way it is shown that the four kinds [of modal propositions], which might appear from their names to be complex, are simple, namely: (1) conditional [propositions]; (2) disjunctive [propositions]; (3) negative copulative [propositions]; and (4) relative [propositions].
In a conditional or hypothetical [proposition] there are two parts, the antecedent and the consequent: for example, if God exists, the world is governed by providence. Neither of these is asserted; it is merely asserted that they are connected. Hence this [proposition] also is equally true: If there were no God, there would be no providence.
In disjunctive [propositions] the whole subject is said to be included in two connected predicates; for example, it is either day or night means the same as all time is included in daytime and nighttime.7
In negative copulative [propositions] it is denied that both the predicates are compatible with the subject at the same time: it is not both day and night; i.e., no time is both daytime and nighttime.
In relative [propositions] the terms may be complex, but the judgment is single, namely, that the reasons (rationes) are equal or unequal.
The true complex propositions therefore are (1) copulative, (2) causal, (3) adversative, (4) exclusive, (5) inceptive, and (6) desitive;8 and they are easy to learn.
CHAPTER 6
Some propositions or judgments are abstract, “in which from the comparison of ideas itself, there is seen or shown to be a relationship apart from any consideration of time”; hence they are said to be eternal and unalterable truths.
Other propositions are absolute; they assert that a thing is, was or will be at a certain time, or ascribe a common accident to it as existing at a certain time.
Abstract affirmative propositions, in which ideas are not only viewed in themselves but are related to objects, are all hypothetical and merely predicate attributes on the hypothesis that the thing exists. An absolute conclusion can only be deduced from absolute premisses, and abstract conclusions from abstract [premisses].
Other propositions are [self-]evident; here, by a power natural to the mind, “a certain relation or connection is perceived among the terms in themselves.” Nor is there any other criterion of truth.9 Other [propositions] are probable, when connection of that kind is not certain. And others are manifestly false.
CHAPTER 7
The relative states (affectiones) of propositions are subalternation, conversion, and opposition.
1. Subalternation is “the deduction of a particular proposition from a universal [proposition]”; the former is called the subalternating [proposition], the latter the subalternated; for example, Every man is an animal, therefore, Some man is an animal. This is clear from the dictum de omni. “But from a particular to a universal [proposition] there is no inference.”
2. Conversion is “the transposition of the subject into the place of the predicate.” The given proposition is called the convertend, and the derived proposition the converse. And since every relation, likeness, or equality is mutual, the consequence will be valid provided that the same terms are used in the converse with the same extension and with the same temporal relation (ratio).
Conversion is threefold. It is either (i) simpliciter, “when the same quantity of propositions is kept”: no A is B and no B is A; or (ii) it is per accidens, “when the convertend is universal and the converse is particular”: as in, all A is B, some B is A; or (iii) by contraposition, “when the negations [of the terms] are put in the place of the terms and are transposed”: as in, Every man is an animal, therefore, that which is not-animal is not-man.10
Universal negative and particular affirmative [propositions] are converted simpliciter. Universal affirmative [propositions], as well as [universal] negative [propositions], may be converted per accidens; and it is only in this way that [universal] affirmative [propositions] can [be converted], because their predicates are particular.
Universal affirmative [propositions] and particular negative [propositions] [can be converted] by contraposition: Some man is not European, therefore, some not-European is not a not-man, i.e., is a man.
E and I are converted simpliciter, E or A per accidens,
A and O per contra; that’s all there is to conversion.11
The value of these [conversions] lies in proving the validity of syllogisms, and in perfecting them.
3. Opposition of propositions is said to be complex. Opposed propositions are “two propositions which affirm and deny the same predicate about the same subject, in accordance with the same thing, in the same manner, at the same time.”
There are three kinds of opposed [propositions], namely, contradictory, contrary, and subcontrary. Subaltern [propositions] do not conflict.
Contradictory [propositions] are those “of which one is universal, the other particular, one is affirmative, the other negative”; or which are opposed in quantity and quality, as, A and O, E and I.
Contrary [propositions] are “two universal [propositions], one affirmative, the other negative,”