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,” which conflict in quality, not in quantity, like A and E.
Subcontrary [propositions] are “two particular [propositions], one affirmative, the other negative”; they too are in conflict by quality alone, like I and O. Since they are often both true at the same time, namely when they have contingent content, they are not truly opposed.
The rules of opposition are: (1) “of contradictories, one is always true, the other false”; this is the major opposition. (2) “Contraries are never at the same time true, but are sometimes both false at the same time,” i.e., with contingent content. (3) “Subcontrary [propositions] are never false at the same time.” If it is false that some man is learned, it will not be false that some man is not learned, since the contradictory of the former is true.12
CHAPTER 1
When the relation or connection of two ideas or terms cannot be directly perceived, the relation between them will often be able to be seen by a comparison of both of them with some third or middle [idea or term] or with several middle [ideas or terms] which are clearly connected with each other. This mental process is dianoetic judgment or discourse.
When there is only one middle, we are said to have a syllogism; when there are several middles connected with each other, by which the comparison of the terms is made, it is a sorites, or complex form of reasoning.1 First, therefore, we must deal with the simple and categorical syllogism, for the other more complex forms may be reduced to syllogisms.
A syllogism is “discourse in which a third proposition is inferred from two propositions rightly arranged.”
Before a proof is given by means of a syllogism, there is a question or problem of showing the relationship between two terms. These terms are called the Extremes; they are the Major term and the Minor term. The Major term is “the predicate of the question” or of the conclusion, and the Minor term is “the subject of the question.” The Middle Term is that which is compared with both of the extreme terms in the premissed propositions.
Irrespective of the content of the syllogism, there are these three terms: the Major, the Minor, and the Middle Terms. Taking account of the content, there are three propositions: the Major Proposition, the Minor Proposition (these are also called the Premisses), and the Conclusion. They are distinguished not by their order but by their nature.
1. The major proposition “is that in which the major term is compared with the middle term” and is called the proposition par excellence.
2. The minor proposition is that “in which the minor term is compared with the middle term” and is called the assumption or subsumption.
3.
