Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

The books of the Perihermeneias are so called as if one were to say “On Interpretation.” In them Aristotle treats principally of discourse and proposition. For this purpose it was necessary first to treat their parts, which are the noun and verb, and then their properties, such as opposition, equipollence, contingency, possibility, and the like. We treated these matters in the books of the Summulae, for all of them are ordered to and pertain to Prior-analytic resolution.

Nevertheless, because all these matters are treated in these books under the aspect of interpretation and signification—and since the common instrument of logic is the sign, on which all its instruments depend—it seemed appropriate here, for instruction in these books, to set out those matters concerning the nature and divisions of signs that were indicated in the Summulae but reserved for this place. These questions about signs are not proportioned to beginners. Here, however, they are introduced in their proper place, after knowledge has been acquired of a being of reason and the category of relation, on which this inquiry into the nature and quiddity of signs principally depends.

For clearer and fuller treatment, it seemed best to publish a separate treatise on this subject and not merely reduce it to the category of relation: first, so that the discussion of that category would not be made more tedious by the length added by this extraneous treatise; and second, so that the present inquiry would not be more confused and abbreviated.

Thus, two principal matters arise for discussion concerning the very notion of signs: first, the nature and definition of sign in general; second, its division and each kind in particular. We shall settle the first in this question and the second in the next.

First, however, for the use of students, we set down here Aristotle’s own text, condensed into a brief summary.

SUMMARY OF THE FIRST BOOK OF THE PERIHERMENEIAS.¹

In chapter 1 there are two parts. In the first, Aristotle promises to speak of the noun, the verb, the statement, and discourse. In the second, he teaches three things pertaining to the function of signifying, since signification is common to all of them. First, spoken words are signs of concepts, while written words are signs of spoken words. Second, writing and spoken words do not signify the same things for everyone, but the concepts and things signified by them are the same everywhere. Third, just as some concepts signify the true and others the false, so do spoken words.

In chapter 2 he does two things. In the first part he explains the definition of a noun; in the second he completes it by adding certain clauses. The definition of a noun is this: A noun is a spoken sound signifying by convention, without time, no part of which signifies separately. In the second part he adds that neither infinite nouns nor the oblique cases of nouns are nouns, because when joined to a verb they do not make a discourse true or false. Thus he adds two clauses: that it be finite and in the nominative case.

In chapter 3 he does two things. First, he proposes the definition of a verb; second, he adds two clauses to it. The definition of a verb is: A verb is a spoken sound signifying by convention, with time, no part of which signifies separately. Second, he excludes from the notion of a verb infinite forms and the oblique cases of verbs, just as he excludes them from the notion of a noun; thus he adds that it be finite and in the nominative case.

In chapter 4 he treats discourse, and the chapter is divided into three parts. In the first he defines and divides discourse; in the second he does the same concerning the statement; in the third he treats the opposition of statements. In the first part, the definition of discourse is as follows: Discourse is a spoken sound signifying by convention, some part of which signifies separately. It is divided into assertoric and non-assertoric discourse. In the second part he defines a statement as discourse signifying the true or the false. It is divided into simple and hypothetical; the simple is divided into affirmative and negative. In the third part he says that every negation is opposed to an affirmation, and conversely; this is a contradictory opposition, provided that it is of the same thing about the same thing and observes the other conditions.

In chapter 5 he first divides the statement on the side of quantity, then gathers several oppositions from the difference in quantity. The division is this: some propositions have a universal subject, as “Every man is just”; others have a particular subject, as “Some man is just.” There are three oppositions inferred from this division: contrary, when both propositions are universal; subcontrary, when both are particular; and contradictory, when one is universal and the other particular, as “Every man is just” and “Some man is not just.”

In chapter 6 he gives three rules concerning opposites. First: contraries can both be false, as “Every man is just” and “No man is just.” Second: subcontraries can both be true, as “Some man is just” and “Some man is not just.” Third: contradictories cannot both be true or both be false. Finally, he adds that indefinite propositions, such as “Man is white” and “Man is not white,” can both be true, as can contraries.

In the preceding chapter he had said that one negation is opposed to one affirmation. In chapter 7 he explains that one affirmation: the one in which one thing is affirmed of one thing, that is, of a signifying expression for one thing, as “Every man is white” or “Every man is not white,” affirmed or denied of man alone. But if one noun signifies several things, as in equivocal terms, there will be several negations or affirmations; for example, if one says, “A dog is a body.”

In chapter 8 he explains whether every proposition is determinately true or false, and he sets down two conclusions. First: In propositions about the present and the future, one proposition is necessarily determinately true and the other determinately false, both in universals and in singulars. Second: In propositions about a contingent future, one is indeterminately true and the other indeterminately false. He proves this because otherwise everything would happen necessarily if it were already determinately true, since the opposite could not occur; for then it could be made false, and thus it would not be determinately true.

SUMMARY OF THE SECOND BOOK.²

Aristotle does three things in chapter 1. He treats statements joined by the copula “is,” whether with the copula as second or third adjacent term. He divides them into finite and infinite statements. Finite statements have finite terms, while infinite ones have infinite terms, such as “non-man” and “non-stone.” He teaches that an inference from affirmative to negative, and conversely, is valid when finite terms are changed to infinite ones. Second, he teaches the same about statements with an adjectival verb. Third, after showing the incompatibility of statements, in order to explain further where that incompatibility is found, he specifies which of the enumerated propositions can be true together.

In chapter 2 Aristotle treats the second division of the statement: into one with a conjoined extreme and one with a simple, or divided, extreme. An extreme is conjoined when it has several parts or terms that are predicated; it is simple when only one term is predicated. He first distinguishes a simple statement from a conjoined one, then explains when an inference from a divided statement to a conjoined one is valid, and conversely. This pertains to the rules of appellation. The inference “Socrates is a man, and Socrates is white; therefore, he is a white man” is valid. But “Socrates is large, and Socrates is a physician; therefore, he is a large physician” is not valid, because appellation is lacking.

In chapter 3 he treats modal statements, which consist of the four modes: necessary, possible, contingent, and impossible. He does two things. First, he treats their opposition, which, he says, is to be considered more with respect to the negation and affirmation of the mode than of the verb. Second, he treats their equipollence. Rejecting the Stoic account, which did not divide it correctly, he establishes the account that we set out in the tables Amabimus, Edentuli, and so on, in Book 2, chapter 21, of the Summulae.

In chapter 4 he raises a question: Which propositions are more contrary? Those in which what is affirmed in one is denied of the subject in the other, or those in which two contraries are affirmed of the same subject, as “Every man is just” and “Every man is unjust”? He answers that the former are more contrary, because they proceed by affirmation and negation, and negation is always more opposed to affirmation.

CONCERNING THE BOOKS OF THE PRIOR ANALYTICS

Aristotle divides the first book of the Prior Analytics into three parts. In the first he sets out the foundations of the whole art of resolution and explains the method by which arguments are constructed, both in assertoric and in modal propositions; this extends from the first chapter through chapter 21. In the second part he treats the art of finding the middle term, from chapter 21 through chapter 42. In the third part, through the end of the book, he treats how syllogisms are to be resolved and examined according to a definite figure and mood.

In the second book, Aristotle treats the properties of syllogisms and divides it into three parts. In the first he treats the powers of syllogisms, from chapter 1 through chapter 17. Second, he treats the fallacies of syllogisms, which he reduces to six, and discusses them more fully in the books of the Topics and Sophistical Refutations. In the final part he treats how all other kinds of argumentation are reduced to syllogisms. There is no need to give a chapter-by-chapter summary of this second book.

SUMMARY OF THE FIRST BOOK.³

He does four things in chapter 1. First, he defines and divides a proposition. A proposition is defined as affirmative or negative discourse about something of something. It is divided into universal, particular, and indefinite; then into demonstrative, dialectical, and sophistical. Second, he defines a term as that into which a proposition is resolved, as into predicate and subject. Third, he defines a syllogism as discourse in which, certain things having been posited, something different necessarily follows because of those things. Fourth, he sets out two principles that govern syllogisms: 1. The principle of being said of every, that is, whatever is said of the predicate is said of the subject. 2. The principle of being said of none, that is, whatever is denied of the predicate is denied of the subject.

In chapter 2 he treats the conversion of absolute propositions. First he sets out three divisions of propositions: 1. Into modal and absolute. 2. Into affirmative and negative. 3. Into universal, particular, and indefinite. Second, he gives four rules of conversion: 1. A universal negative converts simply. 2. A universal affirmative converts per accidens, or to a particular. 3. A particular affirmative converts simply. 4. A particular negative converts only by contraposition.

In chapter 3 he gives three rules for the conversion of modal propositions. 1. Affirmative propositions de inesse with an affirmed mode convert like absolute propositions. 2. Propositions about possibility convert like propositions about necessity. 3. Propositions about contingency that signify indifference to either side convert as absolute propositions if affirmative; if negative, the universal does not convert simply, but the particular does.

In chapter 4 he treats the first figure and explains its useful and useless moods. He completes the account of useful moods with two rules. 1. When both premises are universal, if the middle term is affirmed of the minor extreme in the minor premise, while the major extreme is predicated universally of the middle term, affirmatively or negatively, there are two useful moods: Barbara and Celarent. 2. When one premise is universal and the other particular, with the major universal, affirmative or negative, and the minor particular affirmative, two useful moods result: Darii and Ferio.

In chapter 5 he does two things: 1. He explains the nature of the second figure, namely, that it is the figure in which the middle term is predicated in both premises. 2. He distinguishes the useful and useless moods of this figure. There are four useful moods. First, when both premises are universal: if the major is negative, the mood is Cesare; if the minor is negative, it is Camestres. When one premise is universal and the other particular, if the minor is particular affirmative and the major universal negative, the mood is Festino; if the reverse, it is Baroco. The remaining moods are useless.

In chapter 6 he treats the third figure and explains two things: 1. Its nature, namely, that in it the middle term is subject in both premises. 2. He distinguishes the useful and useless moods. There are six useful moods: 1. From two universal affirmative premises, Darapti. 2. From a universal negative major and a universal affirmative minor, Felapton. 3. From a particular affirmative major and a universal affirmative minor, Disamis. 4. From a universal affirmative major and a particular affirmative minor, Datisi. 5. From a particular negative major and a universal affirmative minor, Bocardo. 6. From a universal negative major and a particular affirmative minor, Ferison. The remaining moods are useless.

In chapter 7 he proposes five rules for a fuller understanding of the three figures. 1. If both premises are particular, nothing is concluded. 2. If the major is affirmative, whether universal or particular, and the minor is negative, an indirect particular conclusion is always inferred, as in Fapesmo and Frisesomorum. 3. To posit a particular affirmative in syllogisms is the same as positing an indefinite one. 4. All imperfect syllogisms are reduced to perfect syllogisms of the first figure, either ostensively or by impossibility. 5. All moods, including Darii and Ferio, can be reduced to the first two, Barbara and Celarent, by first reducing them per impossibile. Darii and Ferio are reduced to moods of the second figure—Darii to Camestres and Ferio to Cesare—by taking the opposite of the conclusion as the minor premise. Those two, Cesare and Camestres, are then reduced to Barbara and Celarent.

From chapter 8 through chapter 21 Aristotle treats modal syllogisms, namely, those consisting of the modes necessary, possible, and contingent. There is no need to discuss them in particular here.

In chapters 22 and 23 he shows that there are only three figures of syllogisms.

In chapter 24 he shows that one premise must necessarily be affirmative; in chapter 25, that there must be only three terms; in chapter 26, that there must be only two premises.

From chapter 27 through chapter 32 he treats the method of finding a middle term suitable for inferring a conclusion.

From chapter 32 through the end of the book he treats the resolution of syllogisms both into their form—that is, into the proper figure and mood—and into their matter, whether proximate, which consists of propositions, or remote, which consists of terms. No special difficulty arises concerning these matters. Let this suffice as a summary explanation of the text of these books.

We shall give a summary of the text concerning the books of the Posterior Analytics below, while treating questions about them.