Judgments and Propositions

a) The Judgment

Judging is the operation of mind which results in the judg ment. The judgment is the pronouncement of the mind on the agreement or disagreement of two ideas.

Ideas agree in so far as their respective comprehensions are not in conflict, and also in so far as their subjects or inferiors are found in the same field of extension. In so far as their respective comprehensions are not the same, or not compatible, and also in so far as their subjects or inferiors cannot be classed in the same field of extension, they are said to disagree.

Thus the judgment “man is mortal” is a pronouncement (made upon the investigation of the comprehension or inner meaning of the ideas man and mortal being) that man is contained in the field of extension of mortal being. In other words, it is a pronouncement of the fact that man is the subject or inferior of the idea mortal being, and consequently it enunciates mortal being of man as predicate is enunciated of subject. This pronouncement is an affirmative judgment The judgment “man is not a spirit” is a negative judgment.

We must here briefly recall what we learned in some detail when we studied the logic of Aristotle (Part First, Chap. II, Art. 2, b), that is, the doctrine on the predicables.

When the mind judges it pronounces, it predicates; it declares that a subject-idea (or inferior) is contained or is not contained in the extension of a predicate-idea. Thus in the judgment “man is mortal,” the mind pronounces or judges that the things meant by man are also in the extension (or field of meaning) of the idea mortal being, and that therefore man (taken in extension as all actual and possible human beings) is the subject or inferior of which mortal being is a proper predicate.

Now, when the predicate-idea exactly defines the subject-idea (as in the judgment, “man is a rational animal”) the predicate- idea is called the species of the subject-idea, and the predication is specific. When the predicate-idea expresses part of the subject- idea and that part which the subject-idea has in common with other ideas, the predicate-idea is called the genus of the subject- idea, and the predication is generic; for example, “man is an animal.” When the predicate-idea means (or expresses within the mind) that part of the subject-idea which differentiates it from other ideas with which it has a common genus, the predicate idea is called the specific difference of the subject-idea, and the predication is differential; for example, “man is rational.” When the predicate-idea means no part of the subject-idea but expresses what naturally belongs to the subject-idea, the predicate-idea is called the property or the attribute of the subject-idea, and the predication is proper; for example, “man is risible (that is, a- being-that-can-laugh).” When the predicate-idea expresses or means what may happen to be true of the subject-idea, although it is no part of it nor anything naturally belonging to it, the predicate-idea is called the accident of the subject-idea, and the predication is accidental; for example, “man is a reading animal.”

These then are the predicables: species, genus, specific difference, property or attribute, and accident Note well and remember: the predicables are modes of predication, of judging; they are not modes of being or classes of things.

As we have noticed elsewhere, the judgment is marked by truth or falsity. When the judgment of the mind squares with reality, the judgment has what is called logical truth. When the judgment is mistaken; when, as a fact, the predicate-idea is enunciated of a subject-idea with which it is not in agreement, or when the predicate-idea is denied of a subject-idea with which it is in agreement, the judgment has logical falsity. Remember: truth and falsity are things to be assigned to judgment, not to ideas or concepts.

b) Th e Proposition

The operation of apprehending produces the idea, and the idea is outwardly expressed by the term. Now, the operation of judging produces the judgment, and the judgment is outwardly expressed by the proposition. The proposition is therefore a formula of terms which expresses the agreement or disagreement of a predicate-idea with a subject-idea. The subject-idea is expressed in a term called simply the subject; the predicate-idea is expressed in a term called the predicate; the pronouncement of agreement or disagreement is expressed in the copula, that is, the present tense of the verb to be, used affirmatively or negatively.

A proposition is categorical if it is a straight affirmation or denial; it is hypothetical if it enunciates a dependency of one proposition on another without actually affirming or denying either. Thus, “man is an animal” is a categorical proposition; “if man has sentient life, he is an animal” is a hypothetical proposition. A categorical proposition is simple if it contains one predication; otherwise it is compound. Further, a categorical proposition is affirmative or negative according as the copula is “is” or “is not.” A categorical proposition is absolute if it enunciates the agreement or disagreement of subject and predicate and nothing more; if it tells how they agree or disagree (that is, possibly, necessarily, contingently, impossibly) it is modal: “a circle is round” is an absolute proposition; “a circle is necessarily round” is a modal proposition. Finally, a proposition is universal when its subject is in full extension (“All men are mortal”) ; it is particular when its subject is in partial extension (“Some men are foolish” ) ; it is indefinite when its subject has no expressed extension (“Men are sentimental”) ; it is singular when its subject is a singular term (“This man is angry” ; “John is ill” ). For convenience in handling propositions without the cumbrous titles, the various types of propositions are reduced to four, and these are labelled by letters. We must say a word in explanation of this_

Since we have mentioned four types of propositions on the

1 7 6 basis of quantity or extension (universal, particular, indefinite, and singular) and since what is called the quality of a proposition is twofold (affirmative, negative), it seems that the types of categorical and absolute propositions should number twice four or eight. Yet we reduce the total to four in this way: in respect of quantity, propositions are really universal or particular; for the singular proposition uses its subject in full extension since it has an extension of only one, and it is thus equivalent to a universal proposition; and the indefinite proposition is readily interpreted as either universal or particular. Thus, in the singular proposition “John is ill,” the subject John is in full extension, and the proposition is equivalent to a universal proposition, since having the subject in full extension is the definition of a universal proposition. And the indefinite propositions, “Man is mortal,” “Men are musical” are readily interpreted by the mind to mean, “All men are mortal” (which is a universal proposition) and “Some men are musical” (which is a particular proposition). Therefore, for purposes of logic we declare that there are but four types of categorical absolute propositions, since there are two quantities (universal, particular) and two qualities (affirmative, negative). Thus we have the following propositions:

The universal affirmative, called the A-proposition: “All men are musical” ; The universal negative, called the E-proposition: “No men are musical” ; The particular affirmative, called the I-proposition: “Some men are musical” ; The particular negative, called the O-proposition: “Some men are not musical.”

A proposition for the purposes of logic must b ern logical form. That is, it must be in the present tense, indicative mood, and the verb must be the copula (the verb to be). Thus, “John said he liked music as a child” is made to read, “John is a-person-who- said-he-liked-music-as-a-child.” The entire phrase “a person who said he liked music as a child” is a single term which serves as the predicate of the proposition. In passing, it is hoped that the student will instantly notice that here the mode of predication is accidental.

c) Properties of Propositions

A property of a proposition is something which naturally belongs to a proposition. There are three notable properties of propositions; they are functionable uses or simply functions which the proposition may be made to serve. These functions are useful for they help us to test the full meaning of a proposition, to see all its implications, to make immediate inference of points not noticed at first, and they often enable us to indicate at once the fallacy of a mistaken statement. The running of a proposition through the functions called its properties is a kind of shake-up or analysis which may be a great aid to clear and exact thinking.

The three notable properties of propositions are these, (a) A proposition may be contrasted with its opposites; (b) it may be expressed in equivalent terms; (c) it may, under definite conditions, have its subject and predicate change places. These three properties of propositions are called respectively, opposition, equipollence, and conversion. (a) Opposition of Propositions.—Opposition of propositions is that quality of propositions which renders them capable of contrast with their opposites.

The opposite of a proposition is another proposition which has the same subject and the same predicate, but which differs in quantity (extension of subject) or in quality (character of copula as affirmative or negative) or in both. There are four types of opposites : contradictory propositions, contrary propositions, subcontrary propositions, subaltern propositions.

Contradictory propositions differ in quality (one affirmative, one negative) and also in quantity (one universal, one particular). These propositions are perfectly opposed. They exhaust the possibilities, and so one of them must be true and the other

1 78

false. Contradictory propositions are “A—O” and “E—I.” For example, “All men are musical—Some men are not musical” ; “No men are musical—Some men are musical.”

Contrary propositions are two universal propositions which differ only in quality. They are “A—E.” “All men are musical— No men are musical.” Contraries cannot both be true, but both may be false.

Subcontrary propositions are two particular propositions which differ only in quality. They are “I—O.” “Some men are musical—Some men are not musical.” Subcontraries may both be true, but both cannot be false.

Subaltern propositions are two propositions which differ only in quantity. One is universal and one particular, but both are affirmative or both are negative. They are “A—I” and “E—O.” The universal proposition is the subalternant; the particular proposition is the subalternate. “All men are musical—Some men are musical” ; “No men are musical—Some men are not musical.” If the subalternant is true the subalternate is true, but not vice versa; if the subalternate is false the subalternant is false, but not vice versa.

The opposition of propositions is graphically shown in what is called “The Square of Opposition” or “The Logical Square”:

The Square of Opposition relates the four categorical proposition types. At the corners: A (“All are”), E (“Not any are”), I (“Some are”), O (“Some are not”). The top side (A—E) shows Contrariety: two universal propositions that cannot both be true but can both be false. The bottom (I—O) shows Subcontrariety: two particular propositions that cannot both be false but can both be true. The sides (A—I, E—O) show Subalternation: the universal implies the particular. The diagonals (A—O, E—I) show Contradiction: one is true iff the other is false.

(6) Equipollence of Propositions.—Equipollence means equivalence. It is the property of a proposition which renders it capable of being expressed in equivalent terms. But it has a narrower meaning than this in our present use of it It means the property of a proposition which makes it the equivalent of its opposite by the inserting of negative particles.

To make a proposition the equivalent of its contradictory, insert a negative before the subject Thus, “All men are musical— Not all men are musical.” The second proposition is equivalent to “Some men are not musical.”

To make a universal proposition the equivalent of its contrary, insert a negative before the predicate. Thus, “All men are musical —All men are no/-musical.” The second proposition is equivalent to “All men are unmusical” or “No men are musical.”

To make a particular proposition the equivalent of its subcontrary, follow the same rule as with contraries; insert a negative before the predicate. Thus, “Some men are musical—Some \nen are not musical.”

To make a proposition the equivalent of its subaltern, insert a negative before the subject and also before the predicate. Thus, “All men are musical—Not all men are not musical.” The second proposition is equivalent to “Not all men are unmusical” or “Some men are musical.” Similarly, “Some men are musical— Not some (i.e., any) men are not musical.” The second proposition is equivalent to “Not any men are unmusical” or “All men are musical.”

(c) Conversion of Propositions.—Conversion is the property of A- E- and I-propositions (not of O-propositions) which justifies the mind in putting the subject in the place of the predicate and the predicate in the place of the subject, certain rules being carefully observed.

The rules of conversion are two: there must be no change of quality: affirmatives convert to affirmatives, and negatives to negatives; and there must be no expanding of the extension or denotation of terms. The second rule means that we are not allowed to say more in the converted proposition (called the con verse) than is justified by the original proposition (called the convert end). We may say less in the converse than is said in the convertend, but not more. The reason for the two rules is manifest : it consists in the fact that the converse is taken from the convertend, and therefore must not express anything other or anything more than can be found in the convertend.

When a proposition converts to its own type, we have simple conversion; when it converts to another type, we have accidental conversion. A-propositions convert accidentally; E- and I-propo- sitions convert simply; E-propositions also convert accidentally. As a practical guide, remember the following:

(1) A- converts to /-. Example: “All men are musical— Some musical beings are men.”

(2) E~ converts to E- and E- converts to 0-. Example: “No men are musical—No musical beings are men” ; “No men are musical—Some musical beings are not men.”

( j) 7- converts to /-. Example: “Some men are musical— Some musical beings are men.”

(4) 0 - is not convertible.

An O-proposition cannot be converted without violating the rule which forbids the expanding of terms; therefore, O- is not convertible.

Summary of the Article

In this Article we have studied the second major operation of the mind, that is, judging, and the judgment which is the product of the operation. We have noted that the basis of the judgment is the comparison and analysis of two ideas. We have also seen that judging means predicating, and we have called to mind the five possible modes of predicating, called The Predicables. We have studied the expression of the judgment, that is, the propo sition; we have distinguished various types of propositions,