The Attributive Proposition

Before treating of the attributive proposition, we shall give a brief explanation of the proposition in general.

A proposition is defined as a statement in which anything whatsoever is affirmed or denied. In some propositions the simple existence of a subject is affirmed or denied, as in “God exists” and “Troy is no longer.” In some, an attribute is affirmed or denied of a subject, as in “A dog is an animal” and “A dog is not a cat.” In some, again, relationships, or connections, between member propositions are affirmed or denied, as in “If it is raining, the ground is probably wet” and “It is not because he is a Republican that he will not be elected.”

A proposition is expressed by what grammarians call a declarative sentence, and must be distinguished from a question, exclamation, wish, command, and entreaty. The following are not propositions: “What is a platyhelminth?,” “Ouch!,” “May God grant them peace!,” “Do it immediately!,” and “Please come.” These are not propositions because in them nothing whatsoever is either affirmed or denied.

A proposition may also be defined as discourse that expresses either truth or falsity. A proposition is the only kind of discourse that can be true or false in the strict sense, and every proposition is the one or the other. If things actually are as a proposition says they are, it is true; if things are not as it says they are, it is false. Hence, a proposition is the only kind of discourse that you believe, assume, prove, refute, doubt, or deny. “What is a platyhelminth?,” “Ouch!,” and so on, are neither true nor false; you can neither believe, assume, prove, refute, doubt, nor deny them. There are many kinds of propositions—existential and nonexistential, simple and compound, categorical and hypothetical, causal, inferential, and so on and so on—but for the present we shall treat only of the ATTRIBUTIVE OR CATEGORICAL PROPOSITION.

An attributive, or categorical, proposition is defined as a proposition in which a predicate (P) is affirmed or denied of a subject (S). It has three basic elements: the subject, the predicate, and the copula. The SUBJECT is that about which something is affirmed or denied. The logical subject of a proposition is not always the same as its grammatical subject. Take the example, “We should elect Smith. The grammatical subject of this proposition is “we.” The logical subject, though (at least in many contexts), is “the one we should elect.” In this proposition we are not affirming something about we. Rather, we are telling who it is that we should elect. The one we should elect,” then, is that about which something is affirmed or denied.

The PREDICATE of an attributive proposition is what is affirmed or denied of the subject.

The COPULA is either “is (am, are)” or “is (am, are) not.” If the copula is “is,” the proposition is affirmative; if the copula is “is not, the proposition is negative. Affirmative and negative are the two kinds of QUALITY that a proposition can have.

In the affirmative proposition the copula joins, unites, or “copulates, the predicate with the subject; the subject is declared to exist (at least with mental existence) as something identical with the predicate; and the entire comprehension of the predicate is attributed to, or drawn into, the subject. Thus, when we say “A dog is an animal,” we declare that “a dog” and “ (some) animal” are identical, that the entire comprehension of “animal” belongs to “dog,” and that to exist as a dog is to exist as an animal.

In the negative proposition the copula separates, or divides, the predicate from the subject. The identity of the subject and predicate are denied, and an indeterminate portion of the comprehension of the predicate is excluded from the subject, or vice versa. In other words, the subject and predicate of a negative proposition may have many notes, or intelligible elements, in common; but their comprehension must differ in at least one respect; each must either have an attribute that the other does not have or lack an attribute that the other has. A dog, for instance, is not a cat. Yet both a dog and a cat are substances, bodies, organisms, animals, vertebrates, mammals, and so on; finally, however, you come to differences that make a dog a dog rather than some other animal, and a cat a cat rather than something else; in the notes that are distinctive of each, a dog and a cat must differ.

For a proposition to be negative, the negative particle must modify the copula itself. If the negative particle modifies either the subject or the predicate, but not the copula, the proposition is affirmative. Thus, “Those who have not been vaccinated are likely to get smallpox” and “He who is not with me is against me” are affirmative propositions because the “not” belongs to the subject and does not modify the copula. The following are examples of negative propositions:

• • • • • • • • 1. Socrates is not sick.

                2. Some man is not seated.

                3. No cat has nine tails.

                4. None of the students will go.

                5. He will never go.

Notice that in Example 3 we are not affirming something of a being called “no cat,” but are denying something of every cat. Similarly in Example 4 we are not affirming something of a being called “none,” but are denying something of every student. Hence, since Numbers 3 and 4 deny something of a subject, they are both negative propositions.

Note that the copula does not always imply the actual real existence of a subject. For instance, the proposition “A chiliagon is a polygon of a thousand angles” does not assert that such a figure actually exists in the real order. All it says is that a chiliagon as conceived in the mind is such a figure. However, if a chiliagon exists in the real order, it will exist there as a polygon having a thousand angles.

The mental operation by which we affirm or deny anything whatsoever is called JUDGMENT. The study of judgment belongs to psychology and epistemology rather than to logic. Logic is concerned with the mental proposition, which is the internal product that the act of judgment produces within the mind, and with oral and written propositions insofar as they are signs of mental propositions, but not with judgment itself

The quantity, or extension, of a proposition is determined by the quantity, or extension, of the subject term. A proposition is SINGULAR if its subject term is singular, standing for one definitely designated individual or group; it is PARTICULAR if its subject term is particular, standing for an indeterminately designated portion of its absolute extension; and UNIVERSAL if its subject term is universal, standing for each of the subjects that it can be applied to.

If the subject term is INDETERMINATE—that is, if it is not modified by any sign of singularity (“this,” “that,” and so on), particularity (“some”), or universality (“all,” “every,” “each”)-the proposition too is indeterminate; you must decide by the sense whether it is to be regarded as singular, particular, or universal. For instance, “a man” is universal (at least implicitly) in “A man is a rational animal,” but particular in “A man is laughing loudly.” In the fust example a man stands for man as such and therefore includes every man; but in the second example it stands for one individual man designated indeterminately.

Propositions like “Germans are good musicians” and “Mothers love their children are general propositions. A general proposition expresses something that is true in most instances or on the whole. The proposition “Germans are good musicians” means that Germans on the whole, or as a group, are good musicians and is not to be regarded as false because some German here or there is not a good musician. And the proposition “Mothers love their children” is not false because some abnormal mothers do not love their children. Since general propositions admit of exceptions without destroying their truth, they are particular rather than universal.

Usually you can tell for certain whether an indefinite proposition is singular, particular, or universal. In case of doubt, however, you should assume that it is particular and thus avoid attempting to draw more out of your premises than may actually be in them.

We remind you again that many terms, and therefore many propositions, that are singular from the point of view of grammar are particular or universal from the point of view of logic; thus, in the proposition “Man is mortal,” “man” is singular grammatically, but universal from the point of view of logic. We also repeat that a proposition is singular if its subject definitely designates one group, even if the subject term is plural grammatically. Thus, the proposition “Those five men make up a basketball team” is a singular proposition even though “five men” is plural grammatically.

The form “No S is a P” is the ordinary unambiguous way of ex¬ pressing a universal negative proposition, as in the example “No dog is a cat.”

On the basis of both quality and quantity attributive propositions are designated as A, E, 1, and O. These letters are from the Latin words affirmo, which means “I affirm,” and nego, which means “I deny. A, E, I, and O have the following meanings: A and I (the first two vowels of affirmo) signify affirmative propositions—A either a universal or a singular, and I a particular; E and O (the vowels of nego) signify negative propositions-^ either a universal or a singular, and O a particular. (Image)

Thus, the following are A propositions:

• 1. All voters are citizens.

  2. Every voter is a citizen.

  3. A dog is an animal.

  4. Without exception, the members of the class passed the examination.

  5. John Smith is a doctor.

  6. All who have not already been vaccinated must be vaccinated tomorrow.

The following are E propositions.

• 1. No dog is a cat.

  2. Dogs are not cats.

  3. I am not a colonel.

The following are I propositions:

• 1. Some houses are white.

  2. Some cat is black.

  3. Dogs sometimes bite strangers.

  4. Many men are selfish.

  5. Dogs are pests.

The following are O propositions:

• 1. Some cat is not black.

  2. Not all cats are black.

  3. Not every man is a saint.

  4. All that glitters is not gold.

  5. All horses can't jump.

  6. "Not everyone who says to me: 'Lord, Lord' shall enter into the kingdom of heaven."

Notice that in all of these O propositions the predicate is denied of an indeterminately designated portion of the extension of the subject.

First we shall say a few words about logical form in general, and then we shall explain the logical form of the attributive proposition. Finally we shall explain the notion of subject and predicate more fully, and give some practical aids for the reduction of attributive propositions to logical form.

a. General Notion of Logical Form

Logical form in general is defined as the basic structure, or the basic arrangement of the parts, of a complex logical unit. Complex logical units include propositions and inferences, or arguments, but not terms. [Note: In the present context, where they are opposed to propositions and the various kinds of inference, even so-called complex terms are simple logical units, which have no logical form.] There are as many logical forms as there are distinct structural types of propositions and inferences. The following examples illustrate a few of the innumerable logical forms that we shall study later:

Proposition --

Every dog is an animal.

John is not a sailor.

If the sun is shining, it is day.

He is either going or not going.

He will be chosen because he is the best man.

Arguments or inferences --

Every dog is an animal; but every hound is a dog; therefore every hound is an animal.

No man is twenty feet tall; but John is a man; therefore John is not twenty feet tall.

If the sun is shining, it is day; but the sun is shining; therefore it is day.

Each of these examples illustrates a different kind of logical unit, with a distinct arrangement of parts, and therefore each illustrates a distinct logical form.

In the present chapter we shall treat only of the logical forms of the attributive, or categorical, proposition; but there are many logical forms that we shall treat of later—the forms of the various kinds of propositions (such as conditional, disjunctive, and conjunctive propositions), the forms of eduction (including conversion, obversion, and contraposition), the forms of oppositional inference, the many forms of the categorical and hypothetical syllogism, and so on.

b. Logical Form of the Attributive Proposition

An attributive, or categorical, proposition, as we have already seen, is defined as a proposition in which a predicate (P) is affirmed or denied of a subject (S). This definition indicates the essential parts of the attributive proposition: the subject, the copula, and the predicate. We have already seen that all attributive propositions have the same parts and the same basic structure regardless of their matter or thought content; so far as their structure is concerned, it makes no difference whether they are about men, dogs, swimming pools, peace, walrusses, or Asiatic famines. This basic structure (or generic logical form) is: S—copula—P. This generic basic structure admits of six variations (or species) according to differences in the quantity of the subject and the quality of the copula. The subject can be universal, particular, or singular; and the copula can be affirmative or negative. Each of these six varieties of structure is a distinct logical form, or type, of attributive proposition. Thus, we have the following forms of the attributive proposition:

Su is P. S a P A

Su is not P. S e P E

Sp is P. S i P I

Sp is not P. S o P O

Ss is P. S a P A

Ss is not P. S e P E

These six forms, as we have seen, are symbolized by A, E, I, and O: A and I signifying affirmative propositions—A either a universal or a singular, and I a particular; E and O signifying negative propositions—E either a universal or a singular, and O a particular.

c. Reduction to Logical Form

Reduction to logical form consists in rewording a proposition or argument according to some set plan in order to make its basic structure obvious. The purpose of reduction to logical form is to extricate a part of a complex logical unit (like the subject or predicate of a categorical proposition, or the minor, middle, or major terms of a categorical syllogism) to make it an object of special consideration or to facilitate various logical processes (for instance, conversion).

The logical form of most of the sample propositions we have had up to the present is very obvious, for most of them have been arranged in the order S—copula—P, and there has been no difficulty in recognizing the quantity of the subject term. It is easy to see, for instance, that the proposition “Every dog is an animal” has the logical form “Su is P,” which is also expressed “S a P,” or simply A.

Many propositions, however, do not display their logical form so clearly as these. Consider, for instance, the proposition “He writes editorials.” In this proposition the word “writes” expresses both the copula and a part of the predicate, and (at least in most contexts) the words “writes editorials” are equivalent to “is a writer of editorials.” Hence, if we wish to express this proposition in the order “S—copula—P,” we must change the wording to “He—is—a writer of editorials.” Thus, the reduction to logical form of an attributive proposition consists in rewording it so as to state, first, its logical subject together with an appropriate sign of quantity, such as “all,” “every,” “some,” and so on; next, its copula; and then its predicate. For instance, reduced to logical form, the proposition “Violinists play the violin” becomes “All violinists—are—ones who play the violin.”

We shall now make some observations that should help us to discover the logical subject, copula, and predicate of an attributive proposition and at the same time throw greater light on their nature.

The logical subject, as we have seen, expresses that about which anything whatsoever is affirmed or denied. To find the logical subject of a proposition, ask yourself, About whom or what is the statement made? About whom or what is new information given? Often you will be helped by also asking yourself. To what question does the proposition give an answer? With these suggestions in mind, let us re-examine the proposition “We should elect Smith” in order to determine what its logical subject is in various contexts. If the proposition “We should elect Smith” is an answer to the question Whom should we elect?,” a statement is made, and information is given us, about the one we should elect; hence, “the one we should elect” is the subject, and “Smith” is the predicate.

If the proposition is an answer to the question “Who should elect Smith?,” information is given about the ones who should elect Smith; and so the logical subject is “the ones who should elect Smith,” and “we” is the predicate. On the other hand, if the proposition is an answer to the question “What should we do?,” “what we should do” is the logical subject and “to elect Smith” is the predicate.

To determine the quantity, ask yourself, Is the statement made about the whole extension of the subject, about an indeterminately designated portion of its extension, or about one definitely designated individual or group? We have already mentioned some of the usual signs of universality, particularity, and singularity when we treated of the division of terms into universal, particular, and singular. We might add that words such as “never,” “nowhere,” “at no time,” “always,” “without exception,” and so on, are often signs of universality. Words such as “a few,” “many,” “hardly any,” “generally,” “often,” “sometimes,” “most,” and so on, are usually signs of particularity.

The copula is always “is (am, are)” or “is (am, are) not”; that is, it is always the present indicative of the verb “to be” either with or without a negative particle. Indications of time expressed by the past and future tenses of verbs do not belong to the copula but to the predicate.

The predicate is whatever is affirmed or denied of the subject. Whatever new information is given belongs to the predicate. Often a predicate term can be discovered by asking the question to which a proposition gives the answer and by then giving the answer to this question in a minimum number of words and in an incomplete sentence. For instance, suppose that the proposition “We should elect Smith” is an answer to the question, Whom should we elect? The answer is “Smith.” Hence, “Smith” is the predicate; and, reduced to logical form, the proposition is: “The one we should elect —is—Smith.” Or suppose that the proposition “Tex put the saddle on the horse” is an answer to the question. Where did Tex put the saddle? The answer, expressed in a minimum number of words, is: “on the horse.” Hence, this is the predicate. Expressed in logical form the sentence becomes: “(The place) where Tex put the saddle —is—on the horse.”

Often you will have to supply words such as “one,” “thing,” and so on, with the predicate—for instance, when reduced to logical form, the proposition “All men have free will” becomes “All men— are—ones having free will.” Sometimes you will have to use nouns, adjectives, participles, or relative clauses to express a predicate contained in a verb. For instance, “He runs” becomes “He—is—running” if “runs” signifies a present action, or “He—is—a runner” if “runs” signifies a habitual action.

Many propositions are of mixed type. “All but a few will go,” for instance, is at once I and O. Reduced to logical form, it becomes “Most (some) are ones who will go; the rest (some) are not ones who will go.” We shall now give a few examples of the reduction of propositions to logical form.

1. “When under pressure, he does his best work” becomes “He is one who does his best work when under pressure.” This is an A proposition. “When under pressure” belongs to the predicate.

2. “Not all who are here will go to the concert” becomes “Some who are here are not ones who will go to the concert.” This is an O proposition.

3. “Few men get all they want” can be reduced to either of two logical forms. It can be looked upon as an A proposition and reduced as follows: “The number of men who get all they want is small.” It can also be looked upon as a combination of I and O and reduced as follows: “Some men are ones who get all they want; many men (some) are not ones who get all they want.” “Few” frequently means “some, but not many.”

4. “Dogs are a nuisance” becomes “Some dogs are a nuisance.” All lovers of dogs, at least, will insist that this is an I proposition and not an A.

5. “Canaries sing” becomes “Canaries are singers.” In this con¬ text “sing” does not signify a present action but a habitual or frequently repeated action; it means that canaries can sing and do it often, but not that they are actually singing here and now.