Classification of the Proposition

Article 2. Classification of the Proposition

a) Simple Propositions    b) Compound Propositions

The most general classification of propositions presents them as simple and compound. A simple proposition has one subject and one predicate. A compound proposition is a combination of two or more simple propositions: such combinations may be variously effected. It will be necessary here to discuss these classes of propositions in detail.

a) Simple Propositions

A simple proposition has but one subject and one predicate. Examples: “Man is mortal”; “God is good”; “Aluminum is not heavy”; “A circle is a closed curved line.”

In quality, simple propositions are, of course, either affirmative or negative. In quantity, such propositions are universal, particular, singular, or indefinite. But, for practical purposes, the singular and indefinite propositions are not distinguished as classes, because they are always reducible to the other forms. Thus a singular proposition (that is, a proposition with a singular term as subject) always takes its subject in full Extension; it must, for its subject has the extension of only one; it is individual, and, if used at all, must be used in full Extension. Now the definition of a universal proposition is that it takes its subject in full Extension. Therefore, practically speaking, singular propositions are always universal propositions. And the indefinite proposition (that is, one that uses the subject in indeterminate Extension, such as, “Men like sports”) will always convey by adjunct or context a definite knowledge of the scope of its Extension, and therefore will always be reducible to a universal or a particular proposition. Thus the indefinite proposition, “Men are mortal” obviously means “All men are mortal”; the indefinite proposition is, in effect, universal. And the indefinite proposition, “Men like sports,” quite evidently means that “Most or some men like sports,” and so the indefinite proposition is seen to be really a particular proposition.

Therefore, propositions are distinguished in quantity as universal and particular. A universal proposition is one that has a universal term as its subject. A particular proposition is one that has a particular term as its subject.

To sum up the classifications: simple propositions are:

1. in quantity: universal and particular propositions;
2. in quality: affirmative and negative propositions.

Combining the classifications, it appears that we may have the following kinds of simple propositions:

1. universal affirmative propositions — called “A” propositions;
2. universal negative propositions — called “E” propositions;
3. particular affirmative propositions — called “I” propositions;
4. particular negative propositions — called “O” propositions.

To illustrate the A, E, I, and O propositions, the following examples are offered. The student is to formulate other examples for himself:

• A-propositions: All men are mortal; All colors are beautiful; John is wise.
• E-propositions: No man is wise; No tyrants are just.
• I-propositions: Some man is wise; Some laws are silly; Men like sports.
• O-propositions: Some man is not wise; Some sports are not laudable.

The division of simple propositions on the bases of quantity and quality and the letter-symbols of the different propositions so distinguished are matters of first importance. The student must master these things thoroughly, for they are supposed as known in all that follows.

Two Principles of Distribution

Now we are to study two supremely important principles which determine the Extension of the predicate in simple propositions. The value of these principles will appear when we come to the analysis of the reasoning process.

First Principle: In an Affirmative Proposition the Predicate is undistributed.

The principle means that in affirmative propositions the predicate is not taken in full Extension. Take the proposition, “Every stone is a body.” Here the predicate “body,” while taken in full Comprehension (so that all the notes in the idea body are found in the idea stone) is not taken in full Extension. If it were so taken, the proposition would mean that there is no other sort of body but a stone. It is taken in partial Extension, and the proposition really means, “Every stone belongs to the class (Extension) bodies, although there are other bodies, which are not stones, in that class also.” In other words, the proposition means, “Stones are some members of the class bodies.” When a term is used in full Extension, it is said to be distributed; when used in partial Extension, it is said to be undistributed. We should now be able thoroughly to understand the principle: in an affirmative proposition the predicate is undistributed.

Notice two exceptions to this principle:

1. When the predicate is a singular term. In this case the predicate is individual, it has an Extension of one; if used at all it must be used in full Extension. Example: “That man is Al Smith.”
2. When the predicate is an essential definition. In this case, the definition must be absolutely equal in all respects (Comprehension and Extension) with the subject, and the proposition should read both ways with equal truth. Example: “Man is a rational animal.” The essential definition is necessarily an A-proposition; its subject is therefore a universal term. The predicate is coextensive with the subject, and is therefore taken in full Extension.

Second Principle: In a Negative Proposition the Predicate is distributed.

The principle means that in a negative proposition the predicate is taken in full Extension. Take the proposition, “An animal is not a stone.” Here the predicate “stone,” although not taken in full Comprehension (so as to exclude from the idea animal every essential note found in the idea stone) is taken in full Extension, and the entire class stone is denied to the class animal. The meaning is “No stone at all is predicable as animal.”

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b) Compound Propositions

Compound propositions are combinations of simple propositions. Such combination may be effected in various ways, and we divide compound propositions into the following classes:

1. Modal Propositions;
2. Categorical Propositions (Compound);
3. Hypothetical Propositions;
4. Complex Propositions;
5. Multiple Propositions.

These classes are not entirely exclusive one of the other, but the points at which some of them overlap will be readily seen and understood when the different types have been studied. The present classification seems the least likely to lead to confusion in the student’s mind.

i. Modal Propositions

A modal proposition not only expresses the agreement or disagreement of subject and predicate, but also indicates the manner in which the subject and predicate agree or disagree. This manner of agreement or disagreement is expressed by the use of an adverb, a phrase, a clause, or by the implication of the verb. Now in modal propositions the simple agreement or disagreement of the subject and predicate is expressed in what is called the dictum; while the manner of their agreement or disagreement is expressed in what is called the mode. Thus, in the proposition, “God is necessarily just,” the dictum is: “God is just”; and the mode is, “necessarily.”

We distinguish four types of modal propositions, according as the subject and predicate of such a proposition is expressed as agreeing or disagreeing of necessity, by chance, by possibility, or by impossibility. We name these types necessary, contingent, possible, impossible. Examples will make the matter clear:

i. Necessary modals: “A circle has to be round”; “A sentient being must be alive”; “God is necessarily just.” In each of these propositions the student will distinguish the dictum and the mode. Then he will observe that the mode itself may be expressed in a proposition. Thus it appears that modal propositions are always combinations of at least two simple propositions, one expressing the dictum, the other expressing the mode. Thus we see that modals are always compound propositions, never simple propositions. To illustrate, we may express the modal, “A circle has to be round” in two simple propositions, as follows: “A circle is round”; “This roundness is requisite.”

ii. Contingent modals: “John is, it happens, ill”; “A rider chanced to come his way”; “As luck would have it, the doctor was away from home.” Here again, it appears that the dictum and the mode may be expressed in respective simple propositions; and so we see that modals of this type are necessarily compound, and not simple propositions. Notice that the mode expresses contingency, that is, the chance or accidental relation of subject and predicate.

iii. Possible modals: “The earth may possibly collide some day with another planet”; “A living being may be sentient”; “Such accidents can happen.” Again, dictum and mode show that such modals are compound propositions.

iv. Impossible modals: “God cannot be cruel”; “A circle cannot be square”; “It is not possible that a triangle have four sides.” Here again it is clear that modals are always compound propositions.

Study the types of modal propositions well. Then notice the following facts: 1. Necessary modals are always A-propositions. For if the predicate must be enunciated of the subject, it applies to it universally; that is, the subject of such propositions will always be a universal term. And an A-proposition is precisely a proposition (affirmative) with a universal term for subject. — 2. The impossible modal is always an E-proposition. Why?

ii. Compound Categorical Propositions

A categorical proposition expresses an unconditional judgment. It may be simple or compound, but it is only of compound categoricals that we speak here.

Sometimes it is difficult to determine at sight whether a categorical is simple or compound; sometimes, of course, it is quite obvious that a given proposition is compound. For this reason we divide the present consideration of compound categoricals into two parts: in the first, we study categoricals that are obviously compound; in the second, we study those that are not obviously compound.

I. Categoricals Obviously Compound. There are four types in this group:

i. Copulative propositions. These have more than one subject, more than one predicate, or more than one of each; and these are joined by conjunctions such as and, or, nor, etc. Examples: “Peter and James were Apostles”; “Simon and Jude were Apostles and martyrs”; “John was an Apostle and Evangelist.” The truth of copulative propositions depends upon the truth of the several simple propositions to which they may easily be reduced.

(A note on truth and correctness: the student may be puzzled to find mention of the truth of propositions discussed here, and may ask, “What has Dialectics to do with truth? Its aim is correctness.” We answer: we study nothing of the nature of truth here, nor of tests for truth as such. But we must take account of the fact that propositions are necessarily true or false, and this property sometimes determines them as veritable specimens of a given type of proposition or excludes them from such type. Therefore in determining the limits of types, mention must be made of truth and falsity. Here the questions of truth and correctness have something in common.)

ii. Adversative propositions. These express opposed judgments, and show the opposition by particles like but, however, nevertheless, yet, still, etc. Examples: “Happiness lies not in the possession of earthly but of eternal goods”; “Now you are clean, yet not all”; “Samson was strong; nevertheless he fell through the power of one weaker than himself.” The truth of adversative propositions depends upon the truth of the simple propositions to which they may be reduced, and also upon the fact of true opposition existing between these component simple propositions. Thus we have a false adversative in, “Peter was a martyr; nevertheless he went to heaven.” Here the component simple propositions are true, but the opposition expressed in “nevertheless” does not exist between them.

iii. Relative propositions. These are made up of partial propositions connected by correlative particles like when—then, so—as, as—as, whoever—he, where—there, etc. Examples: “Where a man’s treasure is, there is his heart also”; “Where two or three are gathered together in my name, there am I in the midst of them”; “As the shepherd is, so is the flock”; “Like father, like son”; “Whoever doth the will of my Father, he shall enter the kingdom of heaven.” The truth of relative propositions depends upon the truth of the component simple propositions and also upon the existence of a true relation obtaining between or among them.

iv. Causal propositions. These consist of propositions united by causal particles such as because, since, as, for, etc. Examples: “Man is free because he is rational”; “You will be sick, for you have eaten tainted food”; “Since Simon has no penny, he shall have no pie.” The truth of causal propositions depends upon the truth of the component simple propositions and also upon the truth of that which is assigned as cause. The following is a false causal, for obvious reasons: “You will have a happy life because you were born on Sunday.”

II. Categoricals Not Obviously Compound. Since these propositions need to be drawn out of the obscurity of their composition and shown to be compound, they are called exponible propositions. The simple propositions into which they may be resolved are called their exponents. There are four types of propositions not obviously compound:

i. Exclusive propositions. These have attached to subject or predicate an exclusive particle like only, alone, etc. Examples: “Patrick alone stood up for me”; “God only knows.” The exponents of the second example are: “God knows” and “Others do not know.”

ii. Exceptive propositions. These include the expression of a limited predication, that is, they show that some inferiors of the subject do not receive the predication, or that some inferiors of the predicate are not enunciated of the subject. This exception is indicated by particles such as except, but, save, omitting, etc. Examples: “All save John had gone”; “Mary likes all her studies except history”; “The class, omitting the consistent idlers, passed a brilliant examination.” The exponents of the first example may be stated as follows: “John had not gone”; “All others had gone.”

iii. Comparative propositions. These declare that a predicate is to be enunciated of one subject equally with another; or more or less truly, extensively, emphatically, of one than of another. Comparative particles are used, such as more, less, better, worse, equally, etc. Examples: “Good name is better than great riches”; “Kind hearts are more than coronets”; “John and Jim are equally enthusiastic”; “Mary is less diligent than Alice.”

iv. Reduplicative propositions. These view a subject from different angles, and make partial predications about it, using such words as inasmuch, as, in as far as, etc. Examples: “Shakespeare as a man was of upright character, as a poet he was supreme, as a philosopher he was notable, as a dramatist he was unexcelled, as an actor he was indifferent.” “The physician, inasmuch as he is a physician, treats human ailments; inasmuch as he is a man, he thinks and wills; inasmuch as he is an animal, he eats and sleeps.” If the reduplicative particle is equivalent to because, the proposition is to be first reduced to the causal type, and then resolved into its simple components. If the reduplicative particle merely indicates a changed point of view, the proposition is called specificative, and is to be reduced to the copulative type, and then into its simple exponents. The first example given above is specificative; the second is implicitly causal.

iii. Hypothetical Propositions

A hypothetical proposition is conditioned: it makes no absolute predication, but expresses a dependency existing between two or more propositions. The matter is made clear by an example: “If a fast day falls upon Sunday, the fast is not observed.” Notice that the proposition does not say simply, “The fast is not observed,” but makes that proposition depend upon the fulfillment of a condition. There are three types of hypothetical to be considered:

I. Connective (or simply conditional) propositions. These always have a member introduced by the particle if. The member so introduced is called the condition or antecedent; the other member is called the consequent. We may define a connective hypothetical as a proposition in which the consequent depends in such wise upon the antecedent that if the antecedent be true, the consequent must be true. Examples: “If you go, I shall not remain here”; “If the storm comes before we reach home, we are in for a wetting.” The truth of connective hypotheticals depends solely upon the relation of dependence enunciated as existing between antecedent and consequent. Thus the following is not a true connective hypothetical: “If you vote the Republican ticket, you will go to heaven.” Now you may actually vote the Republican ticket, and you will (one hopes) actually go to heaven by and by; but there is obviously no relation of dependency between these things.

II. Conjunctive propositions. These enunciate the impossibility of two things occurring simultaneously, or of two facts being true at one and the same time. Examples: “Socrates is not at once a philosopher and an ignoramus”; “One cannot stand and sit at the same time”; “Oscar Skavinsky cannot be simultaneously a Republican and a Free-Stater.” The truth of such propositions depends solely upon a true exclusive opposition existing between their component parts. Propositions of this type are easily reduced to two connective hypotheticals. Thus the first example may be reduced as follows: “If Socrates is a philosopher, he is not an ignoramus”; “If Socrates is an ignoramus, he is not a philosopher.”

III. Disjunctive propositions. These enumerate exhaustive lists of possibilities no two of which can be simultaneously true, nor can all be simultaneously false, but one must be true and the rest false. Examples: “It is either day or night”; “It is spring, summer, autumn, or winter”; “The thing is possible or it is not possible.” For a proposition to be a true disjunctive hypothetical two things are required: 1. The enumeration of possibilities must be complete; and 2. There must be an exclusive opposition between or among the enumerated possibilities. The following is therefore no true disjunctive: “It is spring, or autumn, or winter.” The following also fails of the character of a true disjunctive: “It is either white or sweet.”

iv. Complex Propositions

A complex proposition has a complex term as subject. A complex term, as we have learned, is one that consists of two or more simple terms. Such a term has always a principal member and an incidental member. In the term, “the love of God,” the principal member is “love” and the incidental member is “of God.” Now complex propositions may be reduced to their exponents, and these will always be two, one containing the principal member of the complex term, and the other containing the incidental member. Example of the complex proposition: “The fear of God is the beginning of wisdom.”

v. Multiple Propositions

A multiple proposition formally expresses more than one predication. Now a compound proposition may contain many simple propositions as exponents, and still not be multiple. Thus, “Peter, James, and John beheld the Transfiguration” is a compound proposition, and may be reduced to three simple propositions; yet it is not multiple, for it has only one predication, viz., “beheld the Transfiguration.” On the other hand, “John runs and jumps” is a compound and a multiple proposition; even though it has only one subject, there are two distinct predications concerning that subject. Let the student determine whether the following are compound and not multiple, or compound and multiple:

• Brothers and sisters I have none;
• Peter believed and was baptized;
• I hope and pray that you are well;
• The army, the navy, and the marines took part in the battle;
• Gold and silver I have not and desire not.

Learn the axiom: A multiple proposition is always compound, but a compound proposition is not necessarily multiple.

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Summary of the Article

In this Article we have studied in detail the various types of propositions. This study will be well repaid when we come to the consideration of reasoning and the syllogism. Accurate thinking, correct reasoning, demands a clear knowledge of the values of terms and propositions, and of the principles immediately derived from such knowledge. We have learned to classify propositions as follows:

I. In Quantity and Quality:

• A — propositions (Universal affirmative)
• E — propositions (Universal negative)
• I — propositions (Particular affirmative)
• O — propositions (Particular negative)

II. In Structure:

1. Simple
2. Compound
   • a) Modal — necessary, contingent, possible, impossible
   • b) Categorical
     • obviously compounded — copulative, adversative, relative, causal
     • not obviously compounded — exclusive, exceptive, comparative, reduplicative
   • c) Hypothetical — connective, conjunctive, disjunctive
   • d) Complex
   • e) Multiple