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The Jonathan Dolhenty Archive |
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INTRODUCTORY: Part 5 by Jonathan Dolhenty, Ph.D.
When we look at the relationship between the two main groups of propositions, we will notice immediately that they are not exclusive of each other. Of course, single and multiple propositions do exclude each other and categorical and hypothetical propositions do exclude each other. But while the single propositions are always categorical and the hypothetical propositions are always multiple, the categorical propositions may be either single or multiple. Single Categorical Propositions The categorical proposition makes a direct assertion of agreement or disagreement between the subject and the predicate. Simple Categorical Propositions The single categorical proposition contains only a single sentence in its construction. It contains one subject, one predicate, and the copula. If these elements of the sentence are without any qualification or composition, it is a simple categorical proposition. Examples: "Gold is an ore," "Jack is tall," "Man is rational." There should be no difficulty with these types of propositions since they are so simple. Composite Categorical Propositions If, however, a qualification or composition enters into the subject or predicate or copula, we have a composite single categorical proposition, and these may be of two types: complex propositions and modal propositions. Two Kinds of Composite Propositions The complex proposition is a composite single sentence in which both the subject and the predicate or either one is a complex term. Comparative examples: "Man" is a simple term. But "Good man" or "Learned man" or "Intelligent man" are complex terms. These latter terms used a subjects or predicates, or any verb which expresses past or future time used as a predicate, makes the sentence a complex proposition. Consider the following propositions:
In the above propositions, there is only one judgment, with one subject and one predicate. But the subject or the predicate in each proposition is a qualified (complex) term. The modal proposition is a composite single sentence in which the copula is so modified as to express the manner or mode in which the predicate belongs to the subject. The qualification does not affect the subject or the predicate. It affects the copula itself. It states whether the objective connection between the subject and the predicate, expressed by the copula, is necessary, impossible, possible, or contingent. There are, then, four different modes, each producing a different type of proposition. Mode 1. The necessary modal proposition states that the predicate belongs to the subject, and must belong to it. Examples: "A circle is round," "Man is an animal," "Two plus two equal four." Mode 2. The impossible proposition states that the predicate does not and cannot belong to the subject. Examples: "A square has five sides," "A dog is a rational animal," "Four plus four equal nine." Mode 3. The possible proposition states that the predicate is not actually found in the subject, but it might be. Examples: "A diabetic may go into a coma," "My truck can go over 100 miles per hour," "Paul may be a good student." Mode 4. The contingent proposition states that the predicate actually belongs to the subject, but it need not. Examples: "These students need not attain good grades," "It is not necessary that the dog keep on barking," "I need not go to the dance Friday night." Multiple Categorical Propositions Multiple categoricals are propositions which contain two or more sentences in their very construction. Some of these are overtly multiple and some are covertly multiple. The covertly multiple propositions are called exponibles. Overtly Multiple Categoricals The overtly multiple categoricals are plainly composed of two or more propositions. There are five types of these. 1. The copulative proposition is a multiple categorical proposition which has two or more subjects, or two or more predicates, or two or more subjects and predicates. Examples: "Richard Nixon and Gerald Ford were presidents of the United States," "Peter is president and chairman of the board of his company," "Jack and Jill went up the hill and slid back down again." Each of these sentences can be resolved into as many single propositions as there are different subjects and predicates. Examples: "Richard Nixon was president," "Gerald Ford was president," "Peter is president of his company," "Peter is chairman of the board." The truth of copulative categoricals depends on the truth of all the single sentences which compose the multiple proposition. 2. The adversative proposition is a multiple categorical proposition which consists of two propositions united in opposition to each other by conjunctions such as "but," "yet," "although." Examples: "The dog was barking, but no one cared," "Jack lost his business, yet he was not depressed," "The woman bought a purse, although she did not need one." To be true, each sentence must be true, and the opposition must be true. Example: It must be true that "The dog was barking" and it must be true that "no one cared." 3. The relative proposition is a multiple categorical proposition which expresses a relationship of time or place between two sentences. Examples: "Before beginning to eat his salad, he told me the secret," "After hurrying home, Jack called Jane on the telephone." In order to be true, the single statements must be true and the relation of their sequence must be true. It must be true, for instance, that Jack called Jane on the telephone and it must be true that he did it after hurrying home. 4. The causal proposition is a multiple categorical proposition which combines two statements in such a way that the one is given as the reason or cause of the other. The words "because" and "for" commonly appear in this type of proposition. Examples: "The times are good, for people have a lot of money to spend," "Jack is happy, because he got elected class president." The truth of the causal proposition depends on the truth of each categorical proposition contained in it and on the causal connection that is declared to exist between them. It must be true that "Jack is happy" and it must be true it is "because he got elected class president." 5. The comparative proposition is a multiple categorical proposition which compares the relation between a subject and predicate with the same relation between another subject and predicate, and expresses the degree of this relationship as being either less or equal or greater. This may sound complicated, but it really isn't. Example: "As you live, so you shall die." Three statements are actually contained in this proposition. The first one is "Your life has a certain character." The second one is "Your death has a certain character." The third statement is not as obvious but is implied, and states "The character of your death is the same as the character of your life." Now, that wasn't too hard, was it? Let's consider another proposition. Example: "Harry Truman was a greater president than Richard Nixon was." Here again, we have three statements. One, "The quality of Truman's presidency was great." Two, "The quality of Nixon's presidency was great." Three, "The quality of Truman's presidency was the greater of the two." The truth of a comparative proposition depends on the truth of the two separate sentences and on the truth of the degree mentioned as existing between them. Covertly Multiple Categoricals The covertly multiple categorical propositions have the appearance of single propositions but are really multiple. Their composition lies concealed in some word and this needs an exposition to show the multiple character of the proposition. This is why these sentences are called exponibles (from expressed). We can resolve these multiple propositions into individual sentences called exponents. The truth of exponible propositions is determined by looking at the exponents and the logical connection between them. If any parts of an exponible proposition are false, the entire proposition is false. There are four types of exponible propositions. 1. The exclusive proposition is a multiple categorical proposition which contains some word or words such as "only," "alone," "solely," or "none but," which indicates the exclusion of any other predicate from this subject or any other subject from this predicate. Example: "Only the better students will go on the field trip." This proposition may appear to be a single categorical proposition but it is not. This proposition can be resolved by means of a copulative proposition, in which one sentence is affirmative and the other is negative. It becomes the proposition "The better students will go on the field trip and no others will go on the field trip." Now it is obvious it is indeed a multiple categorical proposition. Another example: "None but the brave will receive medals of honor." This appears to be a single categorical proposition. It can, however, be resolved into the following: "The brave will receive medals of honor and no others will receive medals of honor." We can now see clearly that it is really a multiple categorical proposition. 2. The exceptive exponible proposition is a multiple categorical proposition which contains a word such as "except" or "save," to indicate that a portion of the extension of the predicate does not apply to the subject, or a portion of the extension of the subject does not apply to the predicate. Example: "All the athletes except John won an event in the tournament." The resolution of this is not difficult. It becomes, "All athletes in the tournament won an event, and John did not win an event in the tournament." Clearly a multiple categorical. Another example: "All the animals save one were killed in the fire at the zoo." Resolution: "One animal was not killed in the fire at the zoo, and all the other animals were killed." Again, clearly a multiple categorical. 3. The reduplicative exponible proposition is a multiple categorical proposition which contains an expression which duplicates the subject or predicate, giving it special emphasis, such as "as such" or "as a," and implies the reason or cause for the connection between subject and predicate. Confused? Don't be. Examples will help you understand this ponderous definition. Example: "Man, as man, is endowed with free will." This proposition can be resolved into: "Man is endowed with free will, because he is man." Now it appears as a multiple categorical proposition. It is reduplicative because it "reduplicates" itself, that is, the idea of "man" is intrinsically joined with the idea of "free will." You can't have one without the other. A reduplicative proposition is true when both the plain statement and the reduplicative substatement are true. 4. The specificative exponible proposition appears similar to the reduplicative proposition but really is quite different. It is a multiple categorical proposition which contains an expression which duplicates the subject or predicate, giving it special emphasis, such as "as such" or "as a," but merely implies the time element or condition of this connection. Example: "Peter, as a student in high school, took part in the debating society." The fact that Peter is a student has nothing to do with his participating in the debating society as a student. The resolution of this proposition is: "Peter is a student in high school," and "Peter took part in the debating society." Another example: "The professor, as a historian, was a very easy grader." The fact that the professor is a historian has nothing essential to do with the fact that he is an easy grader. He could have one characteristic without the other. The resolution is: "The professor is a historian," and "The professor is an easy grader." Specificative propositions are true when both the plain statement and the substatement are true.
This ends our discussion of single and multiple categorical propositions. Just remember that categorical propositions always make a clean-cut assertion; they always affirm or deny the predicate to the subject outright with no qualifications.
Hypothetical Propositions The Nature of Hypothetical Propositions How does the hypothetical proposition differ from the categorical proposition? While the categorical proposition makes a definite and unqualified assertion, the hypothetical proposition does not declare an unqualified affirmation or denial. It expresses the dependence of one affirmation or denial on another affirmation or denial. There are three types of hypothetical propositions. The Types of Hypothetical Propositions The conditional proposition is a hypothetical proposition which expresses a relation in virtue of which one proposition necessarily flows from the other because a definite condition is verified or not verified. Sometimes these are called the "if" propositions. Examples: "If the barometer falls, there will be a storm." "If Peter is a good boy, he will be able to go on the trip." "If I make a lot of money, then I will be able to buy a mansion." The part of the proposition containing the "if" is called the "condition" or the "antecedent." The other part is called the "conditioned" or the "consequent." Notice there is a strict relation expressed in a conditional hypothetical proposition. The "antecedent" must be true before the "consequent" can follow. The truth of conditional hypothetical propositions does not depend on the truth of the statements taken by themselves or individually. The truth depends on the relation between the statements. For example, take the proposition "If the barometer falls, there will be a storm." We are not asserting that the barometer is falling. We are not asserting that a storm is coming. We are simply saying that the coming of a storm is dependent on low atmospheric pressure which is indicated by the falling of the mercury in a barometer. In a conditional hypothetical proposition, it is the dependence of one idea on the other that is affirmed or denied. The truth of the whole statement rests on the truth of the dependence. The disjunctive hypothetical proposition is one which contains an "either-or" statement, indicating that the implied judgments cannot be true together nor false together, but one must be true and the other must be false. Examples: "Either the sun or the earth moves in an orbit." "An automobile is either in motion or at rest." This type of proposition should present no difficulty. The conjunctive hypothetical proposition is one which expresses a judgment that two alternative assumptions are not or cannot be true at the same time. Examples: "An automobile cannot be in motion and at rest at the same time." "A person cannot be a saint or a sinner at the same time." For the truth of such a proposition, it is necessary that they be really irreconcilable at the same time. If we can prove that they may be present together, we would prove the statement to be false.
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