  1. THREE KINDS OF ARGUMENTS.The proposition, constituting the basic unit of the argument, would of necessity be indicative of the nature of said argument; therefore the three general kinds of propositions, categorical, hypothetical and disjunctive, suggest the three kinds of arguments which are in turn categorical, hypothetical and disjunctive. Categorical arguments are those in which all of the propositions are categorical. Since this kind has been treated, it remains for us to consider the other two. 2. HYPOTHETICAL ARGUMENTS.We have observed that a hypothetical proposition is one in which the assertion depends on a condition; for example, in the proposition, “If it is pleasant, Iwill call on you to-morrow,” the calling depends on the state of the weather. “I will call on you to-morrow,” is the assertion which is limited by the condition, “If the weather is pleasant.” Definition: The hypothetical argument or syllogism is one in which the major premise is hypothetical and the minor premise categorical. ILLUSTRATION: If the people are right more than half of the time, the world will progress; And the people are right more than half of the time, Hence the world will progress. In contradistinction to disjunctives, hypothetical propositions and hypothetical syllogisms are frequently referred to as “conjunctive.” 3. THE ANTECEDENT AND CONSEQUENT.Facility in detecting the antecedent and consequent of hypotheticals is required in order to deal intelligently with the argument. The hypothetical proposition has been defined as one in which the assertion is limited by a condition. The consequent is the assertion and usually follows (though not always) the antecedent which is the limiting condition. First the antecedent and then the consequent is the logical order as the derivative meaning of the words antecedent and consequent would indicate. The antecedent is introduced by such words as “if,” “though,” “unless,” “suppose,” “granted that,” “when,” etc. ILLUSTRATIONS:
4. TWO KINDS OF HYPOTHETICAL ARGUMENTS.The two kinds of hypothetical syllogisms are the constructive and destructive. A constructive hypothetical syllogism is one in which the minor premise affirms the antecedent. A destructive hypothetical syllogism is one in which the minor premise denies the consequent. The constructive hypothetical is sometimes referred to as the “modus ponens”; whereas the destructive hypothetical is called the “modus tollens.” ILLUSTRATIONS:
5. THE RULE AND TWO FALLACIES OF THE HYPOTHETICAL ARGUMENT.From a given hypothetical proposition it is possible to construct four different hypothetical syllogisms, as the attending illustrations make evident: Consider the hypothetical proposition “If it has rained, the ground is damp.” (1) Minor premise affirms antecedent. If it has rained, the ground is damp; It has rained, Therefore the ground is damp. (2) Minor premise denies antecedent. If it has rained, the ground is damp; It has not rained, Therefore the ground is not damp. (3) Minor premise affirms consequent. If it has rained, the ground is damp; The ground is damp, Therefore it has rained. (4) Minor premise denies the consequent. If it has rained, the ground is damp; The ground is not damp, Therefore it has not rained. Without any knowledge of the rules of the hypothetical syllogism let us strive to determine how many of the foregoing are valid. Relative to the first, it would be impossible for any rain to fall without making the ground somewhat damp; a few drops would be sufficient. In short, if the antecedent happens, the consequent must follow. It seems, therefore, that the first argument is This investigation suggests a rule for hypothetical arguments. Since only the first and fourth arguments are valid, this is the rule which must obtain: The minor premise should either affirm the antecedent or deny the consequent. Any violation of this rule would result in the fallacies of denying the antecedent or affirming the consequent. There is one exception to this rule which must not be overlooked; viz.: If the antecedent and consequent of the hypothetical proposition are co-extensive then both may be either affirmed or denied. ILLUSTRATIONS: (1) If the rectangle is equilateral, then it is a square; The rectangle is equilateral, ? It is a square. (2) If the rectangle is equilateral, then it is a square; The rectangle is not equilateral, ? The rectangle is not a square. (3) If the rectangle is equilateral, then it is a square; It is a square, ? The rectangle is equilateral. (4) If the rectangle is equilateral, then it is a square; It is not a square, ? The rectangle is not equilateral. 6. HYPOTHETICAL ARGUMENTS REDUCED TO THE CATEGORICAL FORM.The hypothetical syllogism so closely resembles the categorical that it may be changed to it by a slight alteration in the wording. After testing the hypothetical by its own rule, it may be expedient to reduce the argument to the categorical form, and subject it to a second test in which the categorical rules are applied. This reduction usually necessitates two steps; first, change the propositions which represent the antecedent and consequent to a subject term and a predicate term respectively and then unite them to form the major premise; second, supply a new minor term, if necessary. Illustrations of Reduction; and Comparison of Hypothetical and Categorical Fallacies: Hypothetical Form: (1) If it has rained, the ground is damp; It has rained, ? The ground is damp. Categorical Form: A M A S A ? S It is seen that the argument in the hypothetical form is valid as the minor premise affirms the antecedent. Reducing to the categorical gives to the argument the mode A Hypothetical: (2) If one were wise, he would study; But you will not study, ? You are not wise. Categorical: A A G E ? S E ? S In the hypothetical form the argument is valid since the minor premise denies the consequent. Reducing to Hypothetical: (3) If the wind blows from the south, it will rain; But the wind is not blowing from the south, Hence it is not going to rain. Categorical: A M E S E ? S Hypothetically considered, the minor premise denies the antecedent and consequently the argument is invalid. Reducing to the categorical form, it is found that the major term is distributed in the conclusion, but is not distributed in the major premise; hence the fallacy of illicit major is committed. Hypothetical: (4) If a man is just, he will obey the golden rule; This judge has obeyed the golden rule, Hence he is just. Categorical: A A G A This S A ? This S Hypothetically considered, the minor premise affirms the consequent and thus the argument is fallacious; when changed to the categorical we find the fallacy of undistributed middle. If other examples were taken, it could be proved that the hypothetical fallacy of denying the antecedent is usually equivalent to the categorical fallacy of illicit major; whereas the hypothetical fallacy of affirming the consequent amounts to undistributed middle. In reducing some hypotheticals it is necessary to make use of such expressions as, “the case of” or “the circumstances that.” The attending argument will illustrate this: If Jefferson was right, man was created free and equal; (but) Man was not created free and equal, ? Jefferson was not right. Reduced to the categorical: The G S ? A The argument is valid in both cases. 7. ILLUSTRATIVE EXERCISE TESTING HYPOTHETICAL ARGUMENTS OF ALL KINDS.The following brief outline may be followed in testing hypothetical arguments: 1. Arrange logically. 2. Determine antecedent and consequent. 3. Apply the hypothetical rule; name fallacies giving reasons. 4. Reduce to categorical form. 5. Apply the categorical rules, giving fallacies with reasons. (1) If a man is properly educated, he will not despise manual labor; therefore I conclude that you have not been properly educated, since you dislike to work with your hands. Arranged logically and antecedent and consequent indicated: If a man is properly educated (antecedent), he will not despise manual labor (consequent); You despise manual labor (dislike to work with your hands), ? You have not been properly educated. The minor premise denies the consequent, hence the argument is valid according to the rule, “The minor premise must affirm the antecedent or deny the consequent.” The student should note that the consequent is negative and therefore its denial must be an affirmative proposition. Reduced to the categorical: E A G A S E ? S Regarded categorically this is valid. Why? (2) “If one believes in the tenets of the democratic party, then he should vote for its candidates; and since A does believe in them Ihave asked him to vote for me.” Arranged, and antecedent and consequent indicated. If one believes in the tenets of the democratic party (antecedent), then he should vote for its candidates (consequent); And A does believe in these tenets, ? He should vote for its candidates (I have asked him to vote for me). The minor premise affirms the antecedent and thus the argument is valid according to rule. Reduced to the categorical: A M A S A ? S Reduced to the categorical gives mood A (3) “If the weather had not been pleasant, I could not have come; but as the weather is pleasant, here I am.” Arranged and antecedent and consequent indicated: If the weather had not been pleasant (antecedent), I could not have come (consequent); The weather is pleasant, ? I have come (here I am). The minor premise denies the antecedent and consequently the argument is invalid according to the rule. (An affirmative minor premise denies a negative antecedent.) Reduced to the categorical: E Unpleasant weather would not permit me to come, E This weather is not unpleasant, A ? This weather enabled me to come. Fallacy of two negative premises. (4) “If one pays his debts, he will not be ‘black-listed’; but since you are ‘black-listed,’ Iconclude that you have not paid your debts.” Arranged logically and antecedent and consequent indicated: If one pays his debts (antecedent), he will not be “black-listed” (consequent); You are “black-listed,” ? You have not paid your debts. The minor premise denies the consequent hence the argument is valid. Reduced to categorical form: E No G A S E ? S The mood E (5) “Men would do right for the sake of themselves, if they appreciated the law of retribution; but they never think of that.” Arranged, completed, and tested: If they appreciated the law of retribution (antecedent), But they do not appreciate the law of retribution (never think of that), Hence they do not do right for the sake of themselves. Fallacy of denying the antecedent. Reduced to the categorical: A The case of M E But S E ? S Fallacy of illicit major. (6) “If an animal is a vertebrate, then it must have a backbone; but the books say that this animal is not a vertebrate, hence it cannot have a backbone.” Since the minor premise denies the antecedent it would appear that the argument is invalid; yet common knowledge and common sense dictate that the conclusion is true. Surely no invertebrate can have a backbone. As a matter of fact the antecedent and consequent are co-extensive and therefore the hypothetical rule is not applicable. Reduced to the categorical: A M E This S E ? This S As co-extensive A’s distribute their predicates the possibility of there being a fallacy of illicit major is forestalled. Categorically considered the argument is likewise valid. 8. DISJUNCTIVE ARGUMENTS.It has been observed that a disjunctive proposition is one which expresses an alternative. Adisjunctive syllogism is one in which the major premise is a disjunctive proposition. ILLUSTRATION: The boy is either honest or dishonest, He is honest, ? He is not dishonest. 9. THE TWO KINDS OF DISJUNCTIVE ARGUMENTS.The two forms of disjunctive arguments are the one which by affirming denies and the one which by denying affirms. The former is known by the Latin words “modus ponendo tollens”; while the latter is termed the “modus tollendo ponens.” ILLUSTRATIONS: (1) By affirming denies. The defendant is either guilty or innocent, He is guilty, ? He is not innocent. or The defendant is either guilty or innocent, He is innocent, ? He is not guilty. (2) By denying affirms. The defendant is either guilty or innocent, He is not guilty, ? He is innocent. or The defendant is either guilty or innocent, He is not innocent, ? He is guilty. 10. THE FIRST RULE OF DISJUNCTIVE ARGUMENTS.It may be said that disjunctive arguments depend on two rules. This is the first: The major premise must assert a logical disjunction. Alogical disjunction involves two requisites; first, the alternatives must be mutually exclusive; second, the enumeration must be complete. Illustrations of illogical major premise. Terms not mutually exclusive: This boy is either inattentive or indolent, He is not inattentive, ? He is indolent. It is obvious that the boy might be both inattentive and indolent. Experience teaches that the qualities are usually concurrent, and to assume that the boy must be either one or the other is a clear case of “begging the question.” Some logicians maintain that “either—or” signify that both alternatives cannot be false, but that both may be true. If this viewpoint were adopted, the major premise of the illustration would not be a case of begging the question. It is unnecessary to argue the point, if it is made perfectly clear which view is to obtain in this discussion. Briefly stated the two points are these. First opinion: “Either—or” when used logically, mean that if the first alternative is false the second must be true, or if the first alternative is true the second must be false. Second opinion: “Either—or” when used logically mean that if the first alternative is false, the second must be true; but if the first alternative is true, the other may or may not be true. This treatise adopts the first opinion. With us all alternative arguments to be logical must be mutually contradictory; i.e., when one is false, the other must be true and when one is true the other must be false; both cannot be false, neither can both be true. When it is intended that this implication should not obtain, then the expressed alternative will take this form, “The boy is either inattentive or indolent or both.” Other examples where the terms of the disjunctive may not be mutually exclusive: (1) “Lord Bacon was either exceedingly studious or phenomenally bright.” (Undoubtedly he was both.) (2) “This teacher is a graduate either of Harvard or of Yale.” (Perhaps both.) (3) “The defendant is either a liar or a thief.” (The one often leads to the other.) (4) “To succeed one must either seize the opportunity as it passes or make his own.” (The best success results from doing both.) Incomplete enumeration: The cause of the disease was either the water or the milk, It was not the milk, ? It was the water. When such an argument as this is advanced, it must be with the knowledge that every other alternative has received satisfactory investigation. Without this assurance one could justly claim that the disease might have been caused by the meat or fish supply. Complete enumeration means that the investigation has narrowed the facts to the boundary of the field covered by the alternatives. The fallacy of incomplete enumeration is also one of “begging the question.” Other examples of a possible incomplete enumeration: (1) “Jones lives either in Boston or New York.” (2) “Mary is studying either algebra or geometry.” (3) “He either committed suicide or was lynched.” (4) “Either the Giants or the Boston Americans will win the pennant.” 11. SECOND RULE OF DISJUNCTIVE ARGUMENTS.The second rule is made so self evident by the first that there is little need of a detailed discussion concerning it. The rule is this: When the minor premise affirms or denies one of the alternatives of a logical disjunction, the conclusion must, in order, deny or affirm all of the others. To put it differently: When the “minor” affirms, the conclusion must deny every other alternative, and vice versa. When there are but two alternatives reference to any of the foregoing disjunctive arguments will make the rule clear. There may be, however, more than two alternatives. In such a case, if the first rule is observed then the second becomes applicable. ILLUSTRATIONS: (1) John Doe lives either in Boston, Albany, or New York; He lives in New York, ? He does not live in either Boston or Albany. or He does not live in New York, ? He lives in either Boston or Albany. (2) The season must have been either summer, or autumn, or winter, or spring; It was neither autumn, nor winter, nor spring, ? It must have been summer. or It was either autumn, or winter, or spring, ? It could not have been summer. 12. REDUCTION OF THE DISJUNCTIVE ARGUMENT TO THE HYPOTHETICAL AND THEN TO THE CATEGORICAL.It would seem that the laws of the disjunctive contradict those of the categorical syllogism; for we apparently derive from two affirmatives a negative conclusion, and we also derive an affirmative conclusion when one premise is negative. This objection is seen to be nugatory when the disjunctive is reduced to the categorical form. The reduction involves the two steps of first changing the disjunctive to the hypothetical form and then to the categorical form. The following illustrations will suffice to make the matter clear: (1) Disjunctive. A is either B or C A is B ? A is not C Hypothetical. If A is B, then A is not C A is B ? A is not C Categorical. The case of A being B is the case of A not being C In this case A is B ? A is not C (2) Disjunctive. The defendant is either guilty or innocent; He is not innocent, ? He is guilty. Hypothetical. If the defendant is guilty, then he is not innocent; But he is guilty, ? He is not innocent. Categorical. The case of the defendant being guilty is the case of the defendant not being innocent, In this case the defendant is guilty, ? In this case the defendant is not innocent. 13. THE DILEMMA.The majority of us are acquainted with the dilemma as related to the activities of life. One is in a dilemma when there are two courses open to him but neither is particularly enticing. One is placed in a dilemma when he is forced to choose the lesser of two evils. For example, one may, without the proper equipment, be overtaken by a heavy rain storm; he seeks the shelter of a wayside shed; the rain continues so that he is forced either to miss his train, or to endure the discomfort of a drenching. Thus the logical dilemma limits one to a choice between alternatives, either one of which might well be avoided. Definition. The dilemma is a syllogism in which the major premise consists of two or more hypothetical propositions, while the minor premise is a disjunctive proposition. It being a combination of hypothetical and disjunctive propositions the dilemma is sometimes appropriately referred to as the “hypothetico-disjunctive” argument. The The four forms of the dilemma are the simple constructive, the simple destructive, the complex constructive, and the complex destructive. The following symbolizations illustrate these four kinds: Simple Constructive Dilemma. If A is B, W is X; and if C is D, W is X, But either A is B or C is D, Hence W is X. This is termed a simple dilemma because there is but one consequent; namely, W is X. The conclusion being affirmative makes it constructive. Simple Destructive Dilemma. If A is B, W is X; and if A is B, Y is Z, But either W is not X or Y is not Z, Hence A is not B. This is simple because there is but one antecedent, A is B, and destructive because the conclusion is negative. Complex Constructive Dilemma. If A is B, W is X; and if C is D, Y is Z, But either A is B or C is D, Hence either W is X or Y is Z. This is complex because there are two antecedents and Complex Destructive Dilemma. If A is B, W is X; and if C is D, Y is Z, But either W is not X or Y is not Z, Hence either A is not B or C is not D. This is complex because there are two antecedents as well as two consequents, and destructive because the conclusion is negative. Briefly: (1)A simple dilemma is one where either the antecedent or consequent is repeated; whereas if neither is repeated the dilemma is complex. (2)A constructive dilemma contains an affirmative conclusion; while a destructive dilemma uses a negative conclusion. (3)A simple dilemma has as its conclusion a categorical proposition; whereas the conclusion of a complex dilemma is always disjunctive. If the number of antecedents and consequents be increased, a trilemma, tetralemma, etc., may result. ILLUSTRATION—Trilemma. If A is B, W is X; and if C is D, Y is Z; and if E is F, U is V, But either A is B, or C is D, or E is F, Hence either W is X, or Y is Z, or U is V. Some authorities define a dilemma as a syllogism in which the “major-hypothetical” has more than one antecedent while the “minor” must be disjunctive. This viewpoint necessarily excludes the second form or the simple destructive dilemma. The weight of authority, however, appears to favor the classification here recommended. 15. THE ONE RULE INVOLVED IN DILEMMATIC ARGUMENTS.Since the major premise of the dilemma is hypothetical, the rule for testing such would of necessity be the hypothetical rule; namely, “The minor premise must either affirm the antecedent or deny the consequent.” As this rule and the fallacies incident to it have been treated in detail, further discussion is unnecessary. 16. ILLUSTRATIVE EXERCISE TESTING DISJUNCTIVE AND DILEMMATIC ARGUMENTS.(1) If the arithmetic contains useful facts, it will help to good citizenship; and if it trains the powers of reason, it will help to good citizenship, But the arithmetic either contains useful facts or trains the powers of reason, Hence it will help to good citizenship. This is a simple constructive dilemma in which the minor premise affirms the antecedents. The argument is, therefore, valid since it conforms to the rules of the hypothetical syllogism. The fact that the minor premise may not be a perfect disjunctive does not invalidate the conclusion, inasmuch as it is perfectly obvious that if the arithmetic fulfilled both the requirements of the antecedents, the conclusion would still obtain. It may, therefore, be inferred that if the dilemma conforms to the rules of the hypothetical argument, it is valid, though the disjunctive proposition which it contains may not be strictly logical. (2) A man is either temperate or intemperate; and, as Ihave seen you drunk several times, Iconclude that you are intemperate. Arranged logically. A man is either temperate or intemperate, You are not temperate, ? You are intemperate. It would seem that the major premise is a logical disjunctive, since temperate and intemperate indicate that the alternatives are mutually exclusive and the enumeration complete. And since the minor premise denies one alternative while the conclusion affirms the other, we may infer that the argument is valid. (3) If a man is honest, he will either pay his debts or explain; but this fellow paid no heed to the repeated notifications. Arranged logically. If a man is honest, he will pay his debts; and if he is honest, he will explain in case he cannot pay, This man neither paid his debt, nor explained, ? This man is not honest. This is a simple destructive dilemma, and since the minor premise denies the consequents it is valid. (4) A voter must either favor protection or free trade; and since you do not favor protection, you must be a free trader. The disjunctive is not logical as one might believe in universal reciprocity. The argument is, therefore, invalid. Why? (5) If a man were loyal, he would not be unduly critical; and if he were wise, he would not be too loquacious; but Ifind this clerk has been both unduly critical and too loquacious; hence Iconsider that he has been not only unwise but strikingly disloyal. This complex dilemma is valid since the minor premise denies the two consequents. 17. ORDINARY EXPERIENCES RELATED TO THE DISJUNCTIVE PROPOSITION AND HYPOTHETICAL ARGUMENT.(1) One desires to take a certain trip which involves various routes; information from time tables reveals the fact that there are three routes A, B, and C. Concerning the conditions of the journey the most important factor is the matter of comfort. Further investigation makes evident that route B will be the most comfortable one, and consequently is the route selected. Putting this ordinary experience in argumentative form gives the following: The route is to be either A, or B, or C; I will take route A; if it is the most comfortable; (co-extensive) A is not the most comfortable route, Hence I will not take route A. If B is the most comfortable route, I will take it; B is the most comfortable route, Hence I will take route B. (2) The symptoms suggest either malarial or typhoid fever; the physician is undecided till a blood test makes evident that it is not typhoid. Considered argumentatively. This disease is either malarial or typhoid fever; If it is typhoid, the blood will reveal certain evidences; But the blood does not reveal these evidences, Hence the disease is not typhoid. (3) The natural bent of the youth suggests the profession of either the ministry or teaching. He finally decides to follow the one in which he can best serve his fellows. This, after mature deliberation, appears to him to be the work of the teacher. Thrown into the form of an argument the following results: I am best fitted for either the pulpit or the schoolroom; If the schoolroom furnishes the richest field for helping my fellows, Iwill choose that work; The schoolroom does appear to furnish such a field, Hence I will choose the work of the teacher. It would appear from these ordinary experiences that frequently we are brought face to face with a choice of alternatives which are not unattractive, as in the case of the dilemma. Moreover, some condition suggests itself which, if proved or disproved, will lead to a choice of one of these alternatives. Such circumstances when thrown into the form of an argument present a disjunctive proposition followed by a hypothetical argument. To put it differently: Often in our daily affairs a most prominent limiting condition induces us to select one out of several alternatives. These alternatives are not dilemmatic in nature. 18. OUTLINE.HYPOTHETICAL ARGUMENTS, AND DISJUNCTIVE ARGUMENTS INCLUDING THE DILEMMA. (1) Three kinds of arguments Categorical, hypothetical, disjunctive. (2) Hypothetical arguments Defined, illustrated. (3) Antecedent and consequent. How determined, illustrations. (4) Two kinds of hypothetical arguments Constructive, destructive, illustrations. (5) Rule and two fallacies of the hypothetical argument. Illustrations and application of rules. Fallacy of denying antecedent. Fallacy of affirming consequent. Co-extensive hypotheticals. (6) Hypothetical arguments reduced to the categorical form. Rule, illustrations. Hypothetical and categorical arguments compared. (7) Illustrative exercises testing hypothetical arguments of all kinds. (8) Disjunctive arguments. Defined, illustrated. (9) Two kinds of disjunctive arguments. By “affirming denies,” by “denying affirms.” Illustration. (10) First rule. Stated, illustrated. (11) Second rule Stated, illustrated. (12) Reduction of disjunctive argument Two steps. (13) The dilemma Definition. (14) Four forms of dilemmatic arguments Simple constructive, simple destructive, Complex constructive, complex destructive. Illustrations. (15) The rule. (16) Illustrative exercises testing disjunctive and dilemmatic arguments. (17) Ordinary experiences related to the disjunctive proposition and hypothetical argument. 19. SUMMARY.(1) Just as there are three kinds of propositions so there are three kinds of arguments; namely, categorical, hypothetical, disjunctive. (2) Categorical syllogistic arguments are those in which all of the propositions are categorical. Hypothetical syllogistic arguments are those in which the major premise is hypothetical. In contradistinction to disjunctives, hypothetical arguments may be referred to as “conjunctive”. (3) The hypothetical proposition is composed of antecedent and consequent; the former being the limiting condition; while the latter is the direct assertion. As the words indicate the antecedent usually precedes the consequent. The signs of the antecedent are “if,” “though,” “unless,” “suppose,” “granted that,” “when,” etc. (4) The two kinds of hypothetical syllogisms are the constructive and destructive; the former is involved when the minor premise affirms the antecedent; the latter when the minor premise denies the consequent. These two kinds are sometimes referred to as “modus ponens” and “modus tollens” respectively. (5) Out of the four possible hypothetical syllogisms only two are valid as investigation proves this rule: The minor premise must affirm the antecedent or deny the consequent. In the case of the hypothetical proposition being co-extensive, the rule does not apply. (6) Hypothetical arguments may be reduced to the categorical by contracting the antecedent of the hypothetical proposition to form the subject-term, and by contracting the consequent of the hypothetical proposition to form the predicate-term of the major premise of the categorical syllogism. If it is necessary, supply a new minor term. Denying the antecedent is a matter of illicit major; whereas (7) Hypothetical arguments may be tested by following this outline: (1) Arrange logically. (2) Determine antecedent and consequent. (3) Apply hypothetical rule. (4) Reduce to categorical form. (5) Apply categorical rules. (8) A disjunctive syllogism is one in which the major premise is a disjunctive proposition. (9) The two kinds of disjunctives are those which “by affirming deny” and those which “by denying affirm.” (10) In testing disjunctive arguments there are two rules involved: First, “The major premise must assert a logical disjunction.” This necessitates the two requisites “the alternatives must be mutually exclusive” and the “enumeration must be complete.” The two opinions relative to the nature of an alternative assertion are, first, if one is false, the other must be true and vice versa; and second, if one is false, the other must be true, but both may be true. The first is adopted in this discussion. Second. The second rule involved is “When the minor premise affirms or denies one of the alternatives of a logical disjunctive the conclusion must deny or affirm all of the others.” (11) Subjecting the disjunctive arguments to the categorical test gives evidence to the close relation existing between the two forms. Alogical disjunctive proves to be logical when reduced to the categorical. The reduction entails the two steps, first, reduce to the hypothetical; second, reduce to the categorical. (12) The logical meaning of the dilemma is suggested by the popular conception. One is said to be in a dilemma when two courses are open to him, neither of which is specially attractive. A logical dilemma presents two alternatives either one of which might well be avoided. The major premise of the dilemma is hypothetical; while the minor is disjunctive. (13) The four forms of the dilemma are the simple constructive, the simple destructive, the complex constructive and the complex destructive. (14) The dilemma is subject to the hypothetical rule which (15) The minor premise need not be a logical disjunctive provided the major conforms to the hypothetical rule. (16) Frequently when ordinary experiences are reduced to augmentative form they present a disjunctive proposition followed by a hypothetical argument. 20. REVIEW QUESTIONS.(1) Relate the three kinds of arguments to the three general kinds of propositions. (2) Define and illustrate the hypothetical argument. (3) Explain the term conjunctive with reference to hypothetical arguments. (4) Explain and illustrate antecedent and consequent in hypothetical arguments. (5) Select from the following the antecedent and consequent: (1) “I usually succeed when I try.” (2) “I will not undertake it unless you guarantee half of the sum needed.” (3) “Though I speak with the tongues of men and of angels, and have not charity, Iam become as sounding brass or a tinkling cymbal.” (6) Illustrate the two kinds of hypothetical syllogisms which are valid. (7) State and explain the rule to which hypothetical arguments must conform. (8) State and exemplify the one exception to the hypothetical rule. (9) Explain how hypothetical arguments may be reduced to the categorical form. Illustrate. (10) Show by illustration that denying the antecedent is equivalent to illicit major, while affirming the consequent is equivalent to undistributed middle. (11) Reduce to the categorical form and test: “If Napoleon had possessed more of the spirit of Washington, he would have been less famous but a better man than he was; but he did not possess the spirit of the ‘Father of His Country.’” (12) Test according to outline the following hypothetical arguments: (1) “If it be a good thing to have faith, then certainly he who believes in the bible of a pagan has faith and must have a good thing.” (2) “If a 10-inch charge burst inside of a tank, there would be nothing left of the tank. It would be blown into small pieces.” (3) “If the plate found had been originally on the outside of the ship, Ishould have judged that there must be green paint on it, but I could not find green paint on that part of the ship.” (4) “If I mistake not, you are the man who did not pay me for that pair of shoes. Iam sure that you are the man as Inever forget a face.” (5) “If the maxim ‘Early to bed and early to rise makes one healthy, wealthy and wise’ were true, Iwould have been a millionaire long ago.” (13) Define and illustrate a disjunctive argument. (14) Exemplify the two kinds of disjunctive arguments. (15) What is meant by a logical disjunction? (16) “The alternatives must be mutually exclusive.” Explain this, illustrating fully. (17) Cite cases where the enumeration is not complete. (18) State in complete form both of the rules to which all disjunctive arguments must conform. (19) Show by illustration how the disjunctive syllogism may be reduced to the categorical. (20) Define and illustrate the dilemma. (21) Give examples, using symbols, of the four dilemmatic forms. Explain why these forms are so named. (22) Why does the hypothetical rule apply to the dilemmatic syllogism? (23) Test the validity of the following: Give reasons. (1) “If a substance is solid it possesses elasticity and so also it does if it be a liquid or gaseous; but all substances are either solid, liquid or gaseous; therefore, all substances possess elasticity.” (2) “If men were prudent, they would act morally for (3) “If the majority of those who use public houses are prepared to close them, legislation is unnecessary; but if they are not prepared for such a measure, then to force it upon them by outside pressure is both dangerous and unjust.” (4) “The man is either a liar or a fool and in either case he is beneath my attention.” (5) “Either he is sincere or else he is the most astute impostor the world has ever produced; for me Iprefer to think him sincere.” (24) Explain the relation that many experiences appear to bear toward an argument introduced by a disjunctive proposition and followed by a hypothetical syllogism. Illustrate. 21. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.(1) May both premises of a hypothetical argument be hypothetical propositions? Explain. See Fowler p.115. (2) Which of the two is valid? Explain. (1) If A is B, C is D If A is B, E is F ? If C is D, E is F (2) If A is B, C is D If C is D, E is F ? If A is B, E is F (3) Show by circles that two of the possible four hypothetical arguments are invalid. (4) What categorical rules does the hypothetical argument seem to violate? Explain. (5) Originate a hypothetical syllogism whose antecedent and consequent are both negative. Test its validity. (6) Originate a co-extensive hypothetical argument and show that four valid syllogisms may be derived from it. (7) Explain by word and illustration the two meanings which may be attached to “either-or.” (8) If we accepted the opinion that both alternates of a disjunctive may be true, which kind of disjunctive argument would it invalidate? (9) In a logical disjunction what law of thought is involved? Explain. (10) Why do the laws of the disjunctive seem to contradict the categorical rules? Explain fully. (11) Show by drawing on common experience that a logical dilemma is closely related to the popular conception of dilemma. (12) Illustrate by symbols and then place in good English a pentalemma. (13) State a definition of a dilemma which excludes the simple destructive form. (14) Give a common experience which, when thrown into argumentative form, results in a disjunctive proposition followed by a hypothetical syllogism. Coin a name for such a combination. | ||||||||||||||||||||||||||||||||||||||
|
