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THE POPULAR EDUCATOR. 



governed. So also for the same reason we cannot assert, because 

 a, state is not well governed, that therefore the rights of the 

 weaker are not secure. 



There are, then, only two kinds of conditional syllogisms the 

 one constructive, depending for its validity on the first rule ; 

 and the other destructive, depending for its validity on the 

 second. 



A Disjunctive Proposition is, as has already been explained, 

 composed of two or more categoricals joined together by the 

 disjunctive conjunctions, either, or. It states an alternative, 

 i.e., some one or other of its members must be true : e.g., 

 "This science is either pure, inductive, or mixed." Unless 

 some one of these categoricals is true, the disjunctive must be 

 false. In addition to this, however, there must also be some 

 opposition between the parts, i.e., they must bo incapable of 

 being all true at the same time. Thus : " Either this man is 

 mortal, or he has red hair," though exactly corresponding in 

 form with the proposition given above, is quite useless for any 

 purpose of reasoning. 



If one of the propositions of a syllogism be disjunctive, the 

 syllogism is called disjunctive on that account. Suppose we 

 we have as the major premise, " Either A is B, or C is D," 

 may deny one of the categoricals in the minor, and then affirm 

 the truth of the other in the conclusion : " But A is not B ; 

 therefore C is D ; " or, "But C is not D, therefore A is B." 

 And in the same way, if, instead of being two, there were 

 several categoricals, any one or more of them being granted to 

 be false, some one or other of the remaining ones (if more than 

 one), or the remaining one (if only one), may be inferred true : 

 e.g., " It is either spring, or summer, or autumn, or winter ; but 

 it is neither spring nor summer j therefore, it ia either autumn 

 or winter." 



In most instances, however, not only (as we have already seen 

 must bo the case) is one of the categoricals true, but only 

 one is true. The consequence of this is, that we are also able, 

 if the truth of one or more of the members bo granted, to deny 

 the truth of the remainder : e.g. (referring to the above example), 

 " But it is spring ; therefore, it is neither summer; nor autumn, 

 nor winter." 



We must next speak of the Dilemma, concerning the nature 

 of which different logicians have expressed very different views. 

 Popularly, the dilemma is considered as an alternative argument, 

 such that, if the conclusion of one train of reasoning bo not ad- 

 mitted, that of the other must bo ; so that one has to choose, as 

 is said, between the two " horns " of the dilemma. This is in 

 the outline true, though not logically accurate ; besides which 

 the " horns " may bo and often are more than two in number in 

 the arguments to which the name is properly applied. In 

 reality the dilemma is a complex argument, and partakes both 

 of the nature of the conditional and disjunctive syllogisms. 

 It may be described as a syllogism with the major composed of 

 two or more conditional propositions (having each the same or 

 different antecedents, and the same or different consequents), 

 and with a disjunctive minor. It will thus assume one of 

 three forms : 



I. SIMPLE CONSTRUCTIVE. 

 If A is B, C is D; and if E is F, C is Dj 

 But either A is B, or E is F ; 

 Therefore, C is D. 



Here we have several antecedents in the major, each with 

 the same consequent ; and in the minor these antecedents being 

 granted disjunctively i.e., it being granted that one or other 

 of them is true we infer categorically in the conclusion the 

 truth of the one common consequent. The following is an ex- 

 ample of this kind of dilemma : 



If this man is guilty, he should be placed in confinement ; and if he 



is insane, he should be placed in confinement; 

 But he is eit her guilty or insane ; 

 Therefore, ho should be placed in confinement. 



II. COMPLEX CONSTRUCTIVE. 

 If A is B, C is D ; and if E is F, G is H ; 

 But either A is B, or E is F ; 

 Therefore, either C is D, or G is H. 

 If the criminal knew the consequences of his act, he was wicked ; anc 



if he did not know the consequences, he was insane. 

 But he either knew the consequences, or he did not know them; 

 Therefore, he was either wicked or insane. 

 Here we are given several antecedents in the major, as before 



)ut each has a different consequent ; and consequently when, 

 as before, we are granted in the minor the truth of one or 

 other of the antecedents, we can only disjunctively infer in the 

 conclusion the truth of the several consequents. 



in. DESTRUCTIVE (always complex). 



If A is B, C is D ; and if E is F, G is H ; 



But either C is not D, or G is not H ; 



Therefore, either A is not B, or E is not F. 

 If this man were wise, he would not speak irreverently of the Bible 



in jest ; and if he were good, he would not do it in earnest ; 

 But he does it either in jest or earnest ; 

 Therefore, he is either not wise or not good. 



[n this case we have several antecedents in the major premise, 

 iach with a different consequent. These consequents are dis- 

 junctively denied in the minor, i.e., it is asserted that some one 

 or other of them is false, and then in the conclusion it ia 

 inferred from this that some one or other of the antecedents ia 

 false. 



Before passing from the consideration of hypotheticals, it 

 must be observed (in conformity with the statement that the 

 syllogism is the type of all reasoning) v that hypotheticals can 

 by one means or another be reduced to categorical syllogisms, to 

 which the dictum and other rules before given can be applied. 

 All conditional propositions may, for instance, be considered as 

 universal affirmatives, of which the terms are entire propositions, 

 the antecedent being the subject, and the consequent the 

 predicate. Thus, " If A is B, C is D," is equivalent to such a 

 categorical as this : " The case of A being B is a case of C 

 being D," and then (if we are dealing with a simple construc- 

 tive conditional syllogism) the minor and conclusion may be 

 represented thus : " This present case is a case of A being B ; 

 therefore, it is a case of C being D." Sometimes, too, when the 

 antecedent and consequent of a conditional have each the same 

 subject, the syllogism may be reduced by simply substituting 

 a categorical major premise for the conditional one e.g., " If 

 Cffisar was a tyrant, ho deserved death," might be represented 

 by the proposition " All tyrants deserve death," the minor 

 premise and conclusion remaining the same as before. Some of 

 the methods by which hypotheticals are reduced to categoricals 

 may appear somewhat awkward ; but this is not of much 

 consequence, as it is only to show the universality of syllogistic 

 reasoning that such reduction ever is employed. 



An Enthymeme is a syllogism with one of its premises sup- 

 pressed. Which of the two remains to be supplied may be easily 

 ascertained, by observing whether the subject of the suppressed 

 premise occurs in the conclusion or not. If it does, the major, 

 obviously, is wanting ; and if not, the minor : e.g., " Caesar was 

 a tyrant; therefore, Caesar deserved death," is evidently a 

 syllogism in Barbara with the major, " All tyrants deserve 

 death," suppressed. Of course we cannot determine upon the 

 validity of the enthymeme as an argument until we have both 

 the premises before us, and see whether they conform accu- 

 rately to the syllogistic laws. 



The Sorites is an argument composed of a series of proposi- 

 tions, in which the predicate of each is the subject of the 

 next, until finally the conclusion is arrived at, which is formed 

 of the first subject and last predicate in the series : e.g., " Caius 

 is a man ; all men are finite beings ; all finite beings are 

 sentient ; all sentient beings seek happiness ; therefore Caius 

 seeks happiness." (1) " A is B, (2) B is C, (3) C is D, (4) D is 

 E, (5) E is F ; therefore A is F." 



An argument of this kind may be expanded into a series of 

 syllogisms in the first figure, the conclusion of each (with the 

 next in order of the propositions of the sorites, as major) 

 being the minor premise of the next. There will thus be as 

 many syllogisms as there are propositions in the sorites inter- 

 vening between the first premise and the conclusion ; the first 

 being the only minor premise expressed in the sorites. Since, 

 as we have seen, the minor only in the first figure can be 

 particular, it follows that the only proposition in the sorites 

 which may be particular is the first, all the rest being neces- 

 sarily universal, as being major premises in syllogisms in the 

 first figure. For a similar reason no proposition except the last 

 can be negative ; if otherwise, the syllogism in which that 

 proposition occurred would have a negative minor, which is im- 

 possible in the first figure. The following diagram will make 

 the process of the expansion of a sorites into syllogisms 

 much clearer (the numbers referring to the propositions in the 



