CHAPTER IV. OF THE MOODS OF SYLLOGISMS. THE Mood of a syllogism is the legitimate determination of the three propositions, in the order in which they stand, according to their respective quantity and quality; that is, as each proposition is A, E, I, or O: for example All wicked persons are miserable : All tyrants are wicked; therefore, This syllogism is in the mood A, A, A, because each of the three propositions is a universal affirmative. All gold is precious : All gold is a mineral; therefore, Some mineral is precious. This syllogism is in the mood A, A, I, because the major and the minor propositions are universal affirmatives, and the conclusion is a particular affirmative. He that is always in fear is not happy : Misers are not happy. This syllogism is in the mood E, A, E, because the major proposition and the conclusion are universal negatives, and the minor a universal affirmative. Thus, when we designate the three propositions of a syllogism, in their order, according to their respective quantity and quality, we are said to determine the Mood of that syllogism. As there are four kinds of propositions, A, E, I, O, and three propositions in each syllogism, all the possible ways of combining these four propositions by threes will be sixty-four. Each of the four may be a major premise; each of these four majors may have four different minors; and these sixteen pairs of premises may have each four different conclusions. The statement will therefore stand thus: 4 × 4 (= 16) × 4=64. This is a mere arithmetical calculation of all the Moods pos sible, without any regard to logical rules; but many of these are inadmissible in practice, because they violate the rules formerly laid down for judging of a legitimate syllogism. The Mood E, E, E, must be rejected, because it has negative premises; I, O, O, is also inadmissible, because it has particular premises; and so many others, for the same and other faults, must be rejected. Upon examination it has been ascertained that of the sixty-four possible Moods there are only eleven that can be used in a legitimate syllogism. Of these eleven the following enumeration may be useful: A, A, A; A, A, I; A E, E; A, E, O; A, I, I; A, O, O; E, A, E; E, A, O; E, I, O; I, A, I; O, A, O. All these Moods are not allowable in each of the four Figures mentioned above; as they may violate some of the foregoing rules in one Figure, though not in another. For example, I, A, I, is an allowable Mood in the third Figure; thus, I, Some afflictions are salutary : A, All afflictions are unpleasant; therefore, I, Some things that are unpleasant are salutary. But this Mood in the first Figure would be inadmissible; thus, I, Some herbs are fit for food: A, Nightshade is an herb; therefore, I, Some nightshade is fit for food. In this instance we have an undistributed middle, and therefore the syllogism is not valid. In the second Figure A, E, E, is valid; thus, A, Every virtue is praiseworthy : E, Injustice is not praiseworthy; therefore, But in the first Figure this Mood would have an illicit process of the major; thus, A, Every man is an animal : E, A horse is not a man; therefore, In the first Figure the Mood A, A, A, is a valid argument; thus, A, All human beings are entitled to liberty: A, All slaves are human beings; therefore, But in the third Figure this Mood would have an illicit process of the minor; thus, A, All tyrants are cruel : A, All tyrants are men; therefore, A, All men are cruel. Of By applying the Moods to each Figure, it will be found that each Figure will admit of only six Moods which do not violate the rules against undistributed middle, and illicit process. these twenty-four valid Moods some are useless, because they have only a particular conclusion when a universal might have been drawn. For example, A, A, I, in the first Figure, is for this reason useless; thus, A, All human beings are entitled to liberty: Five of the twenty-four Moods are, for this reason, considered unworthy of particular notice. Some of the Moods, however, conclude in one figure, when they do not in another; in this way, the number of legitimate conclusive Moods is increased to nineteen; and to distinguish these Moods, and the Figures in which they are found, names have been devised, and embodied in the following mnemonic lines, which ought to be committed to memory :— Fig. 1. Barbara, Celarent, Darii, Ferio : dato primæ. Fig. 3. Fig. 4. Hæc, Bamarip, Cameres, Dimaris, Feslapo, Fresison. In these words the three vowels denote the Propositions of which the syllogisms are composed, and indicate their quantity. The consonants, besides other uses, serve to keep in mind the Figure of the syllogism. The vowels which occur in the first syllable of each of these names shew the quantity and quality of the major proposition; the vowels of the second syllable shew the quantity and quality of the minor; and the vowels. of the third syllable shew the quantity and quality of the conclusion. Thus, if it be said that any syllogism is Celarent, this shews that it is a Mood of the first Figure; that its major proposition is E, a universal negative; its minor, A, a universal affirmative; and its conclusion, E, a universal nega'tive. By studying these lines carefully, and trying several syllogisms, in different Moods, various particulars respecting these Figures will be ascertained; and the reasons for them will be found in the preceding rules. The following may thus be deduced: 1. In the first Figure the major premise must be universal, and the minor affirmative. It is also the peculiar excellence of this figure that A, E, I, O, that is, all kinds of conclusions, can be proved by it; and A, that is, all universal affirmatives, can be proved only by this Figure. 2. In the second Figure the major premise must be universal, and one of the premises must be a negative. Hence the second Figure can only prove negative conclusions; because the middle term being the predicate in both premises, it would not be distributed unless one premise were negative; and if one premise be negative the conclusion must be negative also. 3. In the third Figure the minor must be affirmative, and hence the conclusion must always be particular; because, as the middle term is the subject of both premises, there would be an illicit process of the minor if a universal conclusion were drawn; since no affirmative proposition distributes the predicate. 4. In the fourth Figure the major term is predicated of the minor, and the minor is predicated of the middle, and the middle is predicated of the major; so that the major appears to be merely predicated of itself. It is, therefore, an inverted and awkward way of stating an argument, which is seldom or never used. One Mood in each Figure may be given as an example, and the student can exercise himself by forming examples of the rest. First, Barbara; (Bar) "all A is B: (ba) all C is A; therefore, (ra) all C is B." Thus, let the major term, represented by B, be "miserable;" the minor term C, be "tyrants; and the middle term A, be "wicked men ;" you will then have the following syllogism in Barbara of the first Figure; thus, Bar- All wicked men are miserable; ba- All tyrants are wicked men; therefore, Second, Cesare; (Ce) "No A is B: (sa) every C is B; therefore, (re) no C is A." Let the major term A, be "tyrant;" and the minor term C, be "benevolent person ;" and the middle term B, be "happy;" you will then have the following syllogism in Cesare of the second Figure: thus, Ce- No tyrant is happy: sa- Every benevolent man is happy; therefore, Third, Darapti; (Da) “ All A is B: (rap) all A is C; therefore, (ti) some C is B." Let the major term B, be “ painful;" the minor term C, "profitable ;" and the middle term A, "afflictions;" you will then have the following syllogism in Darapti of the third Figure; thus, Da- All afflictions are painful : rap- All afflictions are profitable; therefore, ti. Some things that are profitable are painful. Fourth, Bamarip; (Ba) "All A is B: (mar) all B is C; therefore, (ip) some C is A." Let the major term A, be "tyrants;" the minor term C, "unhappy ;" and the middle term B, "proud;" you will then have the following syllogism in Bamarip of the fourth Figure; thus, Ba- All tyrants are proud : mar- All proud persons are unhappy; therefore, |