Q. 20. Repeat the general law of syllogism, commonly called "Aristotle's dictum." 135. Q. 21. What is the definition of a perfect syllogism?* 136. Q. 22. If two terms agree with the same middle term, what is your inference? 137. Q. 23. If one term agrees, and another disagrees with one and the same middle term, what is your inference? 138. Q. 24. What are called the extremes of a syllogism? Q. 25. In what proposition do the extremes stand together? Q. 26. What is the first rule relative to the correct construction of a syllogism? 139. Q. 27. What is the second rule? 140. Q. 28. What is the third rule? 141. Q. 32. Prove that you remember what A distributes. Q. 33. What does E distribute? Q. 34. What does I distribute? Q. 35. What does O distribute? Q. 36. Prove your knowledge of this by analyzing or parsing the syllogism given under Art. 144, note 6, and show whether it is true or false, according to the rules. CHAP. II. On the Moods and Figures of Syllogisms. INTRODUCTORY REMARKS. 1. It will be impossible correctly to understand and practise the subject of this chapter, without the recollection of a rule already given, (Art. 69, 2) relative to the signification of the four symbols, which logicians invariably employ to designate the character, as to quality and quantity, (Art. 94, Rule 5, note 3, and Rule 6, 7, 8, 9,) of the four principal propositions to which all are reducible: viz: A always signifies a universal affirmative, E a universal negative, I a particular * From Σuos, reasoning; which is from Euxλogisqual, to reason; from Zvv, together, and Aw, to say, select, count, infer. affirmative, and O a particular negative. Which is easily remembered by the aid of the mnemonic lines given, (Art. 70) viz: Universally, A AFFIRMS, and E DENIES. Particularly, I AFFIRMS, and O DENIES. 2. It has already been intimated that all syllogisms either are or may be reduced to the four moods of the first figure, which is in strict conformity with the Aristotelian precept, "Whatever is predicated of a whole class, (a distributed middle,) may be predicated of anything contained in that class,' when the four moods will be expressed by the four following associations, A. A. A. E. A. E. A. I. I. and E. I. O. For example, A. Every flower fades. A. Every tulip is a flower; therefore E. No flower is always in bloom. E. No rose is always in bloom. A. All flowers are beautiful. I. Some things deciduous are flowers; therefore I. Some things deciduous are beautiful. E. No star is dark. I. Some unseen are stars; therefore O. Some stars unseen are not dark. 3. According to one of these four moods, viz: A. A. A.; E. A. E.; A. I. I.; E. I. O. ; we may always construct our own syllogisms. In short they appear to be consistent with the usual order of thought, and doubtless are, with the definitions of a perfect syllogism, (Art. 136.) "A perfect syllogism is an * Let it not be supposed, in consequence of syllogism being frequently selected, in logical treatises, of a short and simple character, that they often express only an obvious truth. Syllogisms are universal in their application, comprehending all subjects, whether of Divinity, science, of the arts, political economy, or of the general and common business of life; in short, a syllogism exists, expressed or implied, wherever such illative words, as therefore, wherefore, consequently, &c. rationally exists. But were selections, on every occasion made from the sciences, &c. they would not be so generally understood; whilst one of a short compass, expressed in a few words, though it contain an obvious truth, is not selected on that account, but that it might briefly express in a miniature compass, a general form, or be the fac simile to which all others of the same mood and figure, and on any subject, obvious or not, may be reduced. argument so expressed that the major term must be predicated of the minor, consequent on that minor being contained in a middle term of which the same major is predicated. 4. Nothing can be more simple and obvious than this general and infallible law of reasoning: its simplicity is such that it may be even ocularly elucidated by a geometrical figure: All squares are four-sided figures, having all their sides equal, and their angles right angles. The figure z is a square; therefore The figure z is a four-sided figure, having all its sides equal, and its angles right angles. 5. We may at least reduce all our reasoning to this simple and obvious character, the propriety and necessary consequence of which is evident to the understanding, and thus evident to the eye. We shall, however, meet with syllogisms of a different form, whether constructed such designedly or not; and the first process we should, in such case adopt, would we be successful opponents of an adversary, is to convert them into one of the four moods of the first figure in which a fallacy will be more clearly exposed. Hence the necessity of this chapter on the moods and figures of syllogisms, and of the next, containing the rules necessary for their reduction. (Art. 145.) The mood of a syllogism is that order in which the characters of the propositions composing it succeed each other. 1. The character of a proposition is always denoted by either A, E, I, or O. These are sufficiently expressive, and indicate all that it is necessary to attend to in this respect. 2. Since the major premiss may be either A, E, I, or O, and the minor be likewise either, or four times four, the variety in the premises may be sixteen; and since the conclusion is also capable of four variations, four times sixteen, or sixtyfour, is the number of different ways in which A, E, I and O can combine in three propositions. 3. This, however, is a mere arithmetical calculation, without any regard to those logical rules, which reject fifty-three out of the sixty-four, leaving but eleven combinations, viz:AAA, AAI, AEE, AEO, AÏI, AOO, EAE, EAO, EIO, IAI, OAO.* (Art. 146.) The FIGURE of a syllogism is that position which the middle term assumes with respect to the extremes. 1. The extremes of a syllogism are always the minor and major terms, which become the extremes of the conclusion. (Art. 147.) The middle term being the subject of the major, and predicate of the minor premiss, is THE FIRST FIGURE. 1. This figure is the most natural and clear of all; it is to this that Aristotle's dictum applies, and it is the peculiar excellency of this figure, that all questions may be proved by it, universal or particular, affirmative or negative; consequently to this all other figures may be reduced. *The arithmetical combinations are AAA, AAE, AAI, AAO: AEA, AEE, AEI, AEO: AIA, AIE, AII, AIO: AOA, AOE, AOI, AOO: EAA, EAE, EAI, EAO: EEA, EEE, EEI, EEO: EIA, EIE, EII, EIO: EOA, EOE, EOI, EOO: IAA, IAE, IAI, IAO: IEA, IEE, IEI, IEO: IIA, IIE, III, IIO: IOA, IOE, IOI, 100: OAA, OAE, OAI, OAO: OEA, OEE, OEI, OEO: OIA, OIE, OII, OIO: OOA, OOE, OOI, 000. But sixteen of these are excluded by the fifth Rule (Art. 143,) because their premises are negative, viz. EEA, EEE, EEI, EEO: EOA, EOE, EOI, EOO: OEA, OEE, OEI, OEO: OOA, OOE, OOI, 000. Twelve by the same Rule, (Art. 143,) because their premises are particular, viz. IIA, IIE, III, IIO: IOA, IOE, IOI, 100: OIA, ÕIE, OII, OÏO. Twelve by the sixth Rule, (Art. 144,) because one of the premises is negative and not the conclusion, viz. AEA, AEI: AOA, AOI: EAA, EAI: EIA, EII: IEA, IEI: OAA, OAI. Eight by the same Rule, (Art. 144,) because one of the premises is particular and not the conclusion, viz. AIA, AÍE: AOE : EIE : IAA, IAE: IEÈ: OAE. Four, because the conclusion is negative, but neither of the premises: AAE, AAO: AIO: IAO. To which must be added I, E, O, for an illicit process of the major in every figure. Therefore fifty-three moods are excluded, many of which offend against several rules. There consequently remain eleven, which only are useful in syllogism, which are already quoted above. (Art. 148.) The middle term being the predicate of both premises, is the SECOND, and the subject of both is the THIRD FIGURE. (Art. 149.) The middle term being the predicate of the major, and subject of the minor premiss, is the FOURTH FIGURE. 1. This figure, in every respect, is the reverse of the first; and as that is the best, this is the worst, and most awkward; and merits stating only that it may be, as shall be hereafter shown, reduced to the first. 2. The proper order of a syllogism is to place the major premiss, or that which compares the middle term with the major first, and the minor premiss, or that which compares the middle term with the minor next. 3. If, in the following examples, each middle term is marked as usual with a double line, they will show that varied position of the middle term which constitutes, according to the preceding rules, the four figures of syllogism. 1st Figure. All flowers are beautiful. Some things deciduous are flowers. Some things deciduous are beautiful. Every flower is deciduous. No evergreen is deciduous. No evergreen is a flower. 3d Figure. All flowers are beautiful. Some flowers are deciduous. Some deciduous are beautiful. 4th Figure. Every flower is deciduous. Nothing deciduous is an evergreen. No evergreen is a flower. 4. This varied position of the middle term is frequently represented symbolically, by letters. Only let Y, wherever found, signify the middle term, Z the minor, and X the major, and the four figures can be thus exhibited. |