CHAPTER VIII. SYLLOGISM. I. MEDIATE Inference, or Syllogism, forms the principal part of Deductive Logic, and offers a wide scope for useful exercises. I give, in the first place, a brief epitome of the syllogistic rules and forms; I then exemplify them abundantly by question and answer; lastly, I supply chapters full of the largest and most varied collection of syllogistic questions and problems which has ever been published. Some of the more perplexing questions, involving the distinction of formal and material falsity of syllogisms and their premises, are treated apart in the the succeeding chapter (xii.). RULES OF THE SYLLOGISM. (1) Every syllogism has three and only three terms. These terms are called the major term, the minor term, and the middle term. (2) Every syllogism contains three and only three proposi tions. These propositions are called respectively the major premise, the minor premise, and the conclusion. (3) The middle term must be distributed once at least. (4) No term must be distributed in the conclusion which was not distributed in one of the premises. (5) From negative premises nothing can be inferred. nega (6) If one premise be negative, the conclusion must be tive; and vice versâ, to prove a negative conclusion one of the premises must be negative. From the above rules may be deduced two subordinate rules, which it will nevertheless be convenient to state at once. (7) From two particular premises no conclusion can be drawn. (8) If one premise be particular, the conclusion must be particular. FIGURES OF THE SYLLOGISM. MOODS OF THE SYLLOGISM. The following is a compact table of the valid moods "of the syllogism, the numerals showing the figures in which each group of propositions makes a valid syllogism : MNEMONIC VERSES. Barbara, Celarent, Darii, Ferioque, prioris; Certain letters in the above lines indicate the way in which the moods of the second, third, and fourth figures may be reduced to the first figure, as follows s directs you to convert simply the proposition denoted by the preceding vowel. directs you to convert the proposition per accidens, or by limitation. m, for muta, directs you to transpose the premises. k denotes that the mood can only be reduced per impossibile. The initial consonant of each mood in the three last figures corresponds with the initial of the mood of the first figure to which it is reducible. QUESTIONS AND ANSWERS. 2. State the figure and mood to which the subjoined argument belongs : Iron is not a compound substance; for iron is a metal, and no metals are compounds. The conjunction 'for' shows that the proposition preceding is the conclusion-a universal negative. The term 'metal' must be the middle term, because it does not appear in the conclusion. The major term being 'compound substance,' the major premise must be 'no metals are compound substances,' (E) and the other premise 'iron is a metal' must be the minor. The latter is a universal affirmative; for though no mark of quantity is prefixed to ‘iron,' it states a chemical truth concerning iron in general, and may fairly be interpreted universally (A). The argument belongs to the mood EAE in the first figure, or Celarent, thus: E No metals are compound substances. A (all) Iron is a metal. E Iron is not a compound substance. 3. Examine the following argument; throw it into a syllogistic form, and bring out the figure and mood: It cannot be true that all repression is mischievous, if government is repressive and yet is sometimes beneficial. [B.] The conclusion is stated in the form of a denial of the universal affirmative all repression is mischievous'; hence the contradictory of this, or 'some repression is not mischievous' is the real conclusion. The middle term is 'government,' which does not appear in the conclusion. In looking for the major term, we do not find 'mischievous' in the premises, but only its opposite term 'beneficial.' We must assume, then, that we are intended to take 'beneficial' as equivalent to 'not-mischievous,' otherwise there would be a fallacy of four terms. To be brief, then, the syllogism takes this form Some government is not mischievous. All government is repressive (or repression). Therefore, some repression is not mischievous.' It is a valid syllogism in the third figure, and mood OAO, or Bokardo. 4. In what figures is the mood AEE valid? In the first figure we have All M is P. No S is M. No S is P. The negative conclusion distributes the major term P, which is undistributed in the major premise; hence Illicit Process of the Major Term. In the second figure we have All P is M. No S is M. No S is P. The major term is now properly distributed in the major premise, and the middle term being also distributed once, in the minor negative premise, the syllogism is valid in Camestres. The reader may show that in the third figure we have again Illicit Process of the Major, and in the fourth figure a valid syllogism Camenes. 5. What rules of the syllogism are broken by arguments in the pseudo-moods, OAE, and OIE? given than in the words of In the mood OAE the major premise, and the The answer cannot be better Solly (Syllabus of Logic, p. 86). predicate is distributed in the subject in the minor premise, and both subject and predicate in the conclusion. Hence it follows that either some term must be distributed in the conclusion which was not distributed in the premises, or else the middle term cannot be distributed in either premise. We cannot, therefore, determine at once which form the fallacy will take, but may be quite certain that there must be either an illicit process of major or minor, or else an undistributed middle. Again, in the mood OIE, both subject and predicate are distributed in the conclusion, whereas no term is distributed in the minor premise, and it therefore follows that there must be an illicit process of the minor. It is also evident that the middle term cannot be distributed in the minor premise, and that if it is distributed in the major premise the major term must be undistributed, and |