310 



THE POPULAR EDUCATOR. 



process of the major " in the first, while it does nob violate 

 any rule in the second. By trying the different modes which 

 are legitimate in the different figures, we shall find as the 

 result of the experiment that each figure will admit of but 

 six moods. But of the twenty-four thus allowable, five are 

 useless (e.g., A A I in Pig. 1), as having a particular conclusion 

 when the premises are such as to warrant a universal one. 

 There are thus nineteen moods remaining. 



Logicians have devised names for each of these nineteen 

 moods to distinguish the figure in which it occurs, and also to 

 serve other purposes we shall subsequently point out. The 

 three voivcls in each name denote, by their quantity and quality, 

 the three propositions of which the syllogism is composed. The 

 names are these : 



From an examination of these different moods of each figure, 

 we may perceive, amongst other things, that all four conclu- 

 sions may be proved in the first figure (in which alone A is 

 capable of proof) ; that the second only proves negatives, and 

 the third particulars ; and that any conclusion except A may 

 be established by the fourth figure. These peculiarities follow 

 from the rules already given ; thus, since by Rule 6 the middle 

 must be once at least distributed, and that in the second figure 

 it is the predicate of both premises, one of them must be 

 negative, and therefore the conclusion negative also. A little 

 consideration will enable the reader to account for all other 

 special rules of a like nature, e.g., that the minor premise must 

 always be affirmative in the first figure. This may be proved 

 as follows : If the minor were negative, the conclusion would 

 also be negative (Eule 6), and the major affirmative (Rule 5) ; 

 hence there would be an " illicit process of the major term," it 

 being in the first figure the predicate of both the major 

 premise and the conclusion. By a similar application of the 

 general rules it can be shown that the minor promise is affir- 

 mative in the third figure also ; that the major is universal in 

 the first and second, etc. etc. 



We may take one mood as an example in each figure of the 

 meaning of the name. " All Y is X (Bar) ; all Z is Y (ba) ; 

 therefore, all Z is X (ra)," is an example of Barbara : "All X 

 is Y ; no Z is Y ; therefore, no Z is X," of Camestres: " All Y 

 is X ; all Y is Z ; therefore, some Z is X," of Darapti : and 

 " All X is Y ; no Y is Z ; therefore, no Z is X," of Camenes. 



The four moods of the first figure are called perfect, because 

 the dictum is directly and immediately applicable to them, and 

 all the others imperfect. In the first, the major premise states 

 that the major extreme is predicated of the middle taken dis- 

 tributively; and the minor, that the minor extreme is contained 

 under the middle : so that almost the very words of the dictum 

 can be directly applied. 



Now as all reasoning ultimately depends upon the possibility 

 of the dictum being applied as a test of its validity, we must 

 be able to bring all imperfect moods into the form of some one 

 of the moods of the first figure in order to apply this test. 

 The process by which this is done is called Reduction, which is 

 the changing of an imperfect mood into a perfect, so as to make 

 the force and validity of the reasoning evident, which was not 

 directly evident before. This is of two kinds Ostensive Reduc- 

 tion and Reduction ad Impossibile. 



(1.) Ostensive Reduction. By this method we prove in the 

 first figure (which we know to be correct, because we can 

 apply the dictum to it directly) either the very same conclusion 

 as that of the original Reducend (i.e., the imperfect) mood, or 

 one which directly implies it. Let ua take Darapti as an 

 example : 



Da All wits arc dreaded ; 

 rap All wits are admired; therefore, 

 ti Some who are admired are dreaded. 



This is reduced to Darii by converting the minor premise (per 

 accidens) : 



Da All wits are dreaded ; 



ri Some who are admired are wits ; therefore, 

 i Some who are admired are dreaded. 



Here we have the same conclusion in the reducond and reduct 

 moods. Or, suppose we have Camestres : 



All X is Y ; 

 No Z is Y ; 

 No Z is X. 



We can reduce 

 Celarent, thus 



it to ( 



No T is Z ; 

 All X is Y ; 

 No X is Z. 



This is done by simply converting the minor and then trans- 

 posing the premises ; and we then get the original conclusion 

 from the new one, by converting it simply. And since by 

 applying the test of the dictum we know that the new conclu- 

 sion is true, being correctly deduced from true premises, we 

 know, by the laws of conversion already explained, that its 

 simple converse, the old conclusion, is true also. Thus, in 

 Ostensive Reduction our mode of proof is always to show 

 directly that the conclusion of the reducend is true. 



(2.) In Reduction ad impossibile, however, we prove its truth 

 indirectly by showing it cannot lie false. Let us illustrate this 

 by an example. Suppose we are given in Baroko : 



All good rulers are loved by their subjects ; 

 Some absolute monarchs are not loved by their subjects ; 

 .'. Some absolute monarchs are not good rulers. 



Now, if this conclusion be false, its contradictory must ba 

 true (as we have seen before). This is, " All absolute monarchs 

 are good rulers." If we, then, substitute this proposition for 

 the minor of the original syllogism, and draw a new conclusion 

 from these two new premises, we have the following syllogism 

 in Barbara : 



All good rulers are loved by their subjects ; 

 All absolute monarchs are good rulers ; 

 .'. All absolute monarchs are loved by their subjects. 



This new conclusion is the contradictory of the original minor 

 premise, and therefore must be false ; for as the premises are 

 always granted to be true, it is only the validity of the con- 

 clusion asserted to be deduced from them which has to be 

 investigated. But the new conclusion having been correctly 

 deduced from two premises in the first figure, the falsehood 

 must be in the premises. The major cannot be the false one, 

 because it is ona of those originally laid down as true. Hence 

 it is the minor which must be false, and therefore its con- 

 tradictory must be true ; and this is the original conclusion of 

 which we were seeking to prove the truth. 



It was with a view to pointing out the manner in which the 

 different moods are thus to be reduced that their names above 

 given have been framed. The initial consonants, B, C, D, F, 

 denote the mood of the first figure (Barbara, Celarent, Darii, 

 or Ferio) to which the reduction is to be made. S and P 

 signify that the proposition denoted by the vowel immediately 

 preceding is to be converted in the process (s, simply, and p, 

 per accidens) ; " m " points out that the premises are to be 

 transposed; and "k," the sign of reduction ad impossibile, 

 indicates that the proposition denoted by the vowel immediately 

 before it, is to be omitted, and the contradictory of the conclu- 

 sion substituted for it. K, therefore, occurs only in Baroko 

 and Bokardo, those being the only moods to which this kind of 

 reduction is usually applied. 



LESSONS IN FRENCH. LXXIV. 



79. REPETITION OF THE ARTICLE. 



(1.) GENERAL RULE. The article* is repeated before every 

 noun, and every word used as a noun, having a separate 

 meaning : 



Le coeur, 1'esprit, les moeurs, 

 tout gagne a la culture. 



Le pere et la mere semblaient 

 exciter leur petite compagne a 

 s'en repaitre la premiere. 



BUFFON. 



(2.) The article will, therefore, be repeated, when one of 

 two adjectives, united by the conjunction et, qualifies a noun 

 expressed, and the other a noun understood : 



The heart, the mind, the manners, 

 everything improves by cultivation. 



Tiie father and mother seemed to 

 excite their little companion to feed, 

 upon it first. 



L'histoire ancienne et la mo- 



Ancient and modern history. 



derne. 



that is, 1'histoire ancienne et 1'histoire moderne. 



* This rule applies to the determinative adjectives, mon, ton, son, 

 ce, cet, etc. 



