SYLLOGISM. 



SYLLOGISM. 



1150 



It aloo admit* every s U , bat here z U the major term, and not x. 

 The third admit* a ooncluaion : some ta are xs. The fourth also 

 admits a conclusion : some zs are xs. Consequently, the first figure 

 has a syllogism AAA, the third and fourth have AAI. 



If all the sixty-four cases be examined (a moot useful exeroiae), it 

 will be found that the following syllogisms are valid. We arrange 

 them first by figures, then by moods : 



t'int Fiuure : AAA, KAC, All, Eio. 



ml FujHTt : KAK, AEE, EIO, AOO. 

 Third Figure : AAI, I.U, All, KAO, OAO, I1O. 

 Fourth Figure : AAI, AEK, IAI, KAO, EIO. 



The following is the statement by moods : 

 (AA)A,I,I. , (A)K,K, , (AI)I,I S 



^O.O, , (1)0,0,0,0,, 



Here, for instance, we express by (u)i,i 4 that the mood IA neve r 

 proves anything but I, and that only in the third and fourth figures. 

 From the preceding we may collect that 



As to figures : any proposition may be proved iu the first ; none but 

 negatives in the second ; none but particulars in the third ; and every- 

 thing but the universal attirmative in the fourth. 



As to moods : from premises both negative or both particular, no 

 conclusion follows : where one premiss is negative, the conclusion is 

 negative ; and where one premiss is particular, the conclusion is par- 

 ticular. 



In order to remember the figures certain words have been lung used 

 by writers on logic, which make a grotesque appearance ; but if the 

 reader will tolerate them till we have gone through an example of each 

 syllogism, he shall see that those who made them were at least as good 

 wits as those who laugh at them. The magic words of the fourth 

 figure are different iu different writers ; we have taken those used by 

 Dr. Whately. 



fint Fi</ure : Barbara, Celarent, Darii, Ferio. 



Second Figure : Cesare, Camestres, Festino, Baroko. 



Third Figure : Darapti, Disamis, Datisi, Felapton, Bokardo, Feriso. 



Fourth Figure : Bramantip, Camenes, Dimaris, Fesapo, Fresison. 



Thus the vowels AAA are seen in Barbara, All in JJutisi. The fol- 

 lowing are instances of each form, with an example which may easily 

 be reduced to the form. 



Pint Figurt. 



Ilarbara. Every T is X, every z is Y, therefore every z is x. Ex- 

 ample. They must, as men, have faults : or all men have faults, these 

 persons are men, therefore these persons have faults ; strictly, all men 

 are persons having faults, &c. 



Celarent. No Y is x, every z is T, therefore no z is x. Example. 

 Those who bribe should not, any more than any other lawbreakers, be 

 exempt from punishment. 



/inn't. Every Y is x, some zs are YS, therefore some zs are xs. 

 Example. Exploded doctrines are sometimes true, because capable of 

 proof. 



Ferio. No Y is x, some zs are Ys, therefore some zs are not xs. 

 Example. Some of the earlier principles of science are not well 

 appreciated for want of attention to the usual modes of operation of 

 the mind. 



Second Figure. 



Cetare. No x is Y, every z is Y, therefore no z is x. Example. The 

 presence of horns in this species, and their absence in the other, is a 

 complete distinction between the two. 



Camettrer. Every x is Y, no z is Y, therefore no z is x. The last 

 example will do : this mood is only a consequence of the convention 

 by which the major premiss is to be written first, and of the converti- 

 bility [CONVERSE] of the universal negative proposition. 



Fettino. No X is Y, some zs are YB, therefore some zs are not xs. 

 Example. Persons who pretend to form an opinion on philosophical 

 subjects are oftentimes incapable of doing it properly, from want of 

 acquaintance with the exact sciences. This example is given purposely, 

 as falling more naturally into another figure, though capable of ex- 

 pression in this. 



llarnlen. Every x is Y, some zs are not YS, therefore some zs are not 

 xs. Example. None but the industrious can succeed, so that there 

 must be many failures. 



Third Figure. 



Darapti. Every Y is x, every Y Is z, therefore some zs are xs. Ex- 

 ample. Politics and literature are not necessarily incompatible, for many 

 persons can be named who have cultivated both. 



Daamit. Some YS are xs, every Y is z, therefore some zs are 

 xs. Example. Many things inexpedient, because wrong, are apparently 

 mefaL 



Daliti. Every Y is x, some YS are zs, therefore some zs are xs. The 

 last example will do for this also. 



-No Y is x, every. Y is z, therefore some zs are not x 

 amplr. There are organised bodies to whose existence air Is necessary, 

 and which have no ocomotive power, as plants, for instance. 



Jiokardo. Some YS are not xs, every Y is /., therefore some zs are 

 not xs. Estimplr. Even industry does not always succeed, for mm of 

 great research have been mistaken. 



Perito. No Y is x, some YS are zs, therefore some xs are not xs. 

 Example. It is not true that all who gave evidence were present, f . >r A , 

 B, o, Ac., were many miles off. 



Fourth Figure. 



Bramantip. Every x is Y, every Y is z, therefore some xa are xs. 

 Example. Among repulsive things are the sciences themselves, for they 

 are all difficult. 



Camrna, Every x is Y, no Y is z, therefore no z is x. flnMyfa N.> 

 perfect being can be man, for all men are subject to deeny, the un- 

 failing mark of imperfection. This example would do very well 

 of the most common species of fallacy, that in which the middle t.-nu 

 is. used in different senses, so that there is in fact no middle (or 

 common middle) term. We have seen this argument used > >i>i< uh.'iv, 

 " perfect being " meaning " morally perfect being," and " imperfection" 

 including phytical as well as moral imperfection. 



Dimaris. Some xs are YS, every Y is z, therefore some zs : 

 Example. Some writers who repeat themselves are amn.- 

 prolix writer does it, and the most attractive books are not always the 

 shortest. 



Fetapo. No x is Y, every Y is z, therefore some zs are not xs. i'sample. 

 Some things which are not much written about are not worth learnin<; ; 

 not that this circumstance is otherwise an index, except in this 1 1 

 that all really useful learning has its opponents, and it in only where 

 there is opposition that much discussion ever takes place. Here is a 

 good instance of the ease in which the premises both yield the < 'in- 

 clusion, and explain the sense in which it is to be taken : the piv 

 is no syllogism unless the " writing about " the subject in the con- 

 clusion mean writing about not the subject itself, but whether it be 

 useful or not. 



Fretitou. No x is Y, some YS are zs, therefore some zs are not x<. 

 Example. Some things which are cried up can hardly be relics of anti- 

 quity, for they are valueless. Here is an instance of an argument which, 

 logically undeniable, may be disputable as to the matter. One of the 

 premises is " no relic of antiquity is valueless," which many may be 

 found to deny. 



Some other forms have been given, but they are only some of the 

 preceding with the premises transposed, and which, therefore, do not 

 obey the conventional rule relative to the precedence of the major 

 premiss : as, for instance, one named Jiaralipton (AAI, the last syllable 

 being only a termination) which we may mention particularly, inas- 

 much as this word has been very often quoted as a specimen of logical 

 terms. It runs as follows : Every Y is x, every z is Y, therefore some 

 xs are zs. Transpose the premises, and we have the first syllogism of 

 the fourth figure. 



Of all the four figures the first is the most natural, and every mood 

 of the other three can be reduced to one of the first, in one of the 

 following ways. It will be seen that every name in the last three 

 figures begins with one of the initial letters of the first, and thus it is 

 pointed out to which mood of the first figure each is reducible. Thus 

 Cesare, Camestres, and Camenes are those which are reducible to 

 Celarent of the first figure. 



The other significant letters of the descriptive words are m, s, p, Is, 

 wherever they occur. By m it is implied that the premises are to be 

 transposed ; by s that the premiss marked by its preceding vowel is to 

 be converted, whence s follows only E and I [CONVERSE] ; by /> that the 

 conversion is to be made iu a limited manner, or per accidenn [CON- 

 VERSE] ; and by k that the reduction is made by what is called the 

 m/uctio ad impossitiile, a term which we now explain. It means that 

 the syllogism can be replaced by one in the first figure, which proves, 

 not the truth of the conclusion, but the falsehood of its contradictory. 

 [CONTRARY AND CONTRADICTORY.] For example, take the syh 

 Baroko, or 



Every x is Y, 

 Some zs are not YS, 

 Therefore Some zs are not xs. 



If the conclusion be denied, it must be by affirming that every /. 

 is x. Let this be so, then we must have the syllogism Barbara as 

 follows : 



Every x is Y, 



Every z is x, 



Therefore Every z is Y. 



But, by hypothesis, some zs are not YS, whence this conclusion con- 

 tradicts one of the admitted premises, or must be false. One, then, 

 of the premises which gives it must be false ; but since Every x is v is 

 supposed true, it must be Every z is x, which is false, or Some zs are 

 not xs, w'hich is true. This is a specimen of the persevering deter- 

 mination of the older logicians to make everything reducible to the 

 first figure. 



It appears then that few words have ever been invented which have 

 really so much meaning as the now despised appellations of syllogisms. 

 Take, for example, Diwmi* ; every letter is a sentence. D means that 

 the mood of the first figure into which this can be reduced is Darii ; I, 

 that the major premiss is a particular affirmative proposition ; S, that 



