CHAMBERS'S INFORMATION FOR THE PEOPLE. 



which its validity or invalidity is at once conspic- 

 uous. Both premises are presumed to be true ; 

 the syllogism has only to exhibit whether the 

 conclusion is contained in them. As a practical 

 machinery, the syllogism is only a safeguard 

 against inconsistency. As such, it is not without 

 its value. Suppose an orator declaiming about 

 the evils of mob-rule as an argument against an 

 extension of the suffrage, you may be unable to 

 question the truth of the ground proposition that 

 mob-rule is an evil thing ; but before you are led 

 away to act upon the conclusion of the orator, 

 you must consider whether you believe the apply- 

 ing proposition that the new electorate would be 

 a mob. 



In elaborating the forms and canons of the 

 syllogism, logicians have found it useful to divide 

 each proposition into its two terms, its subject and 

 predicate. As a matter of practice, the best rule 

 that can be given you is, to reduce every deduc- 

 tion to three propositions : an assertion concern- 

 ing a class ; an assertion that something (an 

 individual or another class) belongs to that class ; 

 and finally, as a legitimate conclusion, an asser- 

 tion concerning this something of what the first 

 proposition asserted concerning that class. When 

 you have reduced the deduction to this form, you 

 will then be able to decide by the light of your 

 own understanding whether you accept the truth 

 of the premises ; and if so, whether they warrant 

 the conclusion. A conclusion is often presented 

 to you as if founded upon one proposition only : 

 thus, ' This man is a rogue ; he is not to be 

 trusted.' But you will bear in mind that there 

 must be two guaranteeing propositions ; that in 

 all such cases, one of them must be supposed or 

 taken for granted ; and you will exert yourself to 

 discover the lurking premise, so as to state the 

 syllogism in full form. The omitted premise in 

 the above case is : ' No rogue is to be trusted : ' 

 a general proposition concerning a class. 



But though this arrangement is practically suf- 

 ficient, and is founded directly on the funda- 

 mental principle of the syllogism, the forms 

 worked out by Aristotle and other logicians are an 

 interesting study. As we have just said, they 

 divide each proposition into two terms. Alto- 

 gether there must be three, and only three, terms 

 in a syllogism, each being repeated twice in the 

 course of the three propositions. You have the 

 predicate of the leading assertion, the assertion in 

 which you are interested, the conclusion : that is 

 called the Major term. Then you have the sub- 

 ject of this assertion, which is called the Minor 

 term. And most important of all, you have the 

 Middle term : the class involved in the two prem- 

 ises, concerning which the predicate of the con- 

 clusion can be asserted, and to which the subject 

 of the conclusion can be asserted to belong. In 

 the syllogism ' No rogue is to be trusted ; 

 this man is a rogue ; therefore, this man is not 

 to be trusted ' ' trustworthy person ' is the major 

 term, ' this man ' is the minor term, and ' rogue ' 

 is the middle term. 



The normal form of the syllogism, when it is 

 arranged according to its fundamental proposition, 

 presents the middle term or connecting class as 

 the subject of the major or grounding proposi- 

 tion, and the predicate of the minor or applying 

 proposition. But while all valid syllogisms may 

 be reduced to this form, yet when the syllogism is 



366 



viewed as a conjunction of terms, and all possible 

 valid conjunctions of terms are elaborately set 

 forth when, in short, the syllogism is treated 

 mathematically, as a combination of abstract sym- 

 bols considerable variety of syllogistic forms is 

 introduced. These we shall briefly state. 



Syllogisms are divided by some logicians into 

 three figures, by others into four, according to the 

 position of the middle term, which may either be 

 the subject in both premises, the predicate in both, 

 or the subject in one, and the predicate in the 

 other. The most common case is that in which 

 the middle term is the subject of the major prem- 

 ise, and the predicate of the minor, as in the 

 above example. This is reckoned as the first 

 figure. When the middle term is the predicate in 

 both premises, the syllogism belongs to the second 

 figure. ('No liar is to be believed ; every good 

 man is to be believed ; therefore, no good man is a 

 liar.' Here the middle term, ' to be believed,' is 

 the predicate in both premises.) When the middle 

 term is the subject in both, it belongs to the third 

 figure. (' There is some anger which is not blame- 

 worthy ; every kind of anger is a passion ; there- 

 fore, some passions are not blameworthy.' The 

 middle term in this case is 'anger,' which is the 

 ! subject in either premise.) In the fourth figure, 

 ; the middle term is the subject of the minor prem- 

 ise, and the predicate, of the major. This figure 

 is considered to be merely an awkward form of the 

 first, and of no practical value in reasoning. 



Each figure is divided into moods, according to 

 what are called the quantity and quality of the 

 propositions that is, according as they are uni- 

 versal or particular, affirmative or negative. 



The scheme on next page represents all the legiti- 

 mate moods that is, all those where the conclu- 

 sion follows correctly from the premises. A is the 

 minor term ; C, the major ; B, the middle term. 



The invention of the fourth figure is commonly 

 attributed to Galen, but not on the most satisfac- 

 tory evidence. It has often been rejected by 

 logicians, on the ground that it is but the first 

 inverted by the transposition of the premises. 

 This, however, is not exactly the case, although, 

 on the whole, it ought to be excluded as alike use- 

 less and deformed (Baynes's Translation of the 

 Port Royal Logic, Note 48). 



It can be shewn that syllogisms in any of the 

 above forms are legitimate in other words, that 

 if the premises are true, the conclusion must be 

 true also ; and that no other combinations of uni- 

 versal and particular, affirmative and negative 

 propositions can yield true conclusions. 



If, for example, we take the first mood of the 

 first figure All B is C ; all A is B ; therefore, all 

 A is C : all animals are mortal ; all men are 

 animals ; therefore, all men are mortal the 

 reasoning is seen to be true from the very mean- 

 ing of language, or is what may be called self- 

 evident. If we say that ' all animals are mortal,' 

 we have already affirmed that every species or 

 class of animals, everything coming under this 

 designation, has the attribute of mortality, men 

 being necessarily included. So that, in fact, the 

 major premise has already affirmed the conclu- 

 sion, provided only we are sure that the subject 

 of the conclusion (men) belongs to the subject of 

 the major (animal). This assurance is given in 

 the minor (all men are animals), whence the con- 

 clusion is made out as a matter of necessity. In 



