GENERAL RULES OR CANONS OF THE SYLLOGISM 313 



C. (6). A negative premiss necessitates a negative conclusion, 

 because if one premiss is negative the other, by the preceding 

 rule (5), must be affirmative, and they will thus relate the ex 

 tremes in opposite ways to the middle term : hence the extremes 

 cannot agree with each other; and the conclusion, to express 

 this disagreement, must be negative. 



Conversely, if 5 and P disagree with eachiother i.e. if the 

 conclusion be negative it must be that one of them agreed, and 

 the other disagreed, with Mi.e. that one premiss was negative 

 for if both extremes agreed with M they would agree with 

 each other and yield an affirmative conclusion. 



156. COROLLARIES FROM THE GENERAL RULES. The six 

 rules just enumerated are in themselves sufficient for the detection 

 of any fallacy in the formal aspect of syllogistic reasoning. From 

 them, however, are derived three other simple canons, the explicit 

 and distinct remembrance of which will aid the student consider 

 ably in detecting such fallacies. As we shall see presently, the 

 first two of these are sometimes stated as independent rules. 

 They are as follows ; 



1. FROM TWO PARTICULAR PREMISSES NOTHING CAN BE 

 INFERRED ; 



2. IF ONE PREMISS IS PARTICULAR THE CONCLUSION MUST 

 BE PARTICULAR ; 



3. FROM A PARTICULAR MAJOR AND A NEGATIVE MINOR 

 NOTHING CAN BE INFERRED. 



Cor. i. The following proof of the canon that from two par 

 ticulars nothing can be inferred, is given by De Morgan (Formal 

 Logic, p. 14). Since both premisses are particular, the middle 

 term, in order to be distributed once (Rule 3), must be predicate 

 of a negative premiss. Consequently the other premiss must be 

 affirmative (Rule 5), and, being also particular, will distribute neither 

 of its terms. Hence both extremes are undistributed in the pre 

 misses. But since one premiss is negative (to distribute M), the 

 conclusion must be negative (Rule 6), and will therefore distri 

 bute its predicate P, which, however, was undistributed in its 

 premiss. Hence we have Illicit Major. Therefore, with two 

 particular premisses a conclusion is impossible. 



We may state what is practically the same proof by ex 

 amining each possible case separately. We will premise this 

 important truth : that in a valid syllogism the premisses must 

 always contain one distributed term more than the conclusion ; for, 



