GENERAL RULES OR CANONS OF THE SYLLOGISM 315 



Cor. 3. If the major is particular, and the minor negative, 

 the major must be also affirmative (Rule 5), and, therefore, distri 

 butes neither of its terms. The major extreme is therefore 

 undistributed. Hence it must be undistributed in the conclusion 

 (Rule 4). But it cannot ; for the conclusion, being negative 

 (Rule 6), will distribute its predicate. Hence, from a particular 

 major and a negative minor no conclusion can be drawn. 



157. SIMPLIFICATION AND RESTATEMENT OF THE GENERAL 

 RULES. The three corollaries just examined have been shown 

 to be dependent on the general rules. These latter are them 

 selves not independent of one another. The student will, of 

 course, find it useful to remember and utilize both the rules and 

 the corollaries, each for itself and independently of the others. 

 But it will be instructive to see how far the general rules them 

 selves are derivable from one another. 



Abstracting from the first two rules, which merely give the 

 nature of the syllogism, we have four rules which govern the 

 validity of syllogistic inference proper : two rules of quantity 

 and two of quality ; given above as (3), (4), (5), and (6), respec 

 tively. Now it can be shown, firstly, that the violation of (3) 

 involves indirectly * the violation iof (4) and vice versa ; secondly, 

 that (5) may be similarly deduced from (3) ; thirdly, that the first 

 part of (6) is deducible from (5) and vice versa: so that we thus 

 arrive at two ultimate and fundamental rules, one of quantity, and 

 the other of quality, the former of which may be stated in either 

 of two alternative ways. They are as follows : 



(1) Rule of Quantity : The middle term must be distributed in 

 one, at least, of the premisses : 



or, 



No term may be distributed in the conclusion which was not 

 distributed in its premiss. 



(2) Rule of Quality : To prove a negative conclusion requires 

 a negative premiss. 



Dr. KEYNES points out 2 that &quot; the only syllogism rejected by this rule 

 [2] and not also rejected directly or indirectly by the preceding rule [i] is the 

 following : All P is M, All M is S, therefore, Some S is not P. In the 

 technical language explained in the following chapter, this is A A O in figure 4. 

 So far, therefore, as the first three figures are concerned, we are left with a 

 single rule, namely, a rule of distribution, which may be stated in either of 

 the alternatives given above.&quot; 



l i.e. not in the given syllogism itself, but in another essentially involved in the 

 former, v. infra, 169 ; cf. KEYNES, op. cit., p. 294, n. 2. 

 *ibid., p. 294, n. i. 



