SOME LOGICAL IMPOSSIBILITIES 219 



The sixth rule of the syllogism declares two impossibilities, 

 which are as easily surmountable as the other impossibilities 

 of Logic. This rule declares that it is impossible to draw an 

 affirmative conclusion if one of the premisses is negative, or 

 a negative conclusion if both the premisses are affirmative. 

 The first impossibility has already been surmounted in argu- 

 ments IX. and XL, and the second by arguments II. and VII. 

 The following also are to the point : 



Affirmative conclusion from premisses, one of which is 

 negative. 



XV. If Some Scotchmen play the bagpipe, 

 and No Englishman plays the bagpipe ; 



then Some Scotchmen do what no Englishman does. 



It is easy to do better than this, however, for we can draw 

 an affirmative conclusion from premisses both of which are 

 negative, thus : 



XVI. If Not a drum was heard, 

 and Not a funeral note ; 



then All the bands were silent. 



Negative conclusion from affirmative premisses : 



XVII. If Most of them were drowned, 

 and The rest died of exposure ; 



then None of them survived. 



This argument employs two quantities, Most and The Rest, 

 which Logic does not recognise. I do not see why we should 

 bind ourselves in the fetters that Logic loads its votaries with, 

 but to leave logicians the less excuse, I offer the following 

 argument : 



XVIII. If Some of them travelled by express, 

 and Some followed by slow train ; 



then All of them did not arrive together. 



Here again, in the conclusion, I have employed a non-logical 

 quantity. Logic knows of no negative but " None are " and 

 11 Some are not," and here I conclude that All did not. To 

 arrive at any conclusion about what all did not do is another 

 "logical " impossibility ; but, as the reader will have realised by 

 this time, nearly every mode of statement or argument that is of 

 any use is " logically " impossible. 



