SOME LOGICAL IMPOSSIBILITIES 215 



only two propositions, it is no argument. Let us therefore try 

 one with three : 



V. If There was a little man, 

 and He had a little gun ; 



then He was a match for a big man without a gun. 



Again logicians may object that since the little man appears 

 in both premisses, he is the middle term. I don't know how 

 they would reconcile this with his appearance in the conclusion, 

 but to meet the objection let us try again : 



VI. If Little Bo-Peep has lost her sheep, 



and Little Boy Blue let the cow into the corn ; 

 then They were both inefficient, 

 and They ought both to be smacked. 



2. It is impossible to construct an argument unless the 

 middle term appears in both premisses. This impossibility is 

 of course achieved in the preceding arguments which contain 

 no middle term. 



3. It is impossible to construct a valid argument unless the 

 middle term, in at least one premiss, expresses or refers to the 

 whole of a class, or, in other words, is " distributed." Let 

 us try : 



VII. If Hannibal crossed the Alps, 



and The part of the Alps that he crossed is impassable for elephants ; 

 then He took no elephants across with him. 



It would appear to the uninitiated that this argument con- 

 forms to rule, for the whole class of the Alps is mentioned in the 

 first premiss ; but in Logic this does not count, for the Alps is 

 the predicate of an affirmative proposition, and therefore, although 

 we do in fact refer to the whole class of the Alps, the convention 

 of Logic requires us to suppose that we do not. The argument 

 is therefore invalid in Logic, though it is convincing enough to 

 any one who is not a logician. Besides, the argument is quite 

 irregular, and not " logical " for other reasons. For one thing, 

 the term in the minor premiss, " impassable for elephants," does 

 not appear in the conclusion. Let us try again. 



VIII. If Many soldiers fought, 

 and Few soldiers were killed ; 



then Some soldiers survived. 



