2i 4 SCIENCE PROGRESS 



be interpreted together with the assumption that the syllogism 

 is the only mode of argument. It will be seen that argument II. 

 contains no fewer than ten terms — some of the flowers, others 

 of the flowers, the rest of the flowers, the flower-bed, geraniums, 

 calceolarias, stocks, lobelias, begonias, and violas. 



The third rule of the syllogism is that it is impossible to con- 

 struct a valid argument unless the middle term is distributed in 

 at least one of the premisses. To render this rule intelligible it 

 is necessary to explain. According to traditional Logic, the con- 

 clusion of an argument must contain two terms and no more. 

 One of these terms must appear in each premiss, and the 

 premisses must be completed by another term, the middle term, 

 which must be the same in both premisses. Thus, in the 

 model syllogism (I.) the terms in the conclusion are Socrates 

 and mortal, and the middle term, which appears in each premiss 

 but not in the conclusion, is man. The third rule provides that 

 in at least one premiss the middle term should be " distributed," 

 by which is meant that it must include or refer to the whole of 

 a class. In the model syllogism, the middle term in the first 

 premiss is "All men," which really means "every man," and 

 conforms to the rule by including the whole class of men. 

 In the second premiss the middle term is " a man." It is evident, 

 therefore, that the third rule comprises several rules, and 

 declares several impossibilities, as follows : 



i. It is impossible to construct an argument without a 

 middle term. 



2. It is impossible to construct an argument unless the 

 middle term appears in both premisses. 



3. It is impossible to construct an argument unless the 

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

 whole of a class. 



4. It is impossible to construct an argument in which the 

 middle term appears in the conclusion. 



Let us now perform these impossibilities. 



1. It is impossible to construct an argument without a middle 

 term. Both the arguments II. and III. achieve this impossibility, 

 and so does the following : 



IV. If His hands were tied behind him, 



then He could not wipe his nose. 



No doubt a logician will object that as this argument has 



