SOME LOGICAL IMPOSSIBILITIES 213 



the syllogism. There are, it is true, certain minor processes, 

 called immediate inferences, but these are so simple that many 

 logicians deny to them the title of inference, and are so seldom 

 used that they may, for practical* purposes, be neglected. They 

 are open, however, to objections just as damaging as those I shall 

 make to the syllogism itself, which I now proceed to examine. 



The model syllogism, as given in every book on Logic, is 

 as follows : 



I. All men are mortal, 



Socrates is a man ; 



Therefore Socrates is mortal. 



The impossibilities with which the syllogism is fenced about 

 are to be found in its rules, which are eight in number. I will 

 take them seriatim. 



The first rule is that it is impossible to construct a syllogism 

 with more or fewer than three propositions — two premisses and 

 a conclusion — as in the model given above. This rule must be 

 read in connection with the doctrine that the syllogism is the 

 only form of mediate inference ; and when so read, it means 

 that it is impossible to construct any argument with more than 

 three propositions, or any argument except the four immediate 

 inferences with less than three propositions. In fact, nothing 

 is easier than to argue from three or four premisses, and so to 

 construct an argument with at least four propositions ; more- 

 over, the same premisses will often yield two or three conclusions, 

 and thus the whole argument may easily contain double the 

 number of propositions that Logic allows. For instance : 



II. If Some of the flowers in this bed are geraniums, 

 and Others are calceolarias, 



and Others are stocks, 



and The rest are lobelias ; 



then The bed contains no begonias, 



and It contains no violas. 



Nor is it difficult to construct an argument which is not one 

 of the immediate inferences known to Logic, and which yet 

 contains but two propositions, thus : 



III. If The bed contains nothing but geraniums and violas, 

 then It contains no asters. 



The second rule declares that it is impossible to construct 

 a syllogism with more or fewer than three terms. This must 



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