INTRODUCTION. 13 



Symbolic Expression of Logical Inference. 



In developing the results of the Principle of Inference 

 we require to use an appropriate language of signs. It 

 would indeed be quite possible to explain the processes of 

 reasoning by the use of words found in the dictionary. 

 Special examples of reasoning, too, may seem to be more 

 readily apprehended than general symbolic forms. But it 

 has been shown in the mathematical sciences that the 

 attainment of truth depends greatly upon, the invention of 

 a clear, brief, and appropriate system of symbols. Not 

 only is such a language convenient, but it is almost 

 essential to the expression of those general truths which 

 are the very soul of science. To apprehend the truth of 

 special cases of inference does not constitute logic; we 

 must apprehend them as cases of more general truths. 

 The object of all science is the separation of what is 

 common and general from what is accidental and different. 

 In a system of logic, if anywhere, we should esteem this 

 generality, and strive to exhibit clearly what is similar in 

 very diverse cases. Hence the great value of general 

 symbols by which we can represent the form of a reasoning 

 process, disentangled from any consideration of the special 

 subject to which it is applied. 



The signs required in logic are of a very simple kind. 

 As sameness or difference must exist between two things 

 or notions, we need signs to indicate the things or 

 notions compared, and other signs to denote the relations 

 between them. We need, then, (i) symbols for terms, (2) 

 a symbol for sameness, (3) a symbol for difference, and (4) 

 one or two symbols to take the place of conjunctions. 



Ordinary nouns substantive, such as Iron, Metal, Elec- 

 tricity, Undulation, might serve as terms, but, for the 

 reasons explained above, it is better to adopt blank letters, 

 devoid of special signification, such as A, B, C, &c. 

 Each letter must be understood to represent a noun, and, 

 so far as the conditions of the argument allow, any noun. 

 Just as in Algebra, x, y, z, p, q, &c. are used for any 

 quantities, undetermined or unknown, except when the 

 special conditions of the problem are taken into account, 

 so will our letters stand for undetermined or unknown 

 things. 



