INTRODUCTION. 17 



sameness. For this purpose we may generalise in like 

 manner the symbol ~, which was introduced by Wallis 

 to signify difference between quantities. The general 

 formula 



B - C 



denotes that B and C are the names of two objects 01 

 groups which are not identical with each other. Thus 

 we may say 



Acrogens ~ Flowering plants. 



Snowdon ~ The highest mountain in Great Britain. 

 I shall also occasionally use the sign ooi to signify in the 

 most general manner the existence of any relation between 

 the two terms connected by it. Thus coo might mean not 

 only the relations of equality or inequality, sameness or 

 difference, but any special relation of time, place, size, 

 causation, &c. in which one thing may stand to another. 

 By A coo B I mean, then, any two objects of though! 

 related to each other in any conceivable manner. 



General Formula of Logical Inference. 



The one supreme rule of inference consists, as. I have 

 said, in the direction to affirm of anything whatever is 

 known of its like, equal or equivalent. The Substitution 

 of Similars is a phrase which seems aptly to express the 

 capacity of mutual replacement existing in any two objects 

 which are like or equivalent to a sufficient degree. It is 

 matter for further investigation to ascertain when and for 

 what purposes a degree of similarity less than complete 

 identity is sufficient to warrant substitution. For the 

 present we think only of the exact sameness expressed in 

 the form 



A=*B. 



Now if we take the letter C to denote any third con- 

 ceivable object, and use the sign coo in its stated meaning 

 of indefinite relation, then the general formula of all 

 inference may be thus exhibited : 



From A = B 3oo C 



we may infer A <**> C 



or, in words In whatever relation a thing stands to a 

 second thing, in the same relation it stands to the like or 

 equivalent of that second thing. The identity between A 



