r.J 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 or 

 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 coe to signify in the 

 most general manner the existence of any relation between 

 the two terms connected by it. Thus vx> 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 GOO 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 GOO in its stated meaning 

 of indefinite relation, then the general formula of all 

 inference may be thus exhibited : 



From A = B UK C 



we may infer A xn 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 



