I. 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 

 tbrmuia 



B - C 

 denotes tliat B and C are the names of two objects or 

 groups which are not identical with each other. Thus 

 we may siiy 



Acrogens ~ Flowering plants. 



Snowdou ~ The highest mountain in Great Britain. 

 I shall also occasionally use the sign fjor, to signify in the 

 most general manner the existence of any relation between 

 the two terms connected by it. Tlius ooo might mean not 

 Old J- tlie relations of ec^uality or inequality, sameness or 

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

 causation, kjo,. in which one thing may stand to another. 

 By A ooo B I mean, then, any two objects of thought 

 related to each other in au}^ conceivable manner. 



General Formula of Logical Inference. 



The one supreme rule of inference consists, as I have 

 said, in the direction to aiiirm of anything whatever is 

 known of its like, equal or equivalent. The SichstitiUion. 

 of Similars is a phrase which seems aptly to express tlie 

 capacity of mutual replacement existing in any two objects 

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

 matter for iurther investigation to ascertain when and for 

 what purposes a degree of sin)ilarity less than complete 

 identity is sufiicient to warrant substitution. For the 

 present we tliink only of the exact sameness expressed in 

 the form 



A = B. 



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

 ceivable object, and use the sign <y/i in its stated meaning 

 of indcjiintc rdalion, then the general forinuhi of all 

 inference may be thus exhibited : — 



From A = B V5C C 



we may infer A vy- (J 



or, in words — In whatever relation a thing slav/ls to a 



second tiling, in the same relation it stands to the Wee or 



equivalent of that second thing. The identity between A 



c 



