20 THE PRINCIPLES OF SCIENCE. 



one term is identical with that denoted by the other in 

 everything except the names. The general formula 



must be taken to mean that A and B are symbols for the 

 same object or group of objects. This identity may some- 

 times arise from the mere imposition of names, but it 

 may also arise from the deepest laws of the constitution 

 of nature ; as when we say 



Gravitating matter = Matter possessing inertia, 

 Exogenous plants = Dicotyledonous plants, 

 Plagihedral quartz crystals = Quartz crystals rotating 



the plane of polarisation of light. 



We shall need carefully to distinguish between relations 

 of terms which can be modified at our own will and those 

 which are fixed as expressing the laws of nature ; but at 

 present we are considering only the mode of expression. 



We may sometimes, but much less frequently, require a 

 symbol to indicate difference or the absence of complete 

 sameness. For this purpose we may generalise in like 

 manner the symbol ^ , which was introduced by Wallis to 

 signify difference between two numbers or quantities. 

 The general formula 



B - C 



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

 or groups of objects 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 o to signify in the 

 most general manner the existence of any relation between 

 the two terms connected by it. Thus 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 <> B I mean, then, any two objects of thought re- 

 lated to each other in any matter whatsoever. 



