44 THE PRINCIPLES OF SCIENCE. 



of gravity is directly as the product of the masses, and 

 inversely as the square of the distance/ are propositions 

 concerning magnitude or degree. Logicians have not paid 

 adequate attention to the great variety of propositions 

 which can be stated by the use of the little conjunction 

 as, together with so. ' As the home so the people/ is a 

 proposition expressing identity of manner ; and a great 

 number of similar propositions all indicating some kind of 

 resemblance might be quoted. Whatever be the special 

 kind or form of identity, all such expressions of identity 

 are subject to the great principle of inference ; but as we 

 shall in later parts of this work treat more particularly 

 of inference in cases of number and magnitude, we will 

 here confine our attention to the logical propositions 

 which involve only notions of quality. 



Simple Identities. 



The most important class of propositions consists of 

 those which fall under the formula 



A = B, 



and may be called simple identities. I may instance, in 

 the first place, those most elementary propositions which 

 express the exact similarity of a quality encountered in 

 two or more objects. I may compare by memory or 

 otherwise the colour of the Pacific ocean with that of 

 the Atlantic, and declare them identical. I may assert 

 that 'the smell of a rotten egg is that of hydrogen 

 sulphide/ 'the taste of silver hyposulphite is that of 

 cane sugar/ ' the sound of an earthquake is that of distant 

 artillery.' Such are propositions stating, accurately or 

 otherwise, the identity or non-identity of simple physical 

 sensations. Judgments of this kind are necessarily pre- 

 supposed in more complex judgments. If I declare that 

 ' this coin is made of gold/ I must base the judgment upon 



