CHAP. in.J PROPOSITIONS. 37 



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 of identity, all such expressions 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 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 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 

 like that of hydrogen sulphide ; " " the taste of silver hypo- 

 sulphite is like that of cane sugar ; " " the sound of an 

 earthquake resembles that of distant artillery." Such are 

 propositions stating, accurately or otherwise, the 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," 1 must base 

 the judgment upon the exact likeness of the substance in 

 several qualities to other pieces of substance which are 

 undoubtedly gold. I must make judgments of the colour, 

 the specific gravity, the hardness, and of other mechanical 

 and chemical properties ; each of these judgments is ex 

 pressed in an elementary proposition, " the colour of this 

 coin is the colour of gold," and so on. Even when we 

 establish the identity of a thing with itself under a 

 different name or aspect, it i* by distinct judgments 



