HYPOTHESIS 153 



equality springing from the very nature of numbers between 

 the sum the first n odd numbers and 2 . 



(3) More important still than enumerative induction, as a source 

 of hypotheses, indeed by far the most fruitful source, is Analogy. 

 Certain resemblances of an unexplained phenomenon to some 

 other already known and explained phenomenon, will suggest 

 the direction in which we ought to look for an explanation of 

 the former. Thus, Malus, accidentally observing, through a 

 double refracting prism, the light of the setting sun reflected from 

 the windows of the Luxembourg Palace, saw that the light dis 

 appeared at two opposite positions of the prism, like light pol 

 arized by passing through another prism ; and he argued by analogy 

 that this and, apart, all reflected light was likewise probably 

 polarized : an hypothesis which was speedily verified. 



The term &quot; analogy &quot; is commonly understood nowadays to 

 mean a resemblance of any sort ; and by the &quot;argument from 

 analogy &quot; is understood an inference based on such resemblances. 

 Mill s description of it is simple and clear: &quot;Two things re 

 semble each other in one or more respects ; a certain proposition 

 is true of one, therefore it is true of the other &quot;* It is an argu 

 ment from partial resemblance between two phenomena (or 

 groups or series of phenomena) to some further point of resem 

 blance between them. A few simple examples will illustrate the 

 nature of this mode of inference. 



(a) Cholera has been proved to be due to the action of a 

 certain known bacillus. Here is some other disease, which is 

 seen to present many symptoms similar to those of cholera. 

 Therefore, this disease also probably has its origin in the action 

 of some bacillus. 



(b) The planet Mars revolves around the sun, has light and 

 heat from the sun, rotates on its axis, and appears to have 

 mountains and rivers like the earth. Therefore, it may also be 

 the scene of vegetable and animal life. 



(c) A is a man of certain character, disposition, opinions, etc. 

 (say xK) ; and he has acted in a particular way in certain circum 

 stances. B is also a man of the same character, etc. as A (say 

 xR} : x being the known common points, and R, R l , the partially 

 differing and partially unknown residue in the case of each). 

 Therefore, B will probably act in the same way when placed in 

 similar circumstances. 



1 Logic, III., xx., 2. 



