246 THE PRINCIPLES OF SCIENCE. 



of analogical inference is also very correctly described in 

 the Logic attributed to Kant, where the rule of ordinary 

 induction is stated in the words ' Eines in vielen, also in 

 alien,' one quality in many things, therefore in all ; and 

 the rule of analogy is * Vieles in einem, also auch das 

 ubrige in demselben' c , many (qualities) in one, therefore 

 also the remainder in the same. 



It is evident that there may be intermediate cases in 

 which, from the resemblance of a moderate number of 

 objects in several properties, we may infer to other objects. 

 Probability must rest either upon the number of instances 

 or the depth of resemblance, or upon the occurrence of both 

 in sufficient degrees. What there is wanting in extension 

 must be made up by intension, and vice versd. 



Two Meanings of Generalization. 



The term generalization, as commonly used, includes two 

 processes which are of different character, but are often 

 closely associated together. In the first place, we generalize 

 whenever we recognise even in two facts or objects a certain 

 common nature. We cannot detect the slightest similarity 

 without opening the way to inference from one case to 

 the other. If we compare a cubical with a regular octa- 

 hedral crystal, there is little apparent similarity ; but, so 

 soon as we perceive that either can be produced by the 

 symmetrical modification of the other, we discover a 

 groundwork of similarity in the constitution of the 

 crystals, which enables us to infer many things of one, 

 because they are true of the other. Our knowledge of 

 ozone took its rise from the time when the similarity of 

 smell, attending electric sparks, strokes of lightning, 

 and the slow combustion of phosphorus, was noticed by 



c Kant's 'Logik,' 84, Kbnigsberg, 1800, p. 207. 



