xxvii.] GENERALISATION. 597 



properties of frozen water. The inference is of course only 

 probable, and based upon the improbability that aggregates 

 of many qualities should be formed in a like manner in 

 two or more cases, without being due to some uniform 

 condition or cause. 



In reasoning by analogy, then, we observe that two 



objects ABODE and A'B'C'D'E' have 



many like qualities, as indicated by the identity of the 

 letters, and we infer that, since the first has another 

 quality, X, we shall discover this quality in the second case 

 by sufficiently close examination. As Laplace says, 

 " Analogy is founded on the probability that similar things 

 Lave causes of the same kind, and produce the same effects. 

 The more perfect this similarity, the greater is this pro- 

 bability." J The nature of analogical inference is aptly 

 described in the work on 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, there- 

 fore in all ; and the rule of analogy is " Vieles in einem, also 

 auch das ubrige in demselben " 2 many (qualities) in one, 

 therefore also the remainder in the same. It is evident 

 that there may be intermediate cases in which, from the 

 identity of a moderate number of objects in several pro- 

 perties, 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 Generalisation. 



The term generalisation, as commonly used, includes two 

 processes which are of different character, but are often 

 closely associated together. In the first place, we generalise 

 when we recognise even in two objects a 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 crystal with a regular octahedron, there 

 is little apparent similarity ; but, as soon as we perceive 



1 Essai Philosophiqnc RUT les ProbaliHtes, p. 86. 



2 Kant's Lngik } 84, Konigsberg, 1800, p. 207. 



