600 THE PRINCIPLES OF SCIENCE. [CHAP. 



" Every study of a generalisation or extension," De 

 Morgan has well said, 1 " gives additional power over the 

 particular form by which the generalisation is suggested. 

 Nobody who has ever returned to quadratic equations 

 after the study of equations of all degrees, or who has 

 done the like, will deny my assertion that ov /3\e7rei 

 8\7ro)v may be predicated of any one who studies a branch 

 or a case, without afterwards making it part of a larger 

 whole. Accordingly it is always worth while to gener- 

 alise, were it only to give power over the particular. This 

 principle, of daily familiarity to the mathematician, is 

 almost unknown to the logician." 



Comparative Generality of Properties. 



Much of the value of science depends upon the know- 

 ledge which we gradually acquire of the different degrees 

 of generality of properties and phenomena of various kinds. 

 The use of science consists in enabling us to act with 

 confidence, because we can foresee the result. Now this 

 foresight must rest upon the knowledge of the powers 

 which will come into play. That knowledge, indeed, can 

 never be certain, because it rests upon imperfect induc- 

 tion, and the most confident beliefs and predictions of the 

 physicist may be falsified. Nevertheless, if we always 

 estimate the probability of each belief according to the 

 due teaching of the data, and bear in mind that probability 

 when forming our anticipations, we shall ensure the mini- 

 mum of disappointment. Even when he cannot exactly 

 apply the theory of probabilities, the physicist may acquire 

 the habit of making judgments in general agreement with 

 its principles and results. 



Such is the constitution of nature, that the physicist 

 learns to distinguish those properties which have wide 

 and uniform extension, from those which vary between 

 case and case. Not only are certain laws distinctly laid 

 down, with their extension carefully defined, but a scien- 

 tific training gives a kind of tact in judging how far other 

 laws are likely to apply under any particular circumstances. 

 We learn by degrees that crystals exhibit phenomena de- 



1 Syllabus of a Proposed System of Logic, p. 34. 



