xxvii.] GENERALISATION. 625 



one satellite could belong to Saturn, because, with those of 

 Jupiter and the Earth, it completed the perfect number of 

 six. A wliole series of other superstitions and fallacies 

 attach to the numbers six and nine. 



It is by false generalisation, again, that the laws of 

 nature have been supposed to possess that perfection which 

 we attribute to simple forms and relations. The heavenly 

 bodies, it was held, must move in circles, for the circle was 

 the perfect figure. Newton seemed to adopt the question- 

 able axiom that nature always proceeds in the simplest 

 way ; in stating his first rule of philosophising, he adds : ^ 

 " To this purpose the philosophers say, that nature does 

 nothing in vain, when less will servo; for nature is pleased 

 with sin;plicity, and affects not the pomp of superfluous 

 causes." Keill lays down ^ as an axiom that " The causes 

 of natural things are such, as are the most simple, and are 

 su.fticient to explain the phenomena : for nature always 

 proceeds in the simplest and most expeditious method ; 

 because by this manner of operating the Divine Wisdom 

 displays itself the more." If this axiom had any clear 

 grounds of truth, it would not apply to proximate laws ; 

 for even when the ultimate law is simple the results may 

 be infinitely diverse, as in the various elliptic, hyperbolic, 

 parabolic, or circular orbits of the heavenly bodies. Sim- 

 plicity is naturally agreeable to a mind of limited powers, 

 but to an infinite mind all things are simple. 



Every great advance in science consists in a great gene- 

 ralisation, pointing out deep and subtle resemblances. 

 The Copernican system was a generalisation, in that it 

 classed the earth among the planets ; it was, as I'isliop 

 Wilkins expressed it, "the discovery of a new planet," but 

 it was opposed by a more shallow generalisation. Those 

 who argued from the condition of things upon the earth's 

 surface, thought that every object must be attached to 

 and rest upon something else. Shall the earth, they said, 

 alone be free? Accustomed to certain special results of 

 gravity they could not conceive its action under widely 

 (iifferent circumstances.^ No hasty thinker could seize 

 the deep analogy pointed out by Horrocks between a pen- 



^ Privcipia, l)k. iii, nd inittHW. 

 * K(^ill, fntrodudinn to Natural Fhiloxophy, p. 8g. 

 3 Jerem'ue Horroccii Opera Posthuma (1673), pp. 26, 27 



8 S 



