FALLACIES OF GENERALIZATION. 371 



of the Pythagoreans on the subject of numbers. Finding that 

 the distances of the planets bore or seemed to bear to one 

 another a proportion not varying 1 much from that of the divi- 

 sions of the monochord, they inferred from it the existence of 

 an inaudible music, that of the spheres : as if the music of a 

 harp had depended solely on the numerical proportions, and 

 not on the material, nor even on the existence of any material, 

 any strings at all. It has been similarly imagined that certain 

 combinations of numbers, which were found to prevail in some 

 natural phenomena, must run through the whole of nature : 

 as that there must be four elements, because there are four 

 possible combinations of hot and cold, wet and dry ; that 

 there must be seven planets, because there were seven metals, 

 and even because there were seven days of the week. Kepler 

 himself thought that there could be only six planets because 

 there were only five regular solids. With these we may class 

 the reasonings, so common in the speculations of the ancients, 

 founded on a supposed perfection in nature : meaning by nature 

 the customary order of events as they take place of themselves 

 without human interference. This also is a rude guess at 

 an analogy supposed to pervade all phenomena, however dis- 

 similar. Since what was thought to be perfection appeared to 

 obtain in some phenomena, it was inferred (in opposition to 

 the plainest evidence) to obtain in all. " We always suppose 

 that which is better to take place in nature, if it be possible," 

 says Aristotle: and the vaguest and most heterogeneous 

 qualities being confounded together under the notion of being 

 letter, there was no limit to the wildness of the inferences. 

 Thus, because the heavenly bodies were " perfect," they must 

 move in circles and uniformly. For "they" (the Pythago- 

 reans) " would not allow," says Geminus,* " of any such dis- 

 order among divine and eternal things, as that they should 

 sometimes move quicker and sometimes slower, and sometimes 

 stand still ; for no one would tolerate such anomaly in the 

 movements even of a man, who was decent and orderly. The 

 occasions of life, however, are often reasons for men going 



* I quote from Dr. Whewell's Hist. Ind. Sc. 3rd ed. i. 129. 

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