I'ALLACIES OF GENERALISATION. 



523 



ihe 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 cer- 

 tain 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 com- 

 mon in the speculations of the an- 

 cients, founded on a supposed perfec- 

 tion in nature : meaning by nature 

 the customary order of events as they 

 take place of themselves without 

 human intei-ference. 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 Aris- 

 totle ; and the vaguest and most 

 heterogeneous qualities being con- 

 founded together under the notion of 

 being better, there was no limit to the 

 wildness of the inferences. Thus, 

 because the heavenly bodies were 

 '•perfect," they must move in circles 

 and uniformly. Eor "they" (the 

 Pythagoreans) "would not allow," 

 says Geminus,* " of any such disorder 

 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 move- 

 ments even of a man, who was decent 



* I quote from Dr. Whewell's Hist. Ind. 

 Sc, 3d ed. i. 129. < 



and orderly. The occasions of life, how- 

 ever, are often reastms for men going 

 quicker or slower ; but in the incor- 

 ruptible nature of the stars, it is not 

 possible that any cause can be alleged 

 of quickness or slowness." It is seek- 

 ing an argument of analogy very far 

 to suppose that the stars must observe 

 the rules of decorum in gait and car- 

 riage, prescribed for themselves by 

 the long-bearded philosophers sati- 

 rised by Lucian. 



As late as the Copernican contro- 

 versy it was urged as an argument in 

 favour of the true theory of the solar 

 system, that it placed the fire, the 

 noblest element, in the centre of the 

 universe. This was a. remnant of the 

 notion that the order of nature must 

 be perfect, and that perfection con- 

 sisted in conformity to niles of pre- 

 cedency in dignity, either real or con- 

 ventional. Again, reverting to num- 

 bers : certain numbers were perfect, 

 therefore those numbers must obtain 

 in the great phenomena of nature. 

 Six was a perfect number, that is, 

 equal to the sum of all its factors ; 

 an additional reason why there must 

 be exactly six planets. The Pythago- 

 reans, on the other hand, attributed 

 perfection to the number ten ; but 

 agreed in thinking that the perfect 

 number must be somehow realised in 

 the heavens : and knowing only of 

 nine heavenly bodies, to make up 

 the enumeration, they asserted " that 

 there was an antichthon or counter- 

 earth on the other side of the sun,- 

 invisible to us." * Even Huygens 

 was persuaded that when the number 

 of the heavenly bodies had reached 

 twelve, it could not admit of any 

 further increase. Creative power 

 could not go beyond that sacred 

 number. 



Some curious instances of false 

 analogy are to be found in the argu- 

 ments of the Stoics to prove the 

 equality of all crimes, and the equal 

 wretchedness of all who had not re-, 

 alised their idea of perfect virtue* 



* Hist. Ind. Sc, i. 52. = 



