FALLACIES OF GENERALIZATION. 425 



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 consisted in conformity 

 to rules of precedency in dignity, either real or con- 

 ventional. Again, reverting to numbers: 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 Pythagoreans, on the other 

 hand, attributed perfection to the number ten; but 

 agreed in thinking that the perfect number must be 

 somehow realized 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 usf." 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 arguments of the Stoics to prove the 

 equality of all crimes, and the equal wretchedness of 

 all who had not realized their idea of perfect virtue. 

 Cicero, towards the end of his Fourth Book De Fini- 

 bus, states some of these as follows. " Ut, inquit, in 

 fidibus plurimis, si nulla earum ita contenta numeris 

 sit, ut concentum servare possit, omnes seque incon- 

 tentse sint ; sic peccata^ quia discrepant, seque discre- 

 pant : paria sunt igitur." To which Cicero himself 

 aptly answers, " seque contingit omnibus fidibus, ut 



* WHEWELL, Hist, of the Ind. Sc., i., 365. 

 t Ibid., 70. 



