556 - FALLACIES. : 



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 specu- 

 lations of the ancients, founded on a sui^posed perfection in nature; mean- 

 ing by nature the customary order of events as they take place of them- 

 selves without human interference. This also is a rude guess at an analo- 

 gy supposed to pervade all phenomena, however dissimilar. 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 quali- 

 ties being confounded 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. For 

 " they " (the Pythagoreans) " would not allow," says Geminus,* " of any 

 such disorder among divine and eternal things, as that they should some- 

 times 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 quicker or slower ; but in the incorruptible nature of the 

 stars, it is not possible that any cause can be alleged of quickness or slow- 

 ness." It is seeking an argument of analogy very far, to suppose that the 

 stars must observe the rules of decoi-um in gait and carriage prescribed 

 for themselves by the long-bearded philosophers satirized by Lucian. 



As late as the Copernican controversy it was urged as an argument in 

 favor of the true theory of the solar system, that it placed the fire, the no- 

 blest element, in the centre of the universe. This was a remnant of the no- 

 tion that the order of nature must be perfect, and that perfection consisted 

 in conformity to rules of precedency in dignity, either real or conventional. 

 Again, reverting to numbers : certain numbers were perfect, therefore those 

 numbers must obtain in the great phenomena of nature. Six was a per- 

 fect number, that is, equal to the sum of all its factors ; an additional rea- 

 son why there must be exactly six planets. The Pythagoreans, on the oth- 

 er 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 us."f 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, toward the 

 end of his Fourth Book, De Fbiibus, states some of these as follows : " Ut, 

 inquit, in fidibus plurimis, si nulla earum ita contenta numeris sit, ut conceu- 



* I quote from Dr. Whewell's Hist. Ind. Sc, 3d ed., i., 129. f ^ist. Ind. Sc, I, 52. 



