COSMIC PHILOSOPHY 



advanced sciences, and the qualitative reasoning 

 employed in those which are less advanced, 

 may be thus stated : in the first case the rela- 

 tions contemplated are so simple that they may 

 be directly juxtaposed in consciousness, and re- 

 cognized as equal or unequal ; but in the sec- 

 ond case the relations contemplated consist of 

 so many simple relations heterogeneously com- 

 bined, that they can only through a very indi- 

 rect process be juxtaposed in consciousness, 

 and hence are only approximately recognized as 

 like or unlike. That this is the only essential 

 difference between quantitative reasoning and 

 qualitive reasoning is shown by the fact that all 

 qualitative reasoning is vaguely quantitative, 

 while all quantitative reasoning begins by being 

 qualitative. For example — to cite Mr. Spen- 

 cer's admirable illustration — when a brewer de- 

 scribes a vat of fermenting wort as containing 

 carbonic acid, he makes a qualitative statement; 

 yet some rude notion of quantity is involved in 

 it. " He thinks of the carbonic acid as more, 

 certainly, than a cubic foot ; less, certainly, than 

 the total capacity of the vat : the quantity is 

 thought of as in some ratio to the quantity of 

 wort." On the other hand, " a man who has 

 walked a mile in fifteen minutes, and, observ- 

 ing that he has a quarter of a mile still to go, 

 infers the time it will take to reach his destina- 

 tion, does not primarily infer three minutes and 

 152 



