200 



HABIT AJS'D INTELLIGENCE. 



[chap- 



The laws 

 of dyna- 

 micsinjply 

 those of 

 mathe- 

 matics. 



This kind 

 of relation 

 is to be 

 the basis 

 of the 

 classifica- 

 tion, 



which is 

 to be a 

 series. 



Such a 

 series is 

 only 

 approxi- 

 mately 

 possible. 



the means of the telescope and the microscope, is only, 

 as it were, accidental ; that is to say, it does not depend 

 on the nature of the sciences themselves. If this is not 

 quite evident, it will become so on reflecting that it is 

 conceivably quite possible, though unlikely, for a man to 

 understand astronomy wdthout understanding the theory 

 of the telescope, or to be an accomplished physiologist 

 without understanding the theory of the microscope. But 

 the connexion of mathematics with dynamics and astro- 

 nomy is of a different kind from this ; for it would be 

 impossible — impossible, I mean, in the sense of involving 

 a contradiction — to understand dynamics and astronomy 

 without understanding mathematics. The connexion of 

 mathematics with dynamics and with astronomy (which is 

 but a particular application of dynamics) is not in any 

 sense accidental, but is grounded in the nature of dyna- 

 mics. It would be impossible so much as to state the 

 laws of dynamics without taking some of the truths of 

 mathematics as known. Thus, to mention an elementary 

 instance, it would be impossible to prove or to state the 

 theorem of the parallelogram of forces without first know- 

 ing the geometrical properties of the parallelogi'am. Now, 

 this kind of relation between sciences — namely, that in 

 which the truths of one presuppose those of another — is 

 the most fundamental of all relations, and is that whereon 

 any rational classification or co-ordination of the sciences 

 must be based.^ That is to say, we have to arrange the 

 sciences in such an order that the truths of each science 

 presuppose and depend on the truths of that science 

 which comes before it in the series, and are independent 

 of all those which follow it. Thus dynamics depends 

 on mathematics, and mathematics does not depend on 

 dynamics or any other physical science. 



In classifying all the sciences, however, we cannot per- 

 fectly attain to such an arrangement as this : we can only 

 approximate to it. There is no possibility of so framing 



1 I speak of this subject more briefly than I should otherwise do, in 

 consequence of having gone into it in some detail in the chapter on 

 Organic Subordination (Chap. XIII.). 



