204 



HABIT AND INTELLIGENCE. 



[chap. 



most important ; I only mean that logic is the initial 

 science — that which commences the series. Its subject- 

 matter is perfectly simple, and it is absolutely universal in 

 its generality ; for no inference can be made on any sub- 

 ject whatever without involving the principles of logic : 

 and the principles of logic do not depend on those of 

 any other science, but the principles of all the other 

 sciences depend on those of logic. 



Matliema- 

 tical aud 

 physical 

 sciences. 



Mathe- 

 matics 

 comes 

 before 

 physii/s. 



Algebra, 

 arithme- 

 tic, aud 

 geometry. 

 Logic 

 is the 

 initial 

 science. 



We now leave the subject of abstract logic, and proceed 

 to the sciences which consist in applications of logic. 

 Here the first and most important division of subject- 

 matter is into the abstractions of space and time on the 

 one side, and on the other all those things which exist in 

 space and act in time — that is to say, all existing things 

 whatever which are known to us. The science of the 

 properties of space and time is mathematics ; the sciences 

 of the properties of existing things may be called the 

 physical sciences ; though it must be understood that 

 these include psychology and those sciences which depend 

 on psychology, such as the sciences of language and of 

 history. On every ground, mathematics comes in our 

 series before the physical sciences. The subject-matter 

 of mathematical science is the properties of time and 

 space, and time and space are perfectly simple and abso- 

 lutely universal; while matter, which is the primary 

 suliject of physical science, is not simple in its properties, 

 for they are so various that no one knows them all : nor 

 is it universal in its extent, for only part of space is 

 occupied by matter. And, as already remarked, the truths 

 of a large part of the physical sciences, including especially 

 all branches of abstract and applied dynamics, presuppose 

 those of mathematics, while the truths of mathematics do 

 not presuppose any physical truths. 



The three mathematical sciences are algebra, or the 

 science of abstract quantity ; arithmetic, or the science 

 of number ; and geometry, or the science of extension 

 and form. 



We now go on to the physical sciences, or those 



