ch. viii.] ORGANIZATION OF THE SCIENCES. 215 



mineralogy, zoology and botany are more or less special 

 sciences. But the distinction between abstract and concrete 

 is by far the deeper distinction, and because the Comtean 

 classification incorrectly formulates it, there is no alternative 

 but to regard that classification as incurably faulty. 



The above criticism, however, supplies us with materials 

 for making a better one. As the case now stands, we have 

 three abstract sciences, — mathematics, physics, and chemistry. 

 Yet a distinction in degree of abstractness arises between 

 mathematics and the other two. All three were originally 

 obtained by generalization from concrete phenomena. All 

 mathematical analysis starts from numeration, as all geometry 

 starts from measuring. Nevertheless, mathematics has 

 utterly outgrown the processes of concrete observation, and 

 is a purely deductive science, dealing merely with number 

 and figure, or what may be called the blank forms of pheno- 

 mena. It thus becomes more nearly allied to logic than to 

 the physical sciences ; and indeed the chief difference 

 between the two is that logic deals with qualitative relations 

 only, while mathematics deals with relations that are quanti- 

 tative. On the other hand, molar physics, molecular physics, 

 and chemistry, dealing with abstract laws of motion and 

 force that are gained from experience of concrete phenomena, 

 and appealing at every step to the concrete processes of 

 observation and experiment, may be distinguished as abstract- 

 concrete sciences. These sciences analyze concrete pheno- 

 mena, in order to formulate the working of their factors. 

 " In every case it is the aim to decompose the phenomenon, 

 and formulate its components apart from one another; or 

 some two or three apart from the rest." The problem is to 

 ascertain the laws of molar motion, or molecular vibration, 

 or atomic rearrangement, not as these laws are actually realized 

 to perception in any concrete example, "but as they would be 

 displayed in the absence of those minute interferences which 



