ORGANIZATION OF THE SCIENCES 



scribes result, — the ascertaining of all these 

 powers or properties being his sole aim." So 

 that, from first to last, the object of the abstract- 

 concrete sciences is to give an account " of 

 some order of properties, general or special ; 

 not caring about the other traits of an aggre- 

 gate displaying them, ^nd not recognizing ag- 

 gregates at all further than is implied by dis- 

 cussion of the particular order of properties." 



Finally, the abstract sciences deal solely with 

 relations among aggregates or among proper- 

 ties, or with the relations between aggregates 

 and properties, or with relations among rela- 

 tions ; but take no further account of aggre- 

 gates or of properties than is implied in the 

 discussion of a particular order of relations. 

 For example, " the same Logical formula ap- 

 plies equally well, whether its terms are men 

 and their deaths, crystals and their planes of 

 cleavage, or letters and their sounds. And how 

 entirely Mathematics concerns itself with rela- 

 tions, we see on remembering that it has just 

 the same expression for the characters of an in- 

 finitesimal triangle as for those of the triangle 

 which has Sirius for its apex and the diameter 

 of the earth's orbit for its base." ' 



Since then, " these three groups of sciences 

 are, respectively, accounts of aggregates, ac- 

 counts of properties, accounts of relations, it is 

 1 Spencer, Recent Discussions, pp. 107— no. 

 vol. n. 49 



