GENERAL PRINCIPLES 27 



homogeneous, and the specific qualities of things must 

 arise from the variety of their combinations. They could 

 not all really exist and be different from one another 

 without some of them being complex. And in any case 

 the very essence of the theory is that the whole should 

 be taken as a sum or totality, a quantity of parts. 



Leibniz's non-quantitative or intensive Notion of Substance, 



developed through criticism of Cartesian andAtomist views 



regarding material Substance. 



Accordingly, the essence of Leibniz's argument is 

 that a quantitative conception of the relation of whole 

 and parts aifords an inadequate theory of substance. 

 The common element in the contrary positions of the 

 Cartesians and the Atomists is the explicit or implicit 

 reduction of qualitative to quantitative differences \ And 

 it appears to Leibniz that the solution of the dilemma , / 

 is to be found in the opposite hypothesis, namely, that 

 the essence of substance is non-quantitative, and that 

 the relation of whole and parts must be conceived as <jO 

 intensive rather than extensive. Thus a 'simple sub- 

 stance' has no parts, i.e. no quantitative elements 2 , ^ 

 and yet it must comprehend a manifold in unity 3 ; that 

 is to say, it must be real, it must be something, it must 

 be qualitative, specifically determined. 



While the general principle of Leibniz's argument 

 may be stated in this way, he actually develops it through 

 criticism of Descartes's theory of material substance. To 

 regard matter as ultimately pure extension is to make 

 it essentially a substance with nothing more than a 

 shadow of quality. An extended nothing is meaningless. 

 An extended something must have quality. And to call 



1 The mechanical view of things 'has two forms: Cartesianism 

 and Atomism. . . . The one, which makes matter continuous, may 

 be called geometrical mechanism ; the other, which makes it dis- 

 continuous, may be called arithmetical mechanism.' E. Boutroux, 

 La Monadologie de Leibnitz, &c., p. 36. 



2 Monadology, i. 3 Ibid. ra. 



