30 INTRODUCTION 



mentally divisible indeed, but which actually neither is 

 nor has been divided. Not that it cannot be actually 

 divided ; for such atoms do not occur, since they would 

 demand perfect hardness. But it suffices for my defini- 

 tion that there should be corpuscles, whose particles have 

 never been separated, from the foundation of the world 

 to the present day 1 / Every material atom must be at 

 least ideally divisible, if it be real. ' The atoms of matter 

 ... are still composed of parts, since the invincible 

 attachment of one part to another (if one could rationally 

 conceive or suppose it) would in no way destroy their 

 diversity 2 .' 



How the Relation of Whole and Parts is to ~be conceived. 

 The real and indivisible Unit of Substance (Monad\ 

 'Perception ' and l Appetition.' 



Leibniz's problem thus takes the form of an attempt 

 to find a unit of substance which shall avoid the imper- 

 fections of both the Cartesian and Atomist theory. This 

 unit must be at once real and indivisible. Its reality 

 must be of such a kind that it does not conflict with its 

 indivisibility, and it must be indivisible in a sense which 

 is consistent with the continuity of the whole. The basis 

 of its reality cannot be quantity, for no quantity is 

 indivisible. And its indivisibility cannot be exclusive 

 particularity in space or time, for indivisible points in 

 space or time may form an aggregate but cannot become 

 a continuum. The unit of substance must then be inten- 

 sive rather than extensive, and the continuity of the 

 whole must be not a mere empty homogeneity, but a 



1 Epistola ad Bernoullium (1697) (G. Math. iii. 443). 



8 New System, n. Cf. Lettre a Hartsoeker (1710) (G. iii. 507) : 

 'Nothing is large or small, except hy comparison, so that such 

 a particle as an atom is as considerable in itself, and in relation to 

 others proportionately less (and consequently, in the sight of God), 

 as our visible system is considerable in relation to it. Atoms are 

 the effect of the weakness of our imagination, which likes to rest 

 and to hasten to an end in subdividing or analyzing. It is not so 

 in nature, which comes from infinity and goes to infinity.' 



