202 INTRODUCTION 



happen to every body? This seems to me not only easy 

 to conceive, but also worthy of God and of the beauty of the 

 universe, and in a way necessary, since all substances must 

 have a mutual harmony and connexion and all must express 

 in themselves the same universe and the universal cause, which 

 is the will of their Creator, and the decrees or laws which He 

 has established in order to make them fit into one another as 

 well as possible. Thus this mutual correspondence of different 

 substances (which, speaking with metaphysical strictness, can- 

 not act upon one another, and yet are in harmony as if one 

 did act upon another) is one of the strongest proofs of the 

 existence of God or of a common cause which each effect must 

 always express according to its point of view and its capacity 

 of expression. Otherwise the phenomena of different minds 

 would not harmonize, and there would be as many systems as 

 substances ; or rather, it would be entirely a matter of chance 

 if they were sometimes in harmony.' 



APPENDIX B. 



FORMATION OF THE IDEA OF SPACE. 



IN 47 of the fifth letter to Clarke, Leibniz gives an account 

 of the origin of the idea of space. 'I will here show how 

 men come to form to themselves the notion of space. They 

 consider that many things exist at once and they observe in 

 them a certain order of co-existence, according to which the 

 relation of one thing to another is more or less simple. This 

 order is their situation or distance. When it happens that 

 one of those co-existent things changes its relation to a mul- 

 titude of others, without their changing their relations among 

 themselves ; and that another thing, newly come, acquires 

 the same relation to the others as the former had ; we then 

 say it is come into the place of the other ; and this change we 

 call a motion in that body, wherein is the immediate cause 

 of the change. And though several, or even all the co-existent 

 things should change according to certain known rules of 

 direction and velocity, we can always determine the relation of 



