ii THE INFINITE AND THE FINITE 187 



their natural body, as the parts of the earth towards the 

 earth, and those of the moon toward the moon in their own 

 regions ; all motion is therefore limited, each world has, 

 as it were, margins of its own. The idea that if any of 

 the elements, as fire or water, were infinite, there would 

 be infinite lightness or gravity, and hence that the universe 

 would move as a whole upwards or downwards, is equally 

 at fault. To the universe as a whole the terms heavy and 

 light do not apply, but only to its parts, the finite and 

 determinate bodies consisting of finite and determinate 

 elements. These elements, whether they be taken as of 

 one or more kinds, since they cannot move outside of 

 the universe, must have finite movements. 



The fourth argument 1 was based upon the impossi- 4- Action 

 bility of action between an infinite body and a second infinftTand 

 body whether finite or infinite. An infinite cannot act the finitc ' 

 upon a finite because the action would necessarily be 

 timeless. Were it in time we could then find a finite 

 body which in the same time would produce the same 

 effect ; but there can be no such equality between the 

 finite and the infinite. Similarly action between two 

 infinites would occur in infinite time ; in other words, 

 would not take place at all. The conclusion is that 

 neither fire nor earth nor any of the elements can be 

 infinite in quantity. Bruno suggests, in the first place, 2 

 that a change may be produced timelessly ; thus if a 

 body in a large circle cover a certain space in the minimum 

 of time, a body in a smaller circle will cover a less 

 space in no time, for nothing can be smaller than the 

 minimum. 3 In the second place, no action of the whole 

 or effect upon the whole exists, it is only the finite 

 bodies within it, each with its finite force, that act upon 

 one another. Even if two infinite bodies, over against 



1 Bk. ii. ch. 6. 2 Ch. 7. (p. 278) ; cf. Infinite, Lag. 3 3 5 ff. 3 Vide Infra, ch. 5. 



