102 INTRODUCTION 



extension relates to simultaneous things or things which 

 exist together, time to those which are incompatible and 

 which are nevertheless all conceived as existing, and it is 

 this that makes them successive. But space and time 

 taken together constitute the order of the possibilities of 

 a whole universe, so that these orders (that is space and 

 time) square not only with what actually exists but also 

 with whatever might be put in its place, as numbers are 

 indifferent to whatever can be res numerata 1 .' Thus 

 space does not mean any particular situation of bodies, nor 

 time any particular succession of phenomena. Space is 

 simply the indefinitely applicable relation of co-existence, 

 while time is the indefinitely applicable relation of 

 succession or order of successive positions. In each case 

 the things or phenomena related might have been other 

 than they are, and thus the orders are orders of possi- 

 bilities. But in neither case is the order actual apart from 

 some ordered or related things. There is no actual empty 

 space or empty time. These are abstractions, harmless 

 or possibly useful when recognized as abstractions, but 

 hurtful if they are regarded as actual things. 

 ^Tjeibniz's disproof of the independent reality of space 

 and time is directly based by him upon the principle of 

 sufficient reason. 'I say, then, that if space was an 



1 Replique aux Reflexions de Bayle (1702) (E. 189 b ; G. iv. 568). 

 The translation is from Gerhardt's text. Cf. IIl me Lettre a Clarke, 

 4 (Clarke's tr.) (E. 752 a ; G. vii. 363): 'I bold space to be some- 

 thing merely relative, as time is : I hold it to be an order of co-exist- 

 ences, as time is an order of successions. For space denotes, in terms 

 of possibility, an order of things which exist at the same time, con- 

 sidered as existing together ; without inquiring into their particular 

 manner of existing. And when many things are seen together 

 one perceives that order of things among themselves.' The corre- 

 spondence between Leibniz and Clarke is mainly devoted to this 

 question of the meaning of space and time. Clarke endeavoured 

 to defend the view of Newton that infinite space is real, and is to 

 be regarded as a kind of sensorium of God or as His omnipresent 

 perception of things. Leibniz attacks not merely this particular 

 view, but all other theories which make space real, as, for instance, 

 those which confound infinite space with the Immensity of God 

 or with any other of His attributes. Cf. Eraser's ed. of Locke's Essay, 

 vol. i. pp. 259, 260. See also Explanation of the New System, i, note. 



