28 INTRODUCTION 



that quality extension itself is merely to cover up the 

 difficulty with a name : an extended extension is much 

 the same as a shaded shadow of nothing. 'In my 

 opinion corporeal substance consists in something quite 

 other than being extended and occupying a place : we 

 must, in fact, ask ourselves what it is that occupies the 

 place 1 .' 'Those who hold that the extended is itself 

 a substance transpose the order of the words as well as 

 of the thoughts. Besides extension there must be an 

 object which is extended, that is to say a substance 

 which can be repeated or continued. For extension 

 means nothing but a repetition or a continued multi- 

 plicity of that which is spread out, a plurality, continuity, 

 and coexistence of parts ; and consequently it [extension] 

 is not sufficient to explain the very nature of extended 

 or repeated substance, the notion of which is anterior 

 to that of its repetition V 



Again, it cannot be said that pure extension has any 

 real parts. There can be no real unit of mere extension 8 . 

 It would be an erroneous conception to regard mathe- 

 matical surfaces as made up of real lines, and these lines 

 as made up of real points. The line is the limit of the 

 surface, and the point is the limit of the line. A mathe- 



1 Epistolaad Schuleriburgium (1698) (G. Math. vii. 242). 



3 Extrait d'une lettre (1693) (E. u^b ; G. iv. 467). Cf. Lotze, Micro- 

 cosmws, bk. iii. ch. 4, 2 t^Eng. Trans, vol. i. p. 356). Cf. also Examen 

 des principes du R. P. Malebranche (c. 1711) (E. 691 a ; G. vi. 580): 

 ' Ariste. But do you not think that the destruction of extension, 

 which carries with it that of body, proves that body consists only 

 in extension ? Philarete. It proves only that extension enters into 

 the essence or nature of body ; but not that it constitutes its whole 

 essence. Similarly, magnitude enters into the essence of extension, 

 but is not equivalent to it ; for number, time, motion have also 

 magnitude, and yet they are not extension.' Also (E. 693 -b ; G. vi. 

 584) : ' Extension is nothing but an abstraction and requires some- 

 thing which is extended. ... It presupposes some quality, some 

 attribute, some nature in the thing, which quality extends or 

 diffuses itself along with the thing, continues itself.' 



3 'You are right in saying that all magnitudes [grandeurs'] may 

 be divided ad infinitum. None of them is so small that we cannot 

 conceive in it an infinity of divisions which will never be exhausted.' 

 Lettre a Foucher (1692) (E. 115 a ; G. i. 403). 



