THE MONADOLOGY 255 



ference between nature and art, that is to say, between the 

 divine art and ours 105 . (Theod. 134, 146, 194, 403.) 



65. And the Author of nature has been able to employ 

 this divine and infinitely wonderful power of art, because 

 each portion of matter is not only infinitely divisible, as 

 the ancients observed 106 , but is also actually subdivided 

 without end 107 , each part into further parts, of which 



103 Cf. Nicholas of Cusa, Idiotae Libri quatuor, iii. 2, 82 a. 'Humanae 

 artes imagines Divinae arils' 



106 See Aristotle, Phys., Z, 9, 23g b 5. Ov yap avyKfirai 6 xpovos (tc 

 TU>V vvv a.8iaip(TQJv, uancp ov8' d\Xo yw-y60o? ovSev. Cf. Phys., Z, I, 23 i b 

 18 ; Z, 4 (TO Se neral3a\\ov airav avayfcr) Siaipcrov fivai) ; De Caelo, T, I, 

 2 98 b 33. See also Bayle's Dictionary, article ' Zeno,' notes F and G. 



107 Cf. Reponse a la Uttre de M. Foucher (1693), (E. 118 b. ; G. i. 

 416). ' There is no part of matter which is not, I do not say 

 divisible, but actually divided ; and consequently the smallest 

 particle must be considered as a world filled with an infinity of 

 different creatures.' The paradox in such statements as these 

 arises from the way in which Leibniz speaks of matter as composed 

 of non-spatial elements. Leibniz regards matter as a mere aggregate 

 and as therefore not itself a real substance. But he never explains 

 what he means by an aggregate of Monads, each of which is non- 

 quantitative. Again it may be asked whether a real whole can 

 consist of an infinite number of real parts ? Does not infinite 

 divisibility mean that it is impossible to bring to an end the 

 enumeration of parts, because the relation of whole to parts is so 

 indefinite that we have no means of determining what exactly 

 is a part? Thus the -term 'infinite' here means that the process 

 of division is one which can never be completed. Consequently 

 it seems self-contradictory to speak of things as 'actually sub- 

 divided without end' or infinitely. (Cf. Kant's Critique of Pure 

 Reason, First and Second Antinomies. See also Bosanquet's Logic, 

 vol. i. pp. 172 sqq.) It was Euler, the mathematician, who first 

 brought this criticism against Leibniz, saying that the existence 

 of units in the shape of Monads implies the finite divisibility of 

 matter, while Leibniz at the same time maintains its infinite 

 divisibility. (Lettres a une Princesse d'Allemagne (1761), Brewster's 

 Trans , vol. ii. pp. 30 sqq.) Euler's argument is directed mainly 

 against the Wolffian adaptation of Leibniz's position. Leibniz 

 might reply that matter as infinitely divisible, is a mere pheno- 

 menon, resulting from an actual infinity of real Monads. But 

 even in this explanation the idea of ' infinite ' seems to be used in 

 two opposite senses (i) as equivalent to 'incapable of completion," 

 (2) as equivalent to ' absolutely complete.' 



