THE MONADOLOGY 237 



34. It is thus that in Mathematics speculative Theorems 

 and practical Canons are reduced by analysis to Definitions, 

 Axioms and Postulates. 



35. In short, there arejiimple ideas, of which no defini- 

 tion can be given 55 ; there are also axioms and postulates, 

 in a word, primary principles, which cannot be proved, 

 and indeed have no need of proof ; and thesa are identical 

 propositions 56 , whose opposite involves an express contra- 

 diction. (Theod. 36, 37, 44, 45, 49, 52, 121-122, 337, 

 340-344.) 



{36) But there must also be a sufficient reason for con- 

 tingent truths or truths of fact ^, that is to say, for the 

 sequence or connexion of the things which are dispersed 

 throughout the universe of created beings, in which the 

 analyzing into particular reasons might go on into endless 

 detail, because of the immense variety of things in nature 

 and the infinite division of bodies 58 . There is an infinity 



writes to Clarke (II me Ecrit de Leibni?, E. 748 a ; G. vii. 355) : ' The 

 principle of contradiction is by itself sufficient for the demon- 

 stration of the whole of Arithmetic and Geometry, that is to say, 

 of all mathematical principles. But in order to pass from Mathe- 

 matics to Physics, another principle also is needed, the principle 

 of sufficient reason.' See Introduction, Part ii. pp. 66 sqq. In the 

 Monadology, Leibniz's position is the same as in the earlier of 

 the passages quoted. 



55 The definition of an idea is, for Leibniz, the statement of the 

 elements which a complete analysis reveals in it. Cf. Meditationes 

 de Cogmtione, Veritate et Inez's (1684) (E. 79 b ; G. iv. 423). 'When 

 everything which is an element in a distinct idea, is in its turn 

 distinctly known, or when analysis has been completely made, 

 knowledge is adequate. I know not whether human knowledge 

 can supply a perfect instance of this : the knowledge of numbers, 

 however, approaches it.' 



56 Leibniz uses the word enondation for enunciatio, which is the 

 usual Latin translation of Aristotle's airu^iavoLs, or ^670? dntxpavTiicus. 



57 Truths of reasoning have their sufficient reason in the self- 

 evident, identical truths to which they may be reduced by analysis. 

 Truths of fact can find a sufficient reason only in God. 



18 Cf. Lotze, Microcosmus, bk. iii. ch. 5, i (Eng. Tr., i. 372). 

 Leibniz says * infinite division' instead of 'infinite divisibility,'' 

 because bodies are infinitely divisible only as phenomena benefundatu 

 and not as real beings. A real thing or substance must be indi- 



