STATEMENT OF LEIBNIZ'S PHILOSOPHY 83 



one thing and another is infinitely little, we have not 

 converted each into the other, but have explained them, 

 both by referring them to a common ground. We can ex- 

 press each in terms of the other, provided we state expli- 

 citly their relations to one another within some system. 

 A parabola is not an ellipse ; but a parabola is an ellipse 

 with one of its foci at an infinite distance from the other. , 



, Continuity and the Logical Calculus. 

 Now it cannot be said that all this was fully manifest 

 to Leibniz himself ; but the truth of it underlies his 

 thinking. The Infinitesimal Calculus in his mathematics 

 is an expression of th& same tendency of thought which 

 makes the principle of sufficient reason so important an 

 influence in his philosophy the tendency to a less 

 abstract, less dogmatic, more intensive way of looking at 

 things, in contrast with the a priori deductive methods 

 of the Cartesians. The influence of the mathematics of 

 Leibniz upon his philosophy appears chiefly in connexion 

 with his law of continuity and his prolonged efforts to 

 establish a Logical Calculus. As to the law of continuity 

 it is unnecessary to say more. It is the law of the end- 

 less relativity of things, the principle of system, of in- 

 finite multiplicity in unity, and we have seen that the 

 Infinitesimal Calculus is an application of it 1 . On the 



1 Cf. Lettre a M. Bayle (1687) (G. iii. 51 ; E. 104 a) : 'I have seen 

 the reply of Father Malebranche to the remark I made on some laws 

 of nature which he laid down in the Recherche de la Verite. He 

 appears somewhat disposed to give them up himself, and his in- 

 genuousness is most laudable ; but he gives reasons for it and makes 

 restrictions which would bring us back into the obscurity from 

 which I think I have delivered this subject, and which conflict 

 with a certain principle of general order that I have observed. I hope, 

 therefore, that he will kindly allow me to take this opportunity of 

 explaining this principle, which is of great use in reasoning, and 

 which does not yet appear to be sufficiently employed nor known 

 in all its scope. It has its origin in the conception of the Infinite ; 

 it is absolutely necessary in Geometry, and it also holds good in 

 Physics, inasmuch as the Supreme Wisdom, which is the source 

 of all things, acts as a perfect geometrician, and according to a 

 harmony which cannot be bettered. . . . The principle may be stated 

 thus : When the difference between two cases can be diminished below any 



G 2 



