APPENDIX G 275 



all essence exists, all that is possible is actual. As against 

 Descartes's proof Leibniz argues that it is incomplete, for the 

 idea of a most perfect being might perhaps be self-contra- 

 dictory, like the idea of the swiftest possible motion or the 

 greatest possible number. Thus, after stating the Cartesian 

 argument, Leibniz says : ' But it is to be noted that the only 

 logical conclusion is : " If God is possible, it follows that He 

 exists." For we cannot safely use definitions in order to reach 

 a conclusion, until we know that these definitions are real or 

 that they involve no contradiction. The reason of this is that 

 from notions which involve a contradiction opposite conclusions 

 may be drawn at the same time, which is absurd. To illustrate 

 this I usually take the instance of the swiftest possible motion, 

 which involves an absurdity. For, suppose a wheel to revolve 

 with the swiftest possible motion, is it not evident, that if any 

 spoke of the wheel be made longer ' [produced, in the mathe- 

 matical sense] 'its extremity will move more swiftly than 

 a nail on the circumference of the wheel ; wherefore the 

 motion of the circumference is not the swiftest possible, as was 

 supposed by the hypothesis. Yet at first sight it, may appear 

 that we have an idea of the swiftest possible motion ; for we 

 seem to understand what we are saying, and nevertheless we 

 have no idea of impossible things.' Meditationes de Cognitione, 

 Veritate et Ideis (1684), (E. 80 a ; G. iv. 424.) ' Therefore there is 

 assuredly reason to doubt whether the idea of the greatest of all 

 beings is not uncertain, and whether it does not involve some 

 contradiction. For I quite understand, for instance, the nature 

 of motion and velocity, and what " the greatest " is. But -I do 

 not understand whether these are compatible, and whether 

 it is possible to combine them into the one idea of the greatest 

 velocity of which motion is capable. In the same way, although 

 I know what "being" is, and what the "greatest" and the 

 " most perfect " are, nevertheless I do not therefore know that 

 there is not a hidden contradiction involved in combining these 

 together, as there actually is in the instances I have just given 

 . . . Yet I admit that God has here a great advantage over 

 all other things. For, in order to prove that He exists, it is 

 sufficient to prove that He is possible, which is not the case 

 with regard to anything else that I know of. ... Simple 

 forms [i. e. living principles] are the source of things. Now 

 I maintain that all simple forms are compatible with one 

 another. ... If this be granted, it follows that the nature of 



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