206 INTRODUCTION 



APPENDIX D. 

 LEIBNIZ'S LOGIC. 



IN the Nouveaux Essais, bk . iv. ch. 1 1 , 14 (E. 379 a ; G. v. 428 ), 

 there is an interesting passage explaining in more detail a part 

 of the logic of Leibniz. It contains some remarkable anticipa- 

 tions of more modern views. ' Propositions of fact also may 

 become general in a way, but it is by induction or observation ; 

 so that it ' [the general proposition of fact] * is nothing but 

 a multitude of similar facts, as when we observe that all 

 quicksilver evaporates by the force of fire ; and this is not 

 a perfect generality, because we do not see its necessity. 

 General propositions of reason are necessary, although reason 

 also furnishes some which are not absolutely general and are 

 only probable, as for instance, when we presume that an idea 

 is possible, until a more strict investigation reveals its contrary. 

 There are, finally, mixed propositions, which are drawn from 

 premises, of which some come from facts and observations, 

 while others are necessary propositions : and such are numerous 

 geographical and astronomical conclusions about the globe of 

 the earth and about the course of the stars, which conclusions 

 are obtained by combining the observations of travellers and 

 astronomers with the theorems of geometry and arithmetic. 

 But as, according to the usage of logicians, the conclusion follow* 

 the weaker of the premises, and cannot have more certainty than 

 they, these mixed propositions have only the certainty and 

 generality which belong to observations. As to eternal truths, 

 it is to be noted, that at bottom they are all conditional and say 

 in effect : Granted such a thing, such another thing is. For 

 instance, when I say, Every figure which has three sides will 

 also have three angles, I say nothing but this, that supposing 

 there is a figure with three sides, this same figure will have 

 three angles. I say this same figure, and it is in this respect that 

 categorical propositions, which can be stated unconditionally 



