PHILOSOPHY OF NATURE LEIBNITZ'S IDEAS. 45 



The classification of genera and species in the vegetable 

 kingdom is a difficult task. Botanists in the seventeenth 

 century thought that distinctions, founded on the shapes 

 of the flower, made the nearest approach to the natural 

 order in arranging a series of classes. Leibnitz judges 

 that it would be best to make the comparison not only in 

 respect to a single characteristic, such as that of the flower, 

 which may after all be the most useful in arranging a con- 

 venient system, but also in respect to the characteristics 

 of other parts in plants. He thus suggests the rule of 

 subordination in characteristics, as a result of his ideas 

 upon the harmony of beings. 



Thus all these labors and hypotheses issue directly from 

 Leibnitz's metaphysical conceptions as to the system of 

 mundane elements. A still more direct outcome from them 

 is the invention of the infinitesimal calculus. Were the 

 calculus of itself nothing more than a splendid curiosity, 

 even then it would be much to have discovered a means 

 of working upon and with infinite quantities as with finite 

 ones. Fortunately that method of calculation has found 

 occasion in astronomy, mechanics, and physics, for applica- 

 tions so rich in results that those sciences have gained a 

 new being from it. It is a new instrument, a new lever 

 supplied to them for the highest researches. We thus 

 learn the extent of Leibnitz's familiarity with the most 

 difficult problems. 



m. 



What has been the influence of the metaphysics of 

 Leibnitz over the great processes of advance in modern 

 science, beginning with those of the last century ? It is 

 an old saying that the eighteenth century had no original 

 philosophy; in fact, it lived on borrowed doctrines. It 

 had among others one system of teaching proceeding from 

 that of Leibnitz, and Diderot may be said to have been its 



