558 PHILOSOPHICAL THOUGHT. 



life, the early stages of culture and society, of language 

 and poetry, were connected with the elemental forces of 

 nature. Nature was studied in a human interest as the 

 alma mater of Mind. 

 15. These aims and tendencies of the Philosophy of Nature 



Vague ideas 



of develop- were entirely opposed to the tendencies of exact science. 



ment kept 



mathemati- ^ ne tendency of the latter was, as I have shown in the 

 a spirit. g rg sec tj on O f thjg wori^ to discover everywhere fixed 

 mathematical relations, to reduce everything to definite 

 quantities which could be measured and calculated. The 

 ideal of this view was the mathematical formula, the 

 geometrical figure, or the mechanical model. Wherever 

 these could be found or invented, the scientific mind 

 could apply the powerful engine constructed with so 

 much skill from the time of Newton and Leibniz 

 onward : the infinitesimal calculus. Through the work- 

 ings of this, every fixed relation, form, or movement 

 discovered in natural phenomena became the starting- 

 point for the development of new ideas. A whole 

 train of abstract reasoning was set in motion ; this in 

 its course led to new relations and forms requiring 

 only to be reinterpreted in order to reveal phenomena 

 and events which, except for it, would have remained 

 hidden and unknown. Through this powerful engine of 

 research, through this independent movement of thought, 

 the mind acquired an undreamt of mastery over nature, 

 and could for a moment imagine that it had arrived at 

 some of the fundamental data of reality, that it had laid 

 bare the very foundations of existence. 



It is not difficult to realise how the many triumphs 

 achieved within a very short period' in the regions of 



