46 



INTRODUCTION. 



23. 



Oermany 

 has taken 

 the lead in 





All these are merely external signs of the new life, in- 

 dications of progress and change : the inner reason and 

 result, the altered ways of thinking which underlie or are 

 produced by these external changes, will be the object 

 of closer study hereafter ; they constitute the real sub- 

 stance of this work. What I draw attention to here, 

 by way of introduction, are merely fingers on the dial- 

 plate of a complicated clock-work : their motion and posi- 

 tion are patent to every one. Later on I shall invite the 

 reader to remove the outer case, and try with me to under- 

 stand the delicate working parts and the principle of the 

 mechanism, the prime mover and the mode of transmission 

 of motion within. The general curiosity that exists to fol- 

 low the internal and hidden workings of thought is mani- 

 fested especially in that country which in modern history 

 has frequently taken the lead in philosophical reasoning. 

 It is manifested by the huge and increasing historical 

 literature of Germany, which is devoted to tracing out 

 the growth and development of modern science and 

 thought. In that country history seems for the moment 

 to have taken the place of metaphysical speculation. 

 A similar transition from the logical to the historical view 

 can be traced in English literature in the last century, the 



generality is sometimes exaggerated 

 at the expense of simplicity and 

 usefulness, and then leads to ab- 

 struseness and to the enunciation 

 of theorems which have no special 

 application ; precision may degen- 

 erate into an affected brevity which 

 renders a dissertation more difficult 

 to read than to write ; elegance of 

 form has in our days almost be- 

 come the test of the value of a 

 theorem. Yet in spite of all draw- 



backs these conditions of efficient 

 progress are of the greatest import- 

 ance, inasmuch as they keep the 

 scientific matter within those limits 

 which are intrinsically necessary if 

 mathematical research is not to lose 

 itself in minutiae or be drowned in 

 over - abundance." Hankel, ' Die 

 Entwickelung der Mathematik in 

 den letzten Jahrhunderten ' (Tub- 

 ingen, 1869). 



