PHILOSOPHICAL THOUGHT. 



the vexed questions which then exercised the minds 

 of thinkers, was not reached by a detailed psycho- 

 logical investigation such as has since been carried 

 out through the labours of independent thinkers in 

 all the three countries, e.g., Mill, Renouvier, Wundt, 

 and their successors ; it was gained by a much 

 shorter and much more abstract process. Kant relied 

 on two points which he considered were well estab- 

 lished. The first and most important of these was 

 the existence of a definite amount of perfectly certain 

 and assured knowledge contained in the sciences of 

 mathematics and mathematical physics ; the second was 

 a definite body of doctrine contained in the formal logic 

 and the empirical psychology of the schools, both of 

 which Kant himself taught in his academic courses. 

 So far as the first point is concerned, Kant had a 

 broader foundation to build on than Descartes before 

 him, inasmuch as he could not only point to pure 

 mathematics, but had in addition also, what he con- 

 sidered the ideal of scientific achievement the natural 

 philosophy of Newton. 1 So far as the second point is 



1 It has, however, been shown (e.g., 

 by E. Diihring in his ' Kritische 

 Geschichte der Allgemeinen Prin- 

 cipien der Mechanik,' 3rd ed., 1887) 

 that Kant's notions as to the prin- 

 ciples of dynamics and physics were 

 still extremely inaccurate and con- 

 fused. Although in the minds of 

 some of the great mathematicians, 

 such as Newton in England and 

 d'Alembert in France, very precise 

 views existed, these have only very 

 slowly become the property of 

 philosophical thinkers. Nor does 

 it appear as if Kant himself con- 

 tributed much to this important 

 clearance of ideas. Neither his 



early tract, which deals with the 

 measure of vis viva (1753), nor 

 his treatment of dynamical and 

 physical conceptions in the cele- 

 brated 'Natural History of the 

 Heavens' (1755), shows any strict 

 definition or consistent use of 

 dynamical principles. And it is 

 significant that Ernst Mach in 

 his historical Treatise on these 

 subjects (' Mechanik in ihrer Ent- 

 wickelung,' 1883, Eng. trans, by 

 M'Cormick) has no occasion to 

 refer to Kant. With Kant the 

 fundamental notions of arithmetic 

 (numerical and general), of geom- 

 etry (synthetic and analytic), of 



