256 HERMANN VON HELMHOLTZ 



geometry. Twenty years later, in criticizing a book that excited 

 general interest, he observes : 



' The strictest Kantians emphasise the particulars in which 

 Kant in my opinion suffered from the imperfect development 

 of the special sciences in his day, and fell into error. The 

 nucleus of these errors lies in the axioms of geometry, which 

 he regards as a priori forms of intuition, but which are really 

 propositions tested by observation, and which if proved incorrect 

 might eventually be rejected. 



1 This last is the point I have tried to establish. Therewith, 

 however, we reject the possibility of laying down metaphysical 

 foundations for natural science, in which Kant as a matter of 

 fact believed. Now for my point of view it is exceedingly 

 interesting to see in the papers he left behind him, how this 

 contingency disturbed the philosopher as he grew older, how 

 he turned it over and over, again and again seeking new 

 formulae, and finding none that satisfied him. Among these 

 we find in details instances of the most amazing insight, such 

 indeed as we might expect from a man of his intellect, e.g. as 

 to the nature of heat. ... In my opinion it is only possible to 

 retain the great work done by Kant, if one recognizes his error 

 in regard to the pure transcendental significance of the 

 geometrical and mechanical axioms. But along with this we 

 renounce the possibility of making his system the foundation of 

 metaphysics, and this appears to me the reason why all of his 

 disciples who cherish metaphysical hopes and tendencies 

 adhere so tenaciously to these disputed points/ 



In his inquiry into the sense-perceptions Helmholtz had 

 proposed to himself the question, What in the simplest forms 

 of our spatial perception had been derived from experience, 

 and what could not have originated therein, and how much 

 must necessarily have been inferred from experience, in order 

 to give support to the other ? Arguments and counter-arguments 

 had already been brought forward, stating either that the axioms 

 of geometry were a priori forms of our mode of intuition, anterior 

 to all experience, and fundamental to our mental organization, 

 or, on the other hand, that they were empirical theorems of the 

 most universal character. In his attempt to transfer this inquiry 

 from philosophical physiology to mathematics, Helmholtz en- 

 deavoured for the more precise definition of the question to 



