266 HERMANN VON HELMHOLTZ 



physical processes or circumstances will take their course, the 

 equality being demonstrable by means of measurements with 

 compasses. We should then obtain a geometry, the propositions 

 of which would indeed be covered by our axioms, but which 

 would be founded solely on empirical data, so that we should not 

 require a priori axioms at all. Kant's assumption that spatial 

 relations that contradict the Euclidean axioms are unrepresent- 

 able is, however, invalidated by the preceding discussion, since 

 Helmholtz interprets the whole of Kant's conception as a simple 

 process that cannot be further analysed, and is influenced by the 

 whole developmental state of the physiology of the senses. 



'When it is possible to state completely and unequivocally 

 the whole series of sensory impressions, which must, in accord- 

 ance with known laws, ensue from an object that has never 

 been seen, then in my opinion the object must be held to be 

 conceivable ; since ex hypothesi the object has never been seen, 

 no earlier experience can help us, or direct our imagination in 

 the discovery of the necessary series of impressions ; this can 

 only arise from the concept of the object or relation to be 

 represented. The concept of spatial figures that do not corre- 

 spond to our ordinary intuitions can only be developed with 

 certainty by the calculations of analytical geometry/ 



Helmholtz was greatly fatigued by the mathematico-philoso- 

 phical studies necessitated by his work on the axioms of 

 geometry. On March 28, 1869, he writes to Ludwig : 



' I have for the moment returned to electrical work on the 

 time-relations and dispersion of discharges, to which I was 

 incited by physiological experiments and problems. For the 

 time being I have laid physiological optics and psychology 

 aside. I found that so much philosophizing eventually led to 

 a certain demoralization, and made one's thoughts lax and 

 vague; I must discipline myself awhile by experiment and 

 mathematics, and then come back later to the Theory of 

 Perception. It is well to hear in between what others have 

 to say about it, what they have to object, what they mis- 

 understand, and so on, and whether they take any interest 

 at all in these questions. My following in these matters has 

 been small enough so far, but I have some good people 

 with me'. 



As a matter of fact his philosophical views spread but slowly 



