RELATIONS OF APPLIED MATHEMATICS 597 



concepts and words, to give the most useful expression of facts in a 

 manner which is independent of our inherited habits. Then all these 

 complications and contradictions must vanish. It must be made 

 clear what is stone in the structure of our thoughts and what is 

 mortar, and the oppressive sentiment, that the simplest things are 

 the most inexplicable and the most trivial are the most mysterious, 

 becomes mere imagination-change. 



To call upon logic seems to me as if one were to put on for a trip 

 into the mountains a long flowing robe, which always wrapped 

 itself about the feet so that one fell at the first steps while on the level. 

 The source of this kind of logic is the immoderate trust in the so- 

 called laws of thought. It is certain that we could not gather experi- 

 ence did we not have certain forms of connecting phenomena, that is 

 to say, of thought, innate. If we wish to call these laws of thought, 

 they are indeed a priori to the extent that they accompany every 

 experience in our soul, or if we prefer, in our brain. Only nothing 

 seems to me less reasonable than the conclusion from the reasoning 

 in this sense to certainty, to infallibility. These laws of thought 

 have been developed according to the same laws of evolution as 

 the optical apparatus of the eye, the acoustic apparatus of the ear, 

 and the pumping arrangements of the heart. In the course of human 

 development everything useless was eliminated, and thus a unity 

 and finish arose which might be mistaken for infallibility. Thus the 

 perfection of the eye, of the ear, of the arrangement of the heart 

 excite our admiration, without the absolute perfection of these 

 organs being emphasized, however. Just so little should the laws of 

 thought be regarded as absolutely infallible. They are the very ones 

 which have developed with regard to seizing that which is most 

 necessary and practically useful in the maintenance of life. With 

 these, the results of experimental investigation show more relation 

 than the examination of the mechanism of thought. We should, 

 therefore, not be surprised that the customary forms of thought 

 for the abstract are not entirely suited to practical applications 

 in far removed problems of philosophy, and that they have not 

 become applicable since the days of Thales. Therefore the simplest 

 things seem to be the most puzzling to the philosopher. And he 

 finds everywhere contradictions; these are nothing more, however, 

 than useless, incorrect facsimiles of that which is given us through 

 our thoughts. In facts there can be no contradictions. As soon as 

 contradictions seem unavoidable we must test, extend, and seek 

 to modify that which we call laws of thought, but which are only 

 inherited, customary representations, preserved for aeons, for the 

 description of practical needs. Just as to the inherited discoveries 

 of the cylinder, the carriage, the plow, numerous artificial ones have 

 been consciously added, so must we improve, artificially and con- 



