r,96 APPLIED MATHEMATICS 



although not a specialist; their connection with the aim of my lec- 

 ture is very intimate. 



Let us consult the famous thinker already quoted, Emmanuel 

 Kant, on the question if matter is continuous, or if it is composed 

 of atoms. He treats of this in his Antimonies. Of all the questions 

 there raised, he shows that both the pro and con can be logically 

 demonstrated. It can be shown rigorously that there is no limit to 

 the divisibility of matter while an infinite divisibility contradicts the 

 laws of logic. Kant shows likewise that a beginning and end of time, 

 a boundary where space ceases, are as inconceivable as absolutely 

 endless duration, absolutely endless extension. 



This is by no means the sole instance where philosophical thought 

 becomes tangled in contradictions; indeed, one finds them at every 

 step. The ordinary things of philosophy are sources of insolvable 

 riddles; to explain our perceptions it invents the concept of matter 

 and then finds that it is altogether unsuited to possess perception 

 itself or to generate perception in a spirit. With consummate acumen 

 it constructs the concept of space, or of time, and finds that it is 

 absolutely impossible that things should exist in this space, that 

 events should occur during this time. It finds insurmountable 

 difficulties in the relation of cause to effect, of body and soul, in 

 the possibility of consciousness, in short, everywhere and in every- 

 thing. Indeed, it finally finds it inexplicable and self-contradictory 

 that anything can exist at all, that something originated and is cap- 

 able of continuing, that everything can be classified according to 

 our categories, nor that there is a quite perfect classification. Such 

 a classification will always be a variable one and adapted to the 

 requirements of the moment. Also the breaking up of physics into 

 theoretical and experimental is merely a consequence of the preval- 

 ent division of methods and will not last forever. 



My present thesis is quite different from the one that certain 

 questions are beyond the boundary of human comprehension. For 

 according to the latter, there is a deficiency, an incompleteness in the 

 human intelligence, while I consider the existence of these questions, 

 these problems, as an illusion. By superficial consideration it seems 

 astonishing, after this illusion is recognized, that the impulse to 

 answer those questions does not cease. Habit of thought is much too 

 powerful to release us. 



It is here as with the ordinary illusion which continues operative 

 after its cause is recognized. In consequence of this is the feeling of 

 uncertainty, of want of satisfaction which the scientist feels when he 

 philosophizes. These illusions will yield but very slowly and gradually, 

 and I consider it as one of the chief problems of philosophy to set 

 forth clearly the uselessness of reaching beyond the limits of our 

 habits of thought and to strive, in the choice and combination of 



