xxxi.] LIMITS OF SCIENTIFIC METHOD. 769 



in the denominators of the binomial expansion (p. 190), 

 which are reproduced in the natural constant e, or 



' I ' 1.2 ' I 3.3 



and in many results of mathematical analysis. 1 now 

 perceive, as already explained (pp. 33, 160, 383), that they 

 arise out of the fact that the relations of space do not apply 

 to the logical conditions governing the numbers of com- 

 binations as contrasted to those of permutations. So far 

 am I from accepting Kant's doctrine that space is a 

 necessary form of thought, that I regard it as an accident, 

 and an impediment to pure logical reasoning. Material 

 existences must exist in space, no doubt, but intellectual 

 existences may be neither in space nor out of space ; they 

 may have no relation to space at all, just as space itself 

 has no relation to time. For all that I can see, then, there 

 may be intellectual existences to which both time and 

 space are nullities. 



Now among the most unquestionable rules of scientific 

 method is that first law that whatever phenomenon is, is. 

 We must ignore no existence whatever ; we may variously 

 interpret or explain its meaning and origin, but, if a phe- 

 nomenon does exist, it demands some kind of explanation. 

 If then there is to be competition foi scientific recog- 

 nition, the world without us must yield to the undoubted 

 existence of the spirit within. Our own hopes and wishes 

 and determinations are the most undoubted phenomena 

 within the sphere of consciousness. If men do act, feel, 

 and live as if they were not merely the brief products of a 

 casual conjunction of atoms, but the instruments of a far- 

 reaching purpose, are we to record all other phenomena 

 and pass over these ? We investigate the instincts of the 

 ant and the bee and the beaver, and discover that they are 

 led by an inscrutable agency to work towards a distant 

 purpose. Let us be faithful to our scientific method, and 

 investigate also those instincts of the human mind by 

 which man is led to work as if the approval of a Higher 

 Being were the aim of life. 



3 D 



