RESULTS AND LIMITS OF SCIENTIFIC METHOD. 



that the wonders and subtleties of possible existence sur- 

 pass all that our mental powers allow us clearly to per- 

 ceive, The study of abstract logical and mathematical 

 forms has seemed to convince me that even space itself is 

 no requisite condition of conceivable existence. Every- 

 thing, we are told by materialists, must be here or 

 there, nearer or further, before or after. I deny this 

 and point to logical relations as my proof. 



There formerly seemed to me to be something highly 

 mysterious in the denominators of the binomial expansion 

 (vol. i. p. 216) which are reproduced in that strange 

 natural constant e, or 



I 1.2 1.2.3 



and in many results of mathematical analysis. I now 

 perceive, as already partiaUy explained (vol. i. pp. 40-42, 

 1 80, 1 8 1, 443, 444), that they arise out of the fact 

 that the relations of space do not apply to the logical 

 conditions which govern the numbers of combinations 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 im- 

 pediment 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 

 110 relation to space at all, just as space itself has no re- 

 lation 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 a competition for scientific recog- 



