THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 35 



13. 



On the fascinating subject of the Objectivity of Space and 

 Time, our remarks must be very brief^ and, as before, limited in 

 the main to indicating the grounds upon which it would seem 

 that the existence of absolute Space and Time must be admitted, 

 without any serious attempt to elaborate "the arguments in 

 favour of this view, or to annihilate those which make 

 against it. 



The latter may be considered under three headings. The 

 first of these would contain the philosophical arguments which 

 aim at discrediting continuous Space and Time by showing that 

 they are self-contradictory concepts. Mr. Bradley's attack is 

 too well known tjp need description here, and is typical of this 

 type of objection. (The essence of it is that Space and Time 

 demand terms and relations between these terms, while any 

 attempt actually to exhibit these terms involves the investigator 

 in a hopeless "infinite regress." But in the light of the 

 mathematical theories that we have been sketching, it becomes 

 clear that the attempt in question fails because it is undertaken 

 with inadequate means, not because it is essentially hopeless. 

 In the successive dissection of portions of Space in the hope of 

 finding at last the indissoluble point, one is doomed to failure 

 by the fact that in this way one can never arrive at an infinite 

 number of operations taking the term in the sense that has 

 been explained. Nevertheless, we are able in the manner we 

 have indicated to conceive an infinite number of atomic points, 

 in which we can recognise the final terms which we seek, and to 

 do so without finding ourselves involved in the contradictions 

 which beset us when we embarked upon the quest armed only 

 with an improper concept of an " infinite number." Thus the- 

 classical a priori arguments against points are successfully 

 resisted. 



The other two classes of argument aim at showing that the 

 assumption of the existence of absolute Space is unprovable and 



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