SENSE-DATA AND PHYSICS 155 



which he now occupies, some appearance of the room 

 existed before his arrival. This supposition, however, 

 need merely be noticed and not insisted upon. 



Since the " thing " cannot, without indefensible par- 

 tiality, be identified with any single one of its appear- 

 ances, it came to be thought of as something distinct 

 from all of them and underlying them. But by the prin- 

 ciple of Occam's razor, if the class of appearances will 

 fulfil the purposes for the sake of which the thing was 

 invented by the prehistoric metaphysicians to whom 

 common sense is due, economy demands that we should 

 identify the thing with the class of its appearances. It is 

 not necessary to deny a substance or substratum underly- 

 ing these appearances ; it is merely expedient to abstain 

 from asserting this unnecessary entity. Our procedure 

 here is precisely analogous to that which has swept away 

 from the philosophy of mathematics the useless menagerie 

 of metaphysical monsters with which it used to be in- 

 fested. 



VI. CONSTRUCTIONS VERSUS INFERENCES 



Before proceeding to analyse and explain the am- 

 biguities of the word " place," a few general remarks on 

 method are desirable. The supreme maxim in scientific 

 philosophising is this : 



Wherever possible, logical constructions are to be sub- 

 stituted for inferred entities. 



Some examples of the substitution of construction for 

 inference in the realm of mathematical philosophy may 

 serve to elucidate the uses of this maxim. Take first the 

 case of irrationals. In old days, irrationals were inferred 

 as the supposed limits of series of rationals which had no 

 rational limit ; but the objection to this procedure was 



