1 42 SCIENTIFIC METHOD IN PHILOSOPHY 



the extra weight is small enough, no difference will be 

 perceived in the sensation. After a time, another small 

 extra weight may be added, and still no change will be 

 perceived ; but if both extra weights had been added at 

 once, it may be that the change would be quite easily 

 perceptible. Or, again, take shades of colour. It would 

 be easy to find three stuffs of such closely similar shades 

 that no difference could be perceived between the first 

 and second, nor yet between the second and third, while 

 yet the first and third would be distinguishable. In such 

 a case, the second shade cannot be the same as the first, 

 or it would be distinguishable from the third ; nor the 

 same as the third, or it would be distinguishable from the 

 first. It must, therefore, though indistinguishable from 

 both, be really intermediate between them. 



Such considerations as the above show that, although 

 we cannot distinguish sense-data unless they differ by 

 more than a certain amount, it is perfectly reasonable to 

 suppose that sense-data of a given kind, such as weights 

 or colours, really form a compact series. The objections 

 which may be brought from a psychological point of view 

 against the mathematical theory of motion are not, there- 

 fore, objections to this theory properly understood, but 

 only to a quite unnecessary assumption of simplicity in 

 the momentary object of sense. Of the immediate object 

 of sense, in the case of a visible motion, we may say that 

 at each instant it is in all the positions which remain 

 sensible at that instant ; but this set of positions changes 

 continuously from moment to moment, and is amenable 

 to exactly the same mathematical treatment as if it were 

 a mere point. When we assert that some mathematical 

 account of phenomena is correct, all that we primarily 

 assert is that something definable in terms of the crude 

 phenomena satisfies our formulae ; and in this sense the 



