88 THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 



as a sign that the same state of hotness has recurred presents 

 little difficulty. It is simply a fact that while many hotnesses 

 may be simultaneously perceived around the place which a 

 body " occupies " in the narrower sense of the term, presenta- 

 tions such as the one in question do not appeai\ in such 

 bewildering multiplicity. Thus, the position of the index which 

 is believed to be actually the same for all is readily correlated 

 with the postulated real state of the body. 



Later, when attempts are made to fix with greater accuracy 

 the position of the index, the old difficulty breaks out anew. 

 The assumed uniqueness of the determination vanishes ; for it 

 is found that no observer is consistent with other observers, nor 

 even with himself. This time, moreover, it is not possible to 

 appeal from the fluctuating presentations to a stable one which 

 can be assumed to be correlated with the Objective value which 

 the former fail to indicate unambiguously. We are confined to 

 the circle of the actual discordant observations, and, if we are 

 to reach this real Objective value at all, must place our hopes 

 entirely upon some fortunate manipulation of our data. As is 

 well known, the .mathematical theory of observations indicates 

 a method by which we may calculate the " probable error " of 

 the series of determinations in question that is, a method 

 which enables us to determine a number which represents a 

 deviation from the arithmetical mean of the observations within 

 which it is an " even chance " that the object of our search the 

 real position of the index will fall. 



It would be difficult to decide the true interpretation of this 

 result. It is, of course, possible that the different observers 

 actually have the same presentations but fail to distinguish 

 them with accuracy the error (of which we do not claim to be 

 able to give a rational account)* following the law assumed in 

 the mathematical theory. On the other hand, it is, perhaps, 

 permissible to suggest that when the observations are simply 



* Cf. 6 (last paragraph). 



