120 Measurement of Belief. [CHAP. vi. 



natural objects almost always have before they are capable of 

 being accurately reasoned about. The form in which the 

 series emerges is that of a series with a fixed type. This 

 imaginary or ideal series is the basis of our calculation. 



2. It must riot be supposed that this is at all at vari 

 ance with the assertion previously made, that Probability is a 

 science of inference about real things; it is only by a substi 

 tution of the above kind that we are enabled to reason about 

 the things. In nature nearly all phenomena present them 

 selves in a form which departs from that rigorously accurate 

 one which scientific purposes mostly demand, so we have to 

 introduce an imaginary series, which shall be free from any 

 such defects. The only condition to be fulfilled is, that the 

 substitution is to be as little arbitrary, that is, to vary from 

 the truth as slightly, as possible. This kind of substitution 

 generally passes without notice when natural objects of any 

 kind are made subjects of exact science. I direct distinct 

 attention to it here simply from the apprehension that want 

 of familiarity with the subject-matter might lead some readers 

 to suppose that it involves, in this case, an exceptional de 

 flection from accuracy in the formal process of inference. 



It may be remarked also that the adoption of this imagi 

 nary series offers no countenance whatever to the doctrine 

 criticised in the last chapter, in accordance with which it was 

 supposed that our series possessed a fixed unchangeable type 

 which was merely the &quot;development of the probabilities&quot; of 

 things, to use Laplace s expression. It differs from anything 

 contemplated on that hypothesis by the fact that it is to be 

 recognized as a necessary substitution of our own for the 

 actual series, and to be kept in as close conformity with facts as 

 possible. It is a mere fiction or artifice necessarily resorted 

 to for the purpose of calculation, and for this purpose only. 



This caution is the more necessary, because in the example 



