144 Measurement of Belief. [CHAP. vi. 



readiness to act upon the proposition believed is an insepar 

 able accompaniment of that state of mind. There can be no 

 alteration in our belief (at any rate in the case of sane persons) 

 without a possible alteration in our conduct, nor anything in 

 our conduct which is not connected with something in our 

 belief. We will first take an example in connection with the 

 penny, in which there is full belief; we will analyse it a step 

 further than we did before, and then attempt to apply the 

 same analysis to an example of a similar kind, but one in 

 which the belief is partial instead of full. 



Suppose that I am about to throw a penny up, and con 

 template the prospect of its falling upon one of its sides and 

 not upon its edge. We feel perfectly confident that it will 

 do so. Now whatever else may be implied in our belief, we 

 certainly mean this ; that we are ready to stake our conduct 

 upon its falling thus. All our betting, and everything else 

 that we do, is carried on upon this supposition. Any risk 

 whatever that might ensue upon its falling otherwise will be 

 incurred without fear. This, it must be observed, is equally 

 the case whether we are speaking of a single throw or of a 

 long succession of throws. 



But now let us take the case of a penny falling, not upon 

 one side or the other, but upon a given side, head. To a 

 certain extent this example resembles the last. We are per 

 fectly ready to stake our conduct upon what comes to pass in 

 the long run. When we are considering the result of a large 

 number of throws, we are ready to act upon the supposition 

 that head comes every other time. If e.g. we are betting 

 upon it, we shall not object to paying 1 every time that 

 head comes, on condition of receiving 1 every time that 

 head does not come. This is nothing else than the transla 

 tion, as we may call it, into practice, of our belief that head 

 and tail occur equally often. 



