﻿78 The Measurement of Chance. 



numerically measurable in accordance with Bayes' or any 

 other formula. 



But in most cases where an attempt is made to apply a 

 probability o£ causes, the condition is not fulfilled that it is 

 known that the same die is always used. If that condition 

 is not fulfilled, the probability, according to orthodox theory, 

 depends on certain a priori probabilities which are not chances. 

 The problem then ceases to be one of the connexion between 

 chance and probability, and thus falls without the strict 

 limits of our discussion. 



12. But it is necessary to transgress those limits for one 

 purpose.' It has been often urged by philosophers that 

 probability is characteristically applicable to scientific 

 propositions, which are to be regarded, not as certain, but 

 ouly as more or less probable. If this be so, the con- 

 ception of chance, being a scientific conception deriving 

 its meaning from scientific propositions, must be subsequent 

 to the conception of probability, and the order of our 

 discussion should have been reversed. Of course I do not 

 accept the philosophical view, and perhaps it will be well to 

 explain very briefly why I reject it. 



Doubtless there is a sense in which scientific propositions 

 are not certain ; but in that sense no proposition is certain, 

 so long as its contrary is comprehensible. For if I can 

 understand what is meant by a proposition, I can conceive 

 myself believing it. I am not perfectly certain either that 

 Ohm's law is true, or that (x + a) 2 — a? -\- Zax -\- a 2 : I can 

 conceive myself disbelieving either. If I were forced to say 

 which I. believe more certainly, I should choose Ohm's law ; 

 for I could give a much better account of the evidence on 

 which I believe it. A mathematician, of course, would make 

 the opposite choice. But it appears to me useless to com- 

 pare the " certainties" of two propositions when they are of 

 so different a nature that the source of the uncertainty is 

 perfectly different. If a proposition is as certain as any 

 proposition of that nature can be, and if nothing whatever 

 could make it more certain, then it seems to me misleading 

 to distinguish its probability from certainty. 



Now, fully established scientific propositions are ecrtainin 

 this sense. They are uncertain only in so far as they predict 

 If in asserting Ohm's law, I mean (and I think this is my 

 chief meaning) that it appears to me a perfectly complete 

 and satisfying interpretation of all past experience and that 

 other people appear to share my opinion, then Ohm's law is 



