﻿76 Dr. Norman Campbell on the 



Chance and Probability. 



10. It remains to consider very briefly what connexion, if 

 any, there is between the chance of events and the proba- 

 bilities o£ propositions. 



Probability is usually admitted to be an indefinable 

 conception, applicable to propositions concerning which there 

 is no complete certainty, and roughly describable as the 

 degree of their certainty. It appears to me one of those 

 conceptions which are the more elusive the more they are 

 studied ; I am quite certain that I do not understand what 

 some other writers mean by the term, and am not at all 

 certain that I can attach a perfectly definite meaning to it 

 myself. The observations that I can offer are therefore 

 necessarily tentative. But it is clear, at any rate, that 

 probability is not a property of a system and is not physically 

 measurable ; any propositions connecting it with chance 

 must depend ultimately on fundamental judgments which 

 can be offered for acceptance, but cannot be the subject of 

 scientific proof. 



There are two kinds of propositions the probability of 

 which may plausibly be connected with chance ; and they 

 naturally can apply only to systems that are characterized by 

 chances. Of the first kind the following is typical : — This 

 die will turn up six the next time it is thrown (or on some 

 other single and definite occasion). Here (ef. P. pp. 192-200) 

 it seems that, if the proposition is really applied to a single 

 occasion only, the probability of the proposition must be that 

 characteristic of absolute ignorance ; for the assumption that 

 anything whatever is known of the result of a single trial is 

 inconsistent with the experimental fact that the result of any 

 one trial is random. The only exception occurs when the 

 event is one of which the chance is so small (or so great) that 

 the happening of it (or failure of it) would force us to revise 

 our estimate of the chance or to deny that there was a chance 

 at all. Of such coincidences, in systems of which the chance 

 has been well ascertained, the assertion that they will not 

 (or will) occur may be made with the certainty that is 

 characteristic of any scientific statement. There is no 

 probability. 



On the other hand, it is very difficult to be sure that only 

 a single trial is contemplated. For when such statements 

 are important, there is always a clear possibility of a consider- 

 able number of repetitions of the trial. If this number is 

 so great as to permit a dermination, by derived measurement, 

 of the chance of the event within some limits relevant to the 



