﻿74 Dr. Norman Campbell on the 



are said to be equal when there is no reason to believe 

 that one rather than the other will happen as the result 

 of any trial. But what reason could there be for such 

 a belief based on experiment ? No a priori principle can 

 determine the property of a system, which is an experi- 

 mental fact ; we cannot tell whether a die is fair or loaded 

 without examining it through our senses. The only experi- 

 mental reason I can conceive for believing that one event 

 is more likely to happen than another is that it has 

 happened more frequently in the past. But if an attempt 

 is made to define " more frequently " precisely, the judg- 

 ment of equality is inevitably made to depend on the 

 derived measurement, and the fundamental process ceases 

 to be independent of it. This dependence is often con- 

 cealed by the use of question-begging words. Thus, the 

 principle of sufficient reason may be reasonably held to 

 decide that, in a perfectly shuffled pack of cards, the chance 

 that the card next after a heart is another heart is equal to 

 the chance that it is a club. But if inquiry is made what is 

 meant by a perfectly shuffled pack and how we are to know 

 whether a pack is or is not perfectly shuffled, I can seen no 

 answer except that it is one in which a club occurs after a 

 heart as often as another heart. But, of course, to define 

 perfect shuffling in that way is to admit that the criterion of 

 equality is based upon the derived measurement of 

 " frequency " *. I can find no proposed definition of the 

 equality of chances that is both applicable to experimental 

 facts and independent of frequency ; and I conclude, therefore, 

 that there is not for chance, as there is for resistance, a 

 fundamental process of measurement independent of the 

 derived. 



8. But there is a further difference to be considered. 

 Even if equality of chance could be defined independently, 

 there would still be many chances (and those some of the 

 most important) which could not be connected with the unit 

 by the relations of equality and addition: Any resistance is 

 equal to the sum of some set of resistances such that the sum 

 of another set of them is equal to the unit or to the sum of 

 some set of units. The analogous proposition about chances 



* It is not always realized by those who calculate card chances in 

 great detail that in actual play, even among experienced players, the 

 shuffling is so imperfect as to distort very seriously the chances of such 

 events as the holding of a very long suit. 



