198 The Rule of Succession. [CHAP. vin. 



one surely would attempt to defend such a formula. So 

 far from past occurrence being a ground for belief in future 

 recurrence, there are (as will be more fully pointed out 

 in the Chapter on Fallacies) plenty of cases in which the 

 direct contrary holds good. Then again a rule of this kind 

 is subject to the very serious perplexity to be explained 

 in our next chapter, arising out of the necessary arbitrariness 

 of such inverse reference. That is, when an event has 

 happened but a few times, we have no certain guide ; and 

 when it has happened but once 1 , we have no guide whatever, 

 as to the class of cases to which it is to be referred. In 

 the example above, about the flags, why did we stop short at 

 this notion simply, instead of specifying the size, shape, &c. 

 of the flags ? 



De Morgan, it must be remembered, only accepts this- 

 rule in a qualified sense. He regards it as furnishing a 

 minimum value for the amount of our expectation. He 

 terms it &quot; the rule of probability of a pure induction&quot; and 

 says of it, &quot;The probabilities shown by the above rules 

 are merely minima which may be augmented by other 

 sources of knowledge.&quot; That is, he recognizes only those 

 instances in which our belief in the Uniformity of Nature 

 and in the existence of special laws of causation comes in 



1 When m=l the fraction becomes seen before, how many of the ob- 



|; i.e. the odds are 2 to 1 in favour served characteristics of that single 



of recurrence. And there are writers event are to be considered essential ? 



who accept this result. For instance, Must the pilot precede ; and at the 



Jevons (Principles of Science p. 258) same distance? Must we consider 



says &quot;Thus on the first occasion on the latitude, the ocean, the season, 



which a person sees a shark, and the species of shark, as matter also 



notices that it is accompanied by a of repetition on the next occasion? 



little pilot fish, the odds are 2 to 1 and so on. I cannot see how the 



that the next shark will be so accom- Inductive problem can be even in- 



panied.&quot; To say nothing of the fact telligibly stated, for quantitative 



that recognizing and naming the fish purposes, on the first occurrence of 



implies that they have often been any event. 



