284 THE SCIENCE OF LOGIC 



may not occur again add ^ more, and thus, the probability for its recurrence is 



( m ^ l , which decreases as n increases. In this case, the extension to 4&amp;gt; 



(m + n + 2) 



more cases becomes still more hazardous, as its formula is i!Li_] &amp;gt; 



(m + n + p + i) 

 decreasing as p increases. 



Now, plausible as all this may appear, it can be shown to lead to very 



questionable conclusions. The mathematical formula -pLLIL rightly ex 

 presses the probability of drawing a white ball next time from a bag contain 

 ing &quot; any number, we know not what, of balls each of which is white or black,&quot; l 

 after we have drawn a white ball m times successively. But in applying the 

 formula to determine the probability of the recurrence of any natural pheno 

 menon we are assuming &quot; that the universe may be likened to such a bag &quot; ; 

 an assumption which is at the very least so groundless that we need not be 

 surprised if it leads to some fantastic conclusions. 



Again, it is only by experience we can discover whether or how far the 

 degree of our rational expectation of the recurrence of natural events is in ac 

 cordance with such a formula ; 3 and even in so far as we do detect some such 

 accordance, we feel that our probability is not really based on, or measured by, 

 the formula : in applying the formula to our data &quot; we only give the appearance 

 of logic to a conclusion we have otherwise gained. Without consulting experi 

 ence as to the application of the law, and thus making it superfluous, we should 

 be met by Venn s objection. It has rained for three days ; I have given three 

 false alarms of fire ; I have fed my chickens three times with strychnine. 

 What is the probability for the fourth case ? By the rule it is. four-fifths that 

 it will rain the fourth day, that the neighbours will respond to the next alarm, 

 and that my chickens will die the next time.&quot; 4 



These conclusions are a sufficient rtductio ad absurdum of all attempts to 



employ any such &quot; rule of succession &quot; as that contained in the formula - 



(m + 2) 



for the purpose of determining the probability of the recurrence of a 

 natural event. As a matter of fact, whereas in some cases the repeated oc 

 currence of an event in the past does make its future recurrence more probable, 

 in other cases it has the opposite effect (as in giving false alarms), and in others, 

 again, it has simply no effect : the past facts tell us nothing about the proba 

 bility of the next occurrence (as in fair games of chance). 8 Hence the original 

 assumption, that repeated occurrences always increase the probability of re 

 currence, is illegitimate. 



We pass next to another doubtful application of the calculus, namely, to 

 the domain of human testimony. Professor Welton says 8 that &quot; the theory of 

 probability is applicable to the credibility of testimony as well as to the pre 

 diction of a future occurrence &quot;. But, just as in the latter case, so in the former, 

 we have to make arbitrary or hazardous assumptions which render such appli 

 cations of the theory practically worthless. &quot; Suppose,&quot; he writes, in intro 

 ducing an example, 7 &quot; that two witnesses, the probability of whose accuracy 



1 VENN, op. cit., p. 197. *ibid. s ibid. 



* BOWNE, Theory of Thought and Knowledge, p. 190. 



VENN, op. cit., pp. 358, 363. *of&amp;gt;. /., ii., p. 169. 7 ibid, p. 180, 



