368 Fallacies. [CHAP. xiv. 



ground that All A is B, who might justly plead in his behalf 

 that he never meant it to be a necessary, but only a pro 

 bable inference. The same remarks will of course apply 

 also to the logical fallacy of Undistributed Middle. 



Now for a case of the opposite kind, i.e. one in which 

 Probability fails us, whereas the circumstances seem closely 

 analogous to those in which ordinary inference would be 

 able to make a stand. Suppose that I know that one letter 

 in a million is lost when in charge of the post. I write to a 

 friend and get no answer. Have I any reason to suppose 

 that the fault lies with him ? Here is an event (viz. the 

 loss of the letter) which has certainly happened ; and we sup 

 pose that, of the only two causes to which it can be assigned, 

 the value, i.e. statistical frequency, of one is accurately 

 assigned, does it not seem natural to suppose that something 

 can be inferred as to the likelihood that the other cause had 

 been operative ? To say that nothing can be known about 

 its adequacy under these circumstances looks at first sight 

 like asserting that an equation in which there is only one 

 unknown term is theoretically insoluble. 



As examples of this kind have been amply discussed in 

 the chapter upon Inverse rules of Probability I need do no 

 more here than remind the reader that no conclusion what 

 ever can be drawn as to the likelihood that the fault lay 

 with my friend rather than with the Post Office. Unless we 

 either know, or make some assumption about, the frequency 

 with which he neglects to answer the letters he receives, the 

 problem remains insoluble. 



The reason why the apparent analogy, indicated above, 

 to an equation with only one unknown quantity, fails to hold 

 good, is that for the purposes of Probability there are really 

 two unknown quantities. What we deal with are propor 

 tional or statistical propositions. Now we are only told that 



