CHAPTER XII. 



THE INDUCTIVE OR INVERSE APPLICATION OF THE 

 THEORY OF PROBABILITIES. 



WE have hitherto considered the theory of probability 

 only in its simple deductive employment, by which it 

 enables us to determine from given conditions the probable 

 character of events happening under those conditions. 

 But as deductive reasoning when inversely applied con- 

 stitutes the process of induction, so the calculation of 

 probabilities may be inversely applied ; from the known 

 character of certain events we may argue backwards to 

 the probability of a certain law or condition governing 

 those events. Having satisfactorily accomplished this 

 work, we may indeed calculate forwards to the probable 

 character of future events happening under the same con- 

 ditions ; but this part of the process is a direct use of 

 deductive reasoning (p. 260). 



Now it is highly instructive to find that whether the 

 theory of probabilities be deductively or inductively ap- 

 plied, the calculation is always performed according to 

 the principles and rules of deduction. The probability 

 that an event has a particular condition entirely depends 

 upon the probability that if the condition existed the 

 event would follow. If we take up a pack of common 

 playing cards, and observe that they are arranged in per- 

 fect numerical order, we conclude beyond all reasonable 

 doubt that they have been thus intentionally arranged 



