248 OF THE THEORY OF PROBABILITIES. [CHAP. XVI. 



currence of the events concerning which they make assertion. 

 Thus, instead of considering the numerical fraction p as ex- 

 pressing the probability of the occurrence of an event E, let it 

 be viewed as representing the probability of the truth of the 

 proposition X, which asserts that the event E will occur. Si- 

 milarly, instead of any probability, q, being considered as re- 

 ferring to some compound event, such as the concurrence of the 

 events E and F, let it represent the probability of the truth of 

 the proposition which asserts that E and F will jointly occur; 

 and in like manner, let the transformation be made from disjunc- 

 tive and hypothetical combinations of events to disjunctive and 

 conditional propositions. Though the new application thus as- 

 signed to probability is a necessary concomitant of the old one, 

 its adoption will be attended with a practical advantage drawn 

 from the circumstance that we have already discussed the theory 

 of propositions, have defined their principal varieties, and estab- 

 lished methods for determining, in every case, the amount and 

 character of their mutual dependence. Upon this, or upon some 

 equivalent basis, any general theory of probabilities must rest. 

 I do not say that other considerations may not in certain cases of 

 applied theory be requisite. The data may prove insufficient for 

 definite solution, and this defect it may be thought necessary to 

 supply by hypothesis. Or, where the statement of large num- 

 bers is involved, difficulties may arise after the solution, from this 

 source, for which special methods of treatment are required. 

 But in every instance, some form of the general problem as above 

 stated (Art. 4) is involved, and in the discussion of that problem 

 the proper and peculiar work of the theory consists. I desire it 

 to be observed, that to this object the investigations of the fol- 

 lowing chapters are mainly devoted. It is not intended to enter, 

 except incidentally, upon questions involving supplementary hy- 

 potheses, because it is of primary importance, even with reference 

 to such questions (I. 17), that a general method, founded upon 

 a solid and sufficient basis of theory, be first established. 



7. The following is a summary, chiefly taken from Laplace, of 

 the principles which have been applied to the solution of questions 

 of probability. They are consequences of its fundamental defini- 



