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



those indications available when functions of large numbers, or 

 series consisting of many and complicated terms, are thereby in- 

 troduced. It may, therefore, be fully conceded, that all pro- 

 blems having for their data the probabilities of independent 

 simple events fall within the scope of received methods. 



2ndly. Certain of the principles above enumerated, and espe- 

 cially the sixth and seventh, do not presuppose that all the data 

 are the probabilities of simple events. In their peculiar applica- 

 tion to questions of causation, they do, however, assume, that the 

 causes of which they take account are mutually exclusive, so 

 that no combination of them in the production of an effect is 

 possible. If, as before explained, we transfer the numerical pro- 

 babilities from the events with which they are connected to the 

 propositions by which those events are expressed, the most ge- 

 neral problem to which the aforesaid principles are applicable 

 may be stated in the following order of data and qucesita. 



DATA. 



1st. The probabilities of the n conditional propositions : 

 If the cause A l exist, the event E will follow ; 



2nd. The condition that the antecedents of those propositions 

 are mutually conflicting. 



REQUIREMENTS. 



The probability of the truth of the proposition which declares 

 the occurrence of the event E\ also, when that proposition is 

 known to be true, the probabilities of truth of the several pro- 

 positions which affirm the respective occurrences of the causes 

 A A A 



-"-l j "% *-n 



Here it is seen, that the data are the probabilities of a series 

 of compound events, expressed by conditional propositions. But 

 the system is obviously a very limited and particular one. For 

 the antecedents of the propositions are subject to the condition of 

 being mutually exclusive, and there is but one consequent, the 

 event JE, in the whole system. It does not follow, from our 



