98 Prof. Boole on the Theory of Probabilities. 



Also/? =1—9. If we make these substitutions in the general 

 value of P, we find 



1 



2 1 



P= 



2 2* 



There is therefore, I conceive, no error in the reasoning adopted ; 

 although there may be, as it seems to me (but I state this merely 

 as an opinion), a serious doubt as to the determination of the 

 constant a. We are not, I think, at liberty to assume that it is 

 a priori as likely as not that a sufficient ground for a determi- 

 nate phsenomenon should exist in nature. All that we can infer 

 from the general solution is, that unless the existence of such a 

 ground is a priori highly improbable, then, after frequent expe- 

 rience of the phsenomenon, there exists a high probability in 

 favour of the existence of that ground. 



I have not at present the opportunity of making further refer- 

 ences ; but I think the most just inference from what has been 

 adduced, to be, that while the doctrine objected to has really 

 been put forth, it has not been held uniformly or universally. 

 I would suggest also the consideration, that even the passage 

 quoted from the Edinburgh Review, although certainly conveying 

 the erroneous notion adverted to, might by the omission of the 

 word therefore be understood as expressing the result of a train 

 of reasoning similar to that which Mr. De Morgan has adopted. 

 For if we granted in that case Mr. De Morgan^s determination 

 of the constants, the numerical result obtained would be extremely 

 near to that which the Reviewer has assigned. It seems to me 

 to be the part of justice, to give to such considerations as these 

 their full share in estimating the opinions wliich a writer has 

 expressed. While on the one hand we ought to bring every 

 statement into comparison with the standard of what is abso- 

 lutely true and right, we ought on the other hand to be willing 

 to take into account those possible hjrpotheses upon which there 

 may be reason to think that an author has proceeded, even 

 though no mention of them be retained in his conclusions. 



Upon the whole, I conceive that the following is the true 

 theory of that class of questions which has been under considera- 

 tion : — 



1st. That it is not in any case a question whether a particular 

 phsenomenon which has come under our notice is an effect of 

 causation or not, but whether or not it is an effect of some single 

 predominant cause, or simple combination of causes, the conse- 

 quences of which are in some measure within the reach of our 

 intelligence. 



