176 Prof. Boole on the Theory of Probabilities, 



vol. vii. p. 476) . Mr. Wilbraham's observations are as follows : — 

 " If, beinj^ in ignorance what system of assumptions ought to 

 be made to render the problem determinate, we were to wish to 

 give a definite answer to the problem, it might be in the follow- 

 ing form : ascertain the chance of the required event happening 

 on any one system of assumptions, and the chance of that system 

 representing the true connexion among the simple events, and 

 multiply the values of these chances together ; the sum of a series 

 of these products comprising every possible system of assump- 

 tions would be the true chance of the event. But Prof. Boole's 

 method evidently does not attempt to solve any question of this 

 nature.'^ Now I make no objection against the truth of the 

 principle here enunciated, though I may doubt its efficiency. It 

 is a principle well known to all who are acquainted with the 

 elementary treatises on the theory of probabilities. Moreover, I- 

 think that the principle is not opposed to the method which I 

 have employed, because I have never seen any other method 

 which leads to " assumptions '' (adopting Mr. Wilbraham's lan- 

 guage) accordant with those conditions which, as we have seen, 

 must be satisfied. Leaving such considerations, however, I trust 

 that the following proposal will not be deemed an unreasonable one. 

 If Mr. Wilbraham's method is both correct and sufficient, w hile 

 mine is false, there must surely be some case in which the two 

 would lead to different results, and in which, from the comparison 

 of those results, my own may be proved to be erroneous. I 

 would therefore request Mr. Wilbraham to endeavour to furnish 

 an instance of this kind. Of course I refer only to problems of 

 the kind discussed in my work, viz. those in which the data are 

 the probabilities of events, simple or compound, with or without 

 information respecting the connexion of such events. Should 

 any method, even of limited application, be discovered which 

 should lead to solutions satisfying the conditions to which I have 

 referred, and yet different from those furnished by my own 

 method, which is not of limited application, and which ahvays 

 causes those conditions to be satisfied, I should regard it as a 

 very interesting and remarkable circumstance. But at present 

 I am, as I have said, wholly ignorant of the existence of any such 

 method. 



I trust to be able in another month to forward a demonstra- 

 tion of the general method in probabilities exemplified in the 

 ''Laws of Thought ;'' and I am anxious to do this, because the 

 demonstration may, I think, be presented in a more simple and 

 satisfactory form than it there possesses, and because an import- 

 ant addition, (not correction) justified by recent researches, may 

 be made to the rule there given. 



iiincoln, August 6, 1854. 



