80 
[318 
318. 
ON A QUESTION IN THE THEORY OF PROBABILITIES. 
[From the Philosophical Magazine, vol. XXlli. (1862), pp. 361—365.] 
The question referred to is that discussed in the paper 121; the remarks on that paper in the Notes 
and Beferences to volume II. are in a great measure to the same effect as the present and next papers, 
318 and 319, the existence of which I had entirely overlooked. In the first part (dated 2, Stone Buildings, 
W.C., March 1862) of the present paper 318, after referring to the two modes of statement which may be 
called the Causation statement and the Concomitance statement, I reproduce nearly as in the Notes and 
Beferences first my own solution as completed by Dedekind, next Boole’s solution of the problem, involving 
his logical probabilities; and the paper is then continued as follows. 
The foregoing paper was submitted to Prof. Boole, who, in a letter dated March 26, 
1862, writes: 
“ The observations which have occurred to me after studying your paper are the 
following. 
1st. I think that your solution is correct under conditions partly expressed and 
partly implied. The one to which you direct attention is the assumed independence of 
the causes denoted by A and B. Now I am not sure that I can state precisely what 
the others are; but one at least appears to me to be the assumed independence of 
the events of which the probabilities according to your hypothesis are aX, ¡3g. Assuming 
the independence of the causes as to happening, I do not think that you are entitled 
on that ground to assume their independence as to acting; because, to confine our 
observations to common experience, we often notice that states of things apparently 
independent as to their occurrence, may, when concurring, aid or hinder each other in 
such a manner that the one may be more or less likely to act ‘ efficiently ’ in the 
presence of the other than in its absence. I use the language of your own hypothesis 
of efficient action. 
2ndly. When I say that I think your solution correct under certain conditions, 
I ought to add that it appears to me that such conditions ought to be stated as