610 PROFESSOR BOOLE ON THE COMBINATION 
that the method was founded. As presented in the Laws of Thought, it rests 
upon principles which, to my own mind, have something of an axiomatic character, 
Viewed in this light, its perfect accordance with the requirement above explained 
may be considered as a verification of it @ posteriori. In itself, however, this 
accordance affords a sufficient ground of confidence in the legitimacy of the hypo- 
thesis. On the proof of this accordance I shall say something hereafter. At 
present I will only state the hypothesis, and show in what the accordance 
consists. 
The hypothesis is the following :—Translating our problem by the aid of the 
calculus of logic into a language in which the events whose probabilities are given, 
appear as simple events subject to conditions founded on their definitions, Art. 
11, we ascend above these simple events to another scheme of simple events, 
which are free, and which, when actually subjected to the conditions to which 
the before-mentioned simple events are necessarily subject, shall have the same 
probabilities, and shall in every respect take their place. The unknown proba- 
bilities of the free simple events, which form the elements of this hypothesis, must 
be so determined as to render the substitution possible, and to permit a formal 
construction of the problem, both in its data and by its queesitum, out of those 
new elements. 
The unknown probabilities being thus determined, the problem assumes a 
form in which its elementary data are the probabilities of simple events unre- 
stricted by any condition. In this form the solution of the problem is possible by 
mere consequence of the fundamental definition of probability. The ground 
upon which this hypothesis was presented in the Laws of Thought was its intrin- 
sic reasonableness. On this point I will only refer to my observations in the 
original work. The ground upon which, in the present essay, I wish to rest the 
hypothesis is, that it is the only one which does not impose upon the data other 
conditions than those of conformity with a possible experience. The conditions 
which must be fulfilled in order that p’, q’, &c., in the substituted and hypothetical 
data, may be measures of probability at all—i.e., may be positive proper frac- 
tions,—are precisely the conditions of possible experience in the original data. 
(See Appendix.) 
17. The application of this hypothesis is so fully explained in the Laws of 
Thought, cap. xvii., that I shall here only describe the general method for the so- 
lution of questions in probabilities to which it leads, and show the connection 
which exists between the several parts of that method and the foregoing doctrine. 
General Method. 
Representing the problem to be solved under the form— 
Given Prob. p, (wy, 2%-.)=p Prob. d, (a, y,2 . -)=q ke. 
Required Prob.  (@,y, 2. +) 
a 
