441 



Athly, When, as in the case supposed, the data are not the proba- 

 bilities of simple events, the numerical measures of probability p, q, 

 r, &c., which they involve, will bd subject to certain conditions 

 (beside that of their being positive fractions), in order that these data 

 may be mutually consistent, — may, if considered as furnished by ex- 

 perience, represent an experience which is possible. These condi- 

 tions the author terms the " conditions of possible experience," and 

 he gives a general method for their determination. Thus, for ex- 

 ample, if p is the probability of the conjunction of the events x and 

 y, q of the conjunction of y and z, and r of the conjunction of 2 and 

 .r, the quantities p, q and r, besides the condition of not transgress- 

 ing the limits and 1, must satisfy the conditions 



P^q + r—\,q^r + p— l,r^p + 9-I; 



similar conditions deducible from the data, will in general, limit A 

 priori, the value of the probability sought. 



bthly. The author then lays down the principle, that the hypothe- 

 tical construction (already referred to) of the problem from simple 

 events with unknown probabilities, must be such, that the determi- 

 nation of these unknown probabilities from the data will be possible 

 and deGnite, when the above conditions of possible experience are 

 satisfied. In other words, the hypothesis should involve the exist- 

 ence of no other conditions among the data, than the condition of 

 their being possible, and mutually consistent. 



This principle, he observes, completely limits and determines the 

 nature of the solution, restricting it to the particular method deve- 

 loped in the chapters on probability in the Laws of Thought. He 

 remarks, that the method in question was not, however, as it first 

 presented itself to his own mind, associated with such considerations 

 as these, nor are such considerations even hinted at in the work re- 

 ferred to. The method was there exhibited as resting upon an axio- 

 matic basis. The fact, that the conditions which it involves as con- 

 ditions of mathematical validity and consistency, are identical with 

 the conditions of possible experience, was subsequently discovered. 



The proof of this identity, is not, however, in its present state, to 

 be considered as complete ; neither can it be considered as established 

 that no other method can satisfy the so-called conditions of possible 

 experience. The proof of the former proposition has, however, been 

 carried sufficiently far to leave no doubt of its truth, and the latter 



