OF TESTIMONIES OR JUDGMENTS. 605 



entirely new scheme of simple events as the elements of the hypothesis in 

 question. 



12. To what conditions, then, must the hypothesis be subject? This ques- 

 tion I now proceed to answer. 



The hypothesis must be such that it may be consistently applied, without 

 imposing upon the data any other conditions than those of possibility, i.e., of 

 accordance with a possible experience. 



This principle is so obviously true, that it will only be needful to show how 

 the conditions of possible experience are discovered. I shall subsequently show 

 how their discovery limits and determines the hypothesis upon which the solution 

 of questions in the theory of probabilities, whose elements are logical, depends. 



The data of such problems are the probabilities of events. The object sought 

 is also the probability of an event. The numerical values of these probabilities 

 must be expressible by positive proper fractions. At any rate, they must not 

 transcend the limits and 1. This is one condition to which they are subject. 

 Generally, however, there will exist other conditions dependent upon the mutual 

 relations of the events whose probabilities are given. 



Thus, if p were the probability that an event x will happen, q the probability 

 that x and y will both happen, we have, as a necessary condition, 



Again, if p were the probability that x and y will both happen, q the proba- 

 bility that they will both fail, we must have the condition, 



a condition which does not hold in the previous case. 



I have, in the Laws of Thought, treated of these conditions, and of the prin- 

 ciples by which they may be determined, in a special chapter (Cap. xix., On 

 Statistical Conditions). A more simple, and at the same time perfectly general 

 method, for their determination was afterwards discovered by me, and published 

 in the Philosophical Magazine, Aug. 1854. As the method is of fundamental im- 

 portance, I shall here illustrate it by an example, at the same time introducing 

 a slight change in the mode of treatment, which leaves nothing to be desired 

 in point of simplicity. The conditions to the discovery of which the method 

 is applicable will be termed, in accordance with the language employed in the 

 Philosophical Magazine, — the "Conditions of Possible Experience;" inasmuch, 

 as whenever the numerical data of a problem are derived from actual experience 

 these conditions will be satisfied, and whenever in data professing to be thus 

 derived they are not satisfied, the presence of mistake or fraud may with certainty 

 be affirmed. 



VOL. XXI. PART IV. 8 A 



