the Theory of Probabilities, 485 



Principle I. — Probability is always relative to our actual state 

 of information. Upon the actual connexions of events it depends 

 no further than as such connexions are known to us. 



This doctrine of the nature of probability, it may be added, 

 has been fully recognized by acute and thoughtful minds ap- 

 proaching the subject from a point of view different from the 

 mathematical one*. 



I proceed to the statement of an important principle founded 

 on the nature of language as an instrument of expression. It 

 is, that in the theory of probabilities, as in every other branch of 

 science, the solution of a question ought to depend upon the in- 

 formation conveyed in the data, and not upon the special elements 

 or constructions of the language which may serve as the vehicle 

 of that information. Now one very important point in which 

 languages are observed to differ, is the selection of the objects 

 or events to which simple terms are appropriated. In the rude 

 infancy of nations, the number of such terms is small, and their 

 application is confined within the limits of daily experience. 

 With the progress of society the need of a wider vocabulary is 

 felt, not merely for the expression of things unknown to former 

 experience, but also for the purpose of abbreviation. Simple 

 terms are invented, not solely for the representation of things 

 wholly new, but for the more simple expression of things which 

 it was before possible to express by a combination of terms. 

 Whensoever in this gradual advance of language the combination 

 of two simple terms is replaced by a new simple term, a defini- 

 tion or an equivalent series of ordinary propositions is introduced. 

 Thus, if every combination of rain with snow becomes repre- 

 sented, for abbreviation, by the simple term " sleet,'^ we virtually 

 carry with us, whenever we use that term, the definition " sleet 

 is rain with snow,^^ or the equivalent train of propositions, " If 

 there is sleet there is rain with snow,^' " If there is rain with 

 snow there is sleet -/' and that definition, or its equivalent pro- 

 positions, we must, if need be, express as well as assume. Now 

 it is manifest that there is no limit to this invention of simple 

 terms, and consequent implication of propositions. In a lan- 

 guage possessed of an infinite copiousness of diction, every object 

 of experience, every combination of events, might thus be ex- 

 pressed by a simple term. Supposing that we had such a lan- 

 guage at command, it is evident that we might in various ways 

 express the data and the object of a question in the theory of 

 probabilities. The events whose probabilities are given might, 

 according to one mode of expression, appear as compound events 



* For instance, it is stated with great clearness in an extract from the 

 commonplace book of Bishop Copleston, recently pubhshed by Archbishop 

 Whately. 



