486 Prof. Boole on a General Method in 



expressed by combinations of simple events ; according to an- 

 other mode, as simple events connected together by definitions or 

 by implied propositions. Now the principle which I wish to 

 assert is, that it is wholly indifferent which mode of expression 

 we employ, provided that it be adequate to convey all the infor- 

 mation we possess. Perhaps that principle may be more defi- 

 nitely stated as follows. 



Principle II. — Any events which suffice simply, or by combina- 

 tion, for the expression of the data may be assumed as simple 

 events and symbolized accordingly, provided that we expUcitly 

 determine the whole of the relations which implicitly connect 

 them. To make plain my meaning, let it be supposed that ob- 

 servation has furnished the following elements of a problem : — 

 Probability of rain =p, 

 Probability of rain with snow = q ; 

 the qusesitum of that problem being 



Probability of rain without snow. 



The expression of this problem by an observer in whose lan- 

 guage there should exist no word for " snow,^' but in which 

 every combination of rain with snow should be termed " sleet,'' 

 would be as follows : — 



1st. Probability of rain =jo, 1 

 2nd. Probability of sleet =q, ^Data. 

 3rd. Sleet always implies rain. J 

 Required probability of rain without sleet. 



It is then affirmed that these two statements are equivalent. 

 The expectation of a phaenomenon cannot be affected by the 

 mere mode of statement of it, and of the circumstances upon 

 which it depends. As respects the two modes of statement in 

 the above instance, it will be seen that in the former of them, 

 one of the given probabilities is that of a compound event ; in 

 the latter, both the given probabilities are those of simple events 

 between which an absolute relation (3rd) is affirmed to exist, and 

 in terms of which the event whose probability is sought is 

 directly expressed. 



Now, beside that it is the most obvious course of procedure to 

 determine directly the event whose probability is sought in terms 

 of those whose probabilities are given, an object which we can 

 always effect by the Calculus of Logic, there is a special reason 

 why we should take this course. Consider the problem employed 

 for the purpose of illustration in the first section of this paper. 

 Representing the events xz and yz, since their probabilities are 

 given, by s and t respectively, its data become 



Prob. a7=c„ Prob. y=c^, Prob. s=CiPi, Prob. t=c^p^] (3) 

 the elements x, y, 8 and t, here assumed (Principle II.) as 



