604 PROFESSOR BOOLE ON THE COMBINATION 



since the presence of any two of the phenomena " sleet," " drift," " storm," im- 

 plies that of the third, and involves the conjunction of the phenomena of rain, 

 snow, and wind. 



The data of the problem we are considering might then, in the imagined dia- 

 lect, assume the following form : 



The probability of sleet is p, of drift q, and of storm r ; required the probabi- 

 lity of the concurrence of the phenomena of sleet, drift, and storm. 



But in this form the problem would not, in its data, express all the knowledge 

 which the person using such language must possess of the connection of the events 

 to which it related. He must know that it was impossible that any two of the events 

 sleet, drift, and storm, should occur without the third, so that the problem, if so 

 stated as to embody the same amount of actual knowledge as is conveyed in the 

 previous statement of it, would assume the following form : 



The probability of sleet is p, of drift q, of storm r, and these events are so 

 connected, that no two of them can occur without the third occurring, What is 

 the probability of their concurrence ? 



Now the principle affirmed declares that the solution of the problem must be 

 the same whichsoever of these forms of statement we adopt. 



As languages increase in affluence, the number of their simple terms becomes 

 augmented, partly through the necessity of giving expression to new ideas, partly 

 through the wish to give more convenient expression to definite and oft-recurring 

 combinations of the old ones. With every term invented in subserviency to the 

 latter purpose, a definition must be introduced. A dictionary, setting aside its 

 philological portion (and even this not wholly), is a record of such definitions. As 

 a consequence of such definitions of terms, spring up also propositions innumer- 

 able connecting these terms — propositions which in no degree add to the amount 

 of our absolute knowledge, which are quite distinct from the discovered facts and 

 laws of nature and of human history, but are merely logical deductions from 

 the definitions. We might conceive of a language in which all possible combi- 

 nations of ideas should be expressed by simple terms, with connecting definitions 

 and propositions ad infinitum. The realization of such a conception is neither 

 practicable nor desirable; but it is, nevertheless, the limit toward which all lan- 

 guages, which are not dead or decaying, do actually tend. The progressive ac- 

 tion of this tendency does not affect the laws of expectation, neither, therefore, 

 can it affect any consistent and scientific theory which is founded upon those 

 laws. 



We are not, therefore, permitted to assume that any events which, in the lan- 

 guage of the problem, may be presented as simple events, must therefore be 

 adopted as such into the hypothesis which is to form the basis of our method of 

 solution. Nor, on the other hand, are we forbidden to employ transformations 

 (sanctioned by the rules of Logic) which will have the effect of introducing an 



