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XXXVI. — On the Application of the Theory of Probabilities to the Question of the 

 Combination of Testimonies or Judgments. By George Boole, LL.D., Professor 

 of Mathematics in Queen's College, Cork. Communicated by Bishop Terrot. 



(Read 19th January 1857.) 



1. The method for the solution of questions in the theory of probabilities ap- 

 plied in this paper, is that which was developed by the author in a treatise entitled, 

 " An Investigation of the Laws of Thought, on which are founded the Mathema- 

 tical Theories of Logic and Probabilities." The practical object of the paper is to 

 deduce from that method certain conclusions relating to the combination of tes- 

 timonies or judgments. Beside this, however, it will have a speculative reference 

 to some more general questions connected with the theory of probabilities ; and 

 especially to the following question, viz. : To what extent the different modes in 

 which the human mind proceeds, in the estimation of probability, may be consi- 

 dered as mutually confirming each other, — as manifestations of a central unity 

 of thought amid the diversity of the forms in which that unity is developed. 



The special problems relating to the combination of testimonies or judgments 

 which are considered in this paper are the following : 1st, That in which the 

 testimonies to be combined are merely differing numerical measures of a physical 

 magnitude, as the elevation of a star, furnished by different observations taken 

 simultaneously; 2dly, That in which the testimonies or judgments to be combined 

 relate not to a numerical measure, but to some fact or hypothesis of which it is 

 sought to determine the probability, — the probabilities furnished by the separate 

 testimonies or judgments constituting our data. 



2. I have, in the treatise to which reference has been made, described the 

 method which will be practically applied in this paper as a general one. It will, 

 I think, ultimately appear that there is a true and real sense in which the pro- 

 priety of the description may be maintained. But at present I am anxious to 

 qualify the appellation, and to speak of the method as general only with respect 

 to problems which have been resolved into purely logical elements, or which are 

 capable of such resolution. A more thorough analysis of the mental phenomena of 

 expectation will, I think, tend to establish the position that all questions of proba- 

 bility, in the mathematical sense, admit of being resolved into primary elements 

 of this nature, or, to speak more strictly, admit of being adequately represented 

 by other problems whose elements are logical only. Postponing the consideration 

 of this question, I will first endeavour to explain what is meant by the logical 

 elements of a problem, and how the consideration of such elements affects the 

 mode of its solution. 



VOL. XXI. PART IV. 7y 



