XXXVI.—On the Application of the Theory of Probabilities to the Question of the 
Combination of Testimonies or Judgments. By Gruorce Bootr, LL.D., Professor 
of Mathematics in Queen’s College, Cork. Communicated by Bishop Terror. 
(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: 1s¢, 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 ; 2d/y, 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. 
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