PEOFESSOE BOOLE ON THE THEOEY OE PEOB ABILITIES, 
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positions, the connexion which exists among all the events in question — a connexion 
which in the original form of the data was only implied. 
This leads us to the statement of the second Principle of the Method, 
Principle II. — When the data have been translated into probabilities of events con- 
nected by conditions logical in form and explicitly knovm, the problem may be con- 
structed from a scheme of corresponding ideal events which are free, and of which the 
probabilities are such that when they (the ideal events) are restricted by the same con- 
ditions as the events in the data, their calculated probabilities will become the same as 
the given probabihties of the events in the data. 
To take a material illustration: the problem, in the form to which it is reduced by the 
Calculus of Logic in accordance with Principle I., might be represented by the supposi- 
tion of an urn containing balls distinguished by certain properties, e. g. by colour, as 
white or not white, by form, as round or not round, by material, as ivory or not ivory, 
and by the supposition that, while these properties enter into every conceivable combi- 
nation, all the balls in which certain combinations are found are attached by strings 
to the sides of the urn, so that only the balls in which the remaining combinations 
are realized can be drawn. Suppose, further, that the probabilities of drawing under 
the actual conditions a white ball, a round ball, an ivory ball, &c. are given, and the 
probability of drawing a free ball fully defined with respect to the above elements of 
distinction is required. The principle affii’med is that we must proceed as if the balls 
were all free, and with probabilities such that the calculated probability of drawing any 
one of the balls which under the pre\'ious supposition are free, would be the same as 
under that supposition it is given to be. 
Confining ourselves to the above material case, I remark, that the supposed mode of 
solution represents, 1st, di. possible oi things; 2ndly, an order of things in which no 
preference is given to any one combination over any other which falls under the same 
category, or mode of thought. All the procedure of the theory of probabilities is 
founded upon the mental construction of the problem from some hypothesis, either, 1st, 
of events known to be independent ; or, 2ndly, of events of the connexion of which we 
are totally ignorant ; so that, upon the ground of this ignorance, we can again construct 
a scheme of alternatives all equally probable, and distinguished merely as favouring or 
not favouring the event of which the probability is sought. In doing this we are not at 
hberty to proceed arbitrarily. We are subject, first, to the formal Laws of Thought, 
which determine the possible conceivable combinations; secondly, to that principle, 
more easily conceived than explained, which has been differently expressed as the “ prin- 
ciple of sufficient reason,” the “principle of the equal distribution of knowledge or 
ignorance*,” and the “principle of order.” We do not know that the distribution of 
* Knowledge and ignorance being in tbe theory of probabilities supplementary to each other, the equal 
distribution of the one implies that of the other. 
I take this opportunity of explaining a passage in the ‘ Laws of Thought,’ p. 370, relating to certain 
applications of the principle. Yalid objection lies not against the principle itself, but against its applica- 
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