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XII. Reply to some Observations published by Mr. Wilbraham in 

 the Philosophical Magazine, vol. vii. p. 465, on the Theory of 

 Chances developed in Professor Boole's 'Laws of Thought J 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



CONTROVERSY is in every way so disagreeable to me, that 

 it is with the most unfeigned reluctance I feel myself 

 called upon to reply to the observations of Mr. Wilbraham in- 

 serted in the last Number of your Journal. 



Mr. Wilbraham states that it is his object " to show that 

 Professor Boole does in the greater number of questions rela- 

 ting to chances solvable by his method (or at least in those which 

 are most difficult to treat by other methods), tacitly assume cer- 

 tain conditions expressible by algebraical equations, over and 

 above the conditions expressed by the data of the problem, and 

 to show how these conditions may be algebraically expressed/^ 

 And in a subsequent passage he describes the procedure of that 

 part of my work on the Laws of Thought which relates to the 

 theory of probabilities, thus : — " In cases not determinable by 

 ordinary algebra, his (Professor Boole's) system is this j he takes 

 a general indeterminate problem, applies to it particular assump- 

 tions not definitely stated in his book, but which may be shown, 

 as I have done, to be implied in his method, and with these 

 assumptions solves it ; that is to say, he solves a particular deter- 

 minate case of an indeterminate problem, while his book may 

 mislead the reader by making him suppose that it is the general 

 problem which is being treated of/' (Phil. Mag. vol. vii. pp. 465, 

 475.) 



I fear that the impression produced upon the mind of any 

 person not acquainted with my work by such statements as the 

 above would be, that I have introduced in a covert manner 

 assumptions of the existence of which I was ignorant, or of the 

 recognition of which I was afraid. It may be therefore right 

 for me to state that I have, in the chapter containing the demon- 

 stration of the general method for the solution of questions in 

 probabilities (Laws of Thought, Chap. XVII.), explicitly stated 

 the principles upon which that demonstration proceeds, and with 

 equal explicitness deduced from them the algebraical equations 

 upon which the solution depends. In the practical examples 

 which are contained in the subsequent chapters, the rule to which 

 the above-mentioned principles have led is applied without any 

 reserve or addition whatever. To prove that particular assump- 

 tions not definitely stated in my book are employed, it ought, I 

 conceive, to have been shown that the principles which I have 

 expressly stated are insufficient for the conclusions which are 



