Prof. Boole on the Themij of Probabilities. 101 



has (lone. And I can conceive of nothing as more likely to in- 

 spire a rational confidence in the theory of probabilities^ than a 

 clear and well-marked distinction between these cases^ accom- 

 panied by a distinct statement of the grounds upon which, 

 whenever constants are determined, their determination is effected. 

 The question has been suggested to me by a correspondent =!', 

 to whom I am indebted for some valuable remarks, whether 

 the general method described in my last paper involves any 

 fundamentally different idea of probability from that which is 

 commonly accepted. He observes, that the results which I 

 have given are in accordance with the principles of the established 

 theory. As the same question may present itself to other minds, 

 I would remark that the theory of probabilities has, in the view 

 which I have been led to take of it, two distinct but accordant 

 sources. From whichsoever of these it may be derived, it will 

 be found to involve the idea of numerical magnitude ; but in the 

 one case that idea will have reference simply to the relative fre- 

 quency of the occurrence of events, being in fact the received 

 ground of the theory ; in the other, to the persistency of certain 

 forms of thought, which are manifested equally in the operations 

 of the science of number, and in the reasonings and discourses 

 of common life. Setting out from either of these grounds, we 

 may, I conceive, without difficulty attain to a knowledge of the 

 other. Now it appears to me to be perfectly in accordance with 

 the nature of probability that this should be the case ; for its 

 relation to number is not more essential than its relation to the 

 manner in which events are combined. But while the expression 

 of the former relation belongs to arithmetic, or more generally 

 to algebra, that of the latter belongs to logic. 



I design, as soon as leisure and opportunity shall permit, to 

 publish the general theory to which reference has been made in 

 this and the previous paper. Had it been possible for me to 

 offer in the space which they have aftbrded a satisfactory state- 

 ment of its principles, I should have gladly availed myself of the 

 opportunity of doing so. But for the particular ends here in 

 view this has been the less necessary to be done, as the results 

 actually exhibited admit of verification by known methods. Still 

 I trust that the collateral discussions into which I have entered 

 have not been altogether without interest or profit, even with 

 reference to established doctrines. .i .]j?i'iii»[»;u 



I remain, Gentlemen, ■n ".t -'-'^no^ipi 



^i^offt Your obedient Servant, »• ' 



ft-- ' George Boolb. i ? i 



Lincoln, June 17. 1851. iu^Ih 



* W. F. Donkin, M.A., Savilian Professor of AstronoBiy, Oxford- -/pyv/ 

 Phil, Mag, S. 4. Vol. 2. No. 9. Aug. 1851. ,,ui. ... ., • .i|4 ^aW m 



