432 Prof. Boole on a Gerieral Method in 



in the Theory of Probabilities are limited, Philosophical Maga- 

 zine, vol. viii. p. 91) are. 



Data, 



Probabilities, Prob. x^c^ Prob. y=c^ 1 ,,. 



Prob. xz=c^p^ Prob. yzz=c^p^j 

 Absolute connexion, 



z(\-x){\-y)=0 •• . (2) 



Quasitum. 

 Prob. z. 



Here, beside the probabilities of the several events whose 

 logical expressions are x, y, xz, and yz, we have given the abso- 

 lute connexion z{\—x){\—y)=0, denoting (in the language of 

 the Calculus of Logic) that the event z cannot happen in the 

 absence of the events x and y. The qusesitum is the probability 

 of the event whose expression is z. I design to investigate a 

 general method of solving problems of this kind. Such a 

 method, viewed through the range of its consequences, is entitled 

 to be regarded as a general method in probabilities, because all 

 solvable questions may be referred either directly, or through 

 some intermediate principle, to the above class. And the hope 

 which moves me to repeat here without substantial change the 

 demonstration of such a method contained in my treatise on the 

 Laws of Thought, is that of being able to set forth with greater 

 fulness the distinctive principles upon which the demonstration 

 depends, and of annexing to the final statement of the rule to 

 which it leads, an important addition, 



2. Probability I conceive to be not so much expectation, as a 

 rational ground of expectation, and its numerical measure I de- 

 fine with mathematicians generally* as follows. 



Definition. If, respecting any event, the mind is only able to 

 form a number n of similar and mutually exclusive hypotheses, 

 to none of which it is entitled to give any preference over any 

 other, and if m of those hypotheses are favourable to the event, 

 i. e, such that any one of- them being realized, the event will 

 happen, while the remaining hypotheses are unfavourable to it, 



* To quote, for example, Laplace's definition, " La theorie des hasards 

 consiste i r^duire tous les evenements du me me genre a un certain nombre 

 de cas egalement possibles, c'est a dire, tels que nous soyons egalement 

 indecis sur leur existence ; et a determiner le nombre de cas favorables a 

 I'ev^nement dont on cherche la probabilite. Le rapport de ce nombre k 

 celui de tous les cas possibles est la mesure de cette j)robabilite, &c." — Essai 

 philosophique sur les Probabilit^s, p. 7. Subsequently, Laplace speaks of 

 the different " cases " as " hypotheses," which, indeed, they are. 



