524 Prof. G. Boole on the Theory of Probabilities, 



method of which I have been in possession for a considerable 

 period, and wliich appears to me to answer all the requirements 

 of a general method. Of the particular question which is more 

 immediately before us I shall present a solution to which that 

 method conducted me about two years ago, and from which I 

 was led to take that view of the nature of the fallacies exposed 

 in the preceding pages which I have endeavoured to exhibit. 



Although the immediate business of the theory of probabilities 

 is with the frequency of the occurrence of events, and although 

 it therefore borrows some of its elements from the science of 

 number, yet as the expression of the occurrence of those events, 

 and also of the relations, of whatever kind, which connect them, 

 is the office of language, the common instrument of reason, so 

 the theory of probabilities nmst bear some definite relation to 

 logic. The events of which it takes account are expressed by 

 propositions ; their relations are involved in the relations of pro- 

 positions. Regarded in this light, the object of the theory of 

 probabilities may be thus stated : — Given the separate probabili- 

 ties of any propositions to find the probability of another propo- 

 sition. By the probability of a proposition, I here mean, ac- 

 cording to previous definition, the probability that in any parti- 

 cular instance, arbitrarily chosen, the event or condition which 

 it affirms will come to pass. 



In confirmation of this view, let it be remarked, that as simple 

 events are expressed by simple propositions, so combinations of 

 events are expressed by compound propositions, i. e. by proposi- 

 tions expressing some logical connexion among the simple pro- 

 positions which they involve. Upon the nature of that connexion 

 depends the mode in which the probability of the compound 

 event represented is derived from the probabilities of the simple 

 events. The relation of cause and eff'ect may, in like manner, be 

 resolved into the relation of the terms of a co??//i/«o?i«/ proposition. 

 With any metaphysical inquiries into the nature and the source 

 of that relation we are not concerned. The above and similar 

 instances justify the assertion, that the subject of the theory of 

 probabilities is coextensive with that of logic, and that it recog- 

 nizes no relations among events but such as are capable of 

 being expressed by propositions. We may cany this reasoning 

 one step further. Our data are the probabilities of propositions. 

 That which we seek to determine is also the probability of a 

 proposition. Now, every proposition may be considered with 

 reference either to its matter or to its form. With the matter of 

 propositions however we have no concern, for it imports not 

 what kinds of events they are whose occurrence is asserted in the 

 given premises. There remains then but the form to be con- 

 sidered, the mere logical connexion. Hence it may be inferred 



