Ivi Ap2)endix. 



14. (Inference of Belief) — It is now desirable, in conclusion, to revei*t 

 briefly to the question as to the relation of Probability to Belief. The subject 

 has, in several of its aspects, so much of importance or of interest as to render 

 it worth while to have investigated it closely. It is, then, to be observed, 

 that if the statement of a probability asserted simply the existence of a belief, 

 or of a fraction of belief, there could be no such thing as a demonstrative 

 deduction of probabilities, even from data absolutely assumed. But all agree 

 that from assumed data there are demonstrative deductions of probabilities. 



Let us advert to any case whatever of inference of the simplest possible 

 kind. Employing the usual symbolic syllogism — Every M is P, S is M, 

 therefore S is P — we may attach to these alphabetic symbols whatever meaning 

 •we please. If the data were merely, that each of those two premises is 

 believed by a given individual, whom we may call X. Y., we could not infer 

 absolutely that X. Y. believes the conclusion. He may not have put the 

 premises together; or he may be so unreasonable as not to accept the con- 

 sequence. If we assume that he has combined the premises, this is an 

 assumption additional to that of the two beliefs. Let this additional assump- 

 tion be made, and then we may infer, as a high probability, that X. Y. 

 believes the conclusion ; because, in the great majority of instances of believing 

 and compaiing the premises of a syllogism, the conclusion also is beheved. 

 And it is morally certain that if a hundred persons were experimented upon, 

 especially if at all a favourable specimen of rationality, then, in most or all of 

 the hundred instances, the putting together of believed premises would be 

 accompanied by a belief of the conclusion. But these are inferences from an 

 induction of facts not given in the original premises ; they are not demon- 

 strative inferences, nor inferences from the mere beliefs of X. Y. or his 

 fellows. 



Thus we see that, even with respect to the plainest cases of necessary 

 sequence, we cannot from mere belief demonstrate belief. And why ? Because 

 every act of belief is a distinct event; and, as in the case of other matters of 

 fact, we do not know the machinery of the causation so well as to reason 

 absolutely. We know absolutely that if every M be P, and S be M, then S is 

 P ; but we do not know absolutely, with reference to any person whatever, 

 that if he believe those premises, he also believes this conclusion. 



And if a person's belief of the premises of a syllogism in " Barbara" does 

 not of itself enable us to infer his belief of the conclusion, much less would his 

 belief of two separate probabilities warrant our inferring his belief of their 

 resultant. DAlembert believed that if a given coin were thrown twice, the 

 probability of the obverse side falling uppermost would be in each throw ^ ; 

 but the great mathematician failed to believe tlie necessary resultant, that the 

 probability of an obverse in one or other of the two throws is J. Reasoning 



