l yi Appendix. 



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

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



1 • .... 



in 



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 comparing the premises of a syll _ 



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. 



with 



.nn 



belief is a distinct event; and, as in 



And why 1 Because 



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



absolutely. "We 



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



that if he behV.vA fhnco nmmic,™ t.^ «i t__i* .i • , 



belief 



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

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



resultant. D'Alembert believed that if a o „ _ 



Probability of the obverse side falling uppermost would"bVin'Vaci"throwT 



obability 



failed 



| . Reasoning 



