KiDD. — On Prohahility. H 



nition is given by Sir John Herschel (Edinburgh Review, July, 1850 ; 

 reprinted in '^ Essays," p. 376) : " As Probability," he says, " is the numerical 

 measure of our expectation that an event will happen, so it is also that of our 

 belief that one has happened, or that any proposed proposition is true." In a 

 very recent work of repute, Dr. Bain's "Logic," published in 1870, we read 

 (III. ix. 6) : " Probability expresses a state of the mind, and also a situation 

 among objective facts. As a state of the mind, it is a grade or variety of 

 belief. The highest degree of belief is called Certainty j the inferior degrees 

 are degrees of Probabilitv." 



Now, that there are degrees of belief cannot be questioned ; but how are 

 they to be enumerated, measured, or weighed ? How come we at the denomi- 

 nator in the supposed fraction of belief ? And if we assume a denominator, 

 how are we to determine the numerator? Consciousness merely indicates, 

 without much nicety of discrimination, that we know or are ignorant ; believe, 

 or doubt, or disbelieve ; are more or less certain or dubious. This with 

 respect to each person's own mental phenomena j while as to those of our 

 neighbour we have no direct knowledge whatever. The alleged fractions of 

 belief are, in fact, ascertained, not from definitive investigation into the state 

 of men's minds, but from examination of the objective data to which the belief 

 does or ought to correspond. The quantum of credence, in any given case, 

 ought to be approximately proportional to the quantity and quality of the 

 data j but whether it actually is so or not, is a question as to a matter of fact 

 totally distinct from that which is asserted in the given proposition. Proba- 

 bility and belief are not, therefore, identical ; but they are, or ought to be, 

 correlative j and the interpretation of the degrees of probability is not to be 

 sought or found in the mental conditions of the investigator. Right belief is 

 correspondent to probability ; wrong belief is at variance with probability j 

 and the probability itself is determined by the data. To attempt evolving the 

 logic or calculus of Probability from the metaphysics of Belief, is to set out in 

 the wrong direction j and it would be, at the best, to seek the solution of a 

 problem comparatively easy by substituting what is obscure. The substitution, 

 however, is gratuitous. The probability of a proposition is not constituted by 

 the belief that is actually given to it, whether the belief of an individual, or 

 the average amount of belief entertained by the aggregate of judges, or what- 

 ever other standard of actual belief we may select ; but, as even the etymology 

 of the word " probability" indicates, it is proportional to the degree of belief 

 or acceptance that ought to be given, according to the data of knowledge. 

 Which is equivalent to saying, that probability is determined by evidence; 

 and accordingly as a testimony is trustworthy, or an argument cogent, a 

 proposition so supported is proportionally probable or certain, however scantily 

 or extensively the value of the evidence may be recognized. 



