Hi 



Appendix. 



Of the assumption that Probability is identical with Belief, a further and 

 more demonstrative refutation will present itself, after we shall have referred 

 somewhat more particularly to the numerical notation of Probability. 



11. ( Probability is neither wholly objective nor wholly subjective,) — In the 

 foregoing remarks it was requisite, first, as is usually clone, to disentangle the 

 subject from the current forms of expression, which would imply, prima facie, 

 that probability is a quality of things in themselves, or as objectively 

 considered. We also find it necessary to obviate the other extreme, whereby 

 it has been assumed that Probability is simply Belief. Being aware that 

 Probability could not be identified wdth the objective, writers of deservedly 

 high repute have unwarily adopted the opposite and less obvious fallacy of 

 making Probability to be merely s^&jective. Dr. Bain, in the passage quoted 

 above, appears to have contemplated the untenableness of wholly identifying 

 Probability with Belief ; but he has recourse to an expedient not less unten- 

 able, when he assumes that there are two kinds of Probability, the one resident 

 in the mind of the investigator, and the other in the objective facts. This 

 assumption is made tacitly, and is entirely unsupported. The simple truth is, 

 that Probability is neither wholly objective, nor wholly subjective, inasmuch 

 as it is a claim to acceptance constituted by a relation between the two. 

 Probability is not, on the one hand, a quality of the things themselves respect- 

 ing which we inquire ; nor, on the other hand, does it consist in any mere 

 condition of the mind of the inquirer. The probability of a proposition is the 



un 



this value is estimated by comparing that which is asserted in the proposition 

 with the data that we know. The knowledge is in the mind of the reasoner, 

 and the proposition which states the probability, and which ought to be in 

 accordance with that knowledge, is framed in his mind ; but the data thus 

 known are objective, and the probability of the proposition is its claim to 

 acceptance as constituted by the relation of those data to the matter treated of 

 in the proposition. 



12. (Basis of the Numerical Notation. )— It is now requisite for us to 



an 



designate 



involved. 



Let us suppose that we know an event, which we may call A, to have 



occurred on some day in the month of June, and that this is the whole of the 



data : we would estimate the probability of the following proposition, The 



event A occurred before the 21st day of June. As June consists of 30 clays, 



all equal to one another, the case is distinguishable into 30 alternatives haviu 



equal claims upon our acceptance ; and of these 30 alternatives the proposition 



in question is affirmed by 20, representing two decades of days. The whole 



case, therefore, is appropriately expressed in the following three alternative 

 propositions : 



cr 



o 



