AND THE PROBABILITIES OF AUTHORITY AND ARGUMENT. 393 



There are many remarks to be made on the demonstrative connexion of the parts of this system 

 with one another, and on the explanations in general language of the new varieties of syllogism. 

 The length of this paper, however, is a sufficient reason for stopping here with the formal part of 

 the subject, and proceeding to the consideration of the probabilities of argument and authority. 



Section V. Ow the Application of the theory of Probabilities to questions of Argument 



and Authority. 



Writers on logic have made no effort to apply the mathematical theory of probabilities to the 

 balance of arguments; for we can hardly call by that name the simple statement that the pro- 

 bability of the conclusion of a syllogism is the product of the probabilities of the premises. How 

 far this is correct will appear in the course of the present section, which is intended to investigate the 

 manner in which the probability of a conclusion is to be inferred from opposing arguments and 

 authorities, of which the several probabilities are given. 



Conclusions which are not absolutely demonstrated are established in our minds on two distinct 

 bases, argument and authority. Even if there be appeal to authority in establishing the 

 premises of an argument, the distinction is in no degree lost. This we shall see as soon as the 

 terms are defined. 



Argument is an offer of proof, and its failure is only a failure of proof: the conclusion may yet 

 be true. Authority is an offer of testimony, and its failure is a failure of truth : nothing can 

 furnish absolute reason for distrusting the authority on future occasions except the proof that the 

 conclusion asserted is false. A person who had made a hundred assertions, all supported by 

 inconclusive arguments, but all of which turned out to be true, would give a very high authority 

 to his hundred and first assertion. 



We have an unfortunate use of language in the mathematical application of the word pro- 

 bahility. We say that small probability and great improbability are identical terms ; which is not 

 true in their common meaning. In fact, a being what we call the probability of an event, a — ^ is 

 what we ought to call by that name : and if a — i be negative, we ought to call A — a the 

 improhahility of the event. It would not be wise to introduce the same inaccuracy in the use of the 

 word authority : accordingly, fi being the chance that an assertion of an individual, made on the 

 best of his knowledge and belief, is true, I shall call fx the value of his testimony. When n 

 exceeds i, I shall say that he is authority for the conclusion. And, measuring absolute authority 

 by unity, I shall take 2^-1 as the measure of his authority, which is against the conclusion, if 

 2u- I be negative. Again, if p be the number of times his testimony is given to a truth for once 

 which it is given to a falsehood (which we may call his relative testimony), and if a denote his 

 authority, we shall have the following equations, which will all be useful : 



p - 1 

 p+\ 



M \ + a 



I - IX 1 - a 

 1 + <i n 



II = 



2 p + \ 



In forming our opinions upon argument, we are told to leave authority altogether out of .sight, 



and to consider only what is said, not who says it. It was Bacon, I believe, who first said that 



assertion is like the shot from the long bow, the force of which depends upon the arm which draws 



it ; while argimient is like the shot from a cross bow, wliich a child can discharge as well 



Vol.. VIII. Part. III. SE 



