TESTIMONY AND AUTHORITY. 81 A " self-infirmative chain" is one in which a statement passes from mouth to mouth among persons whose credi- bility in mathematical language is less than unity. The probability of the truth of the final assertion is then measured by the product of a number of fractions corresponding to the number of links in the chain. It, therefore, continually diminishes as the length of the chain increases. The process may be symbolised thus where the assertion X passes from E to A through D, C, B : X E D C B A. In the " self-corroborative chain " a number of persons in- dependently make the same assertion X ; a process which may thus be symbolised : The credibility of the assertion in this case is greater than that of an assertion of any of the witnesses taken separately ; but the process possesses the disadvantage of carrying us but one remove from the fact ; it takes but one step. But if we make use of testimony as to the credentials of our witnesses, which is the method that our examination of the conditions of trustworthiness has led us to if we inquire how far our witnesses satisfy the conditions of reliability we find that we can retain the advantages of the " self- infirmative chain" without sacrificing those of the "self- corroborative chain " ; we can combine the length of the. former with the strength of the latter. The process may be represented in a diagram thus :
