The Problem of the Rationality of Fallible Methods of Inference

The discussion to which this article is devoted comes within the field of methodology and not of formal logic or metascience. We shall be dealing here with inference, convictions, with the degrees of certitude etc., i.e. the article will be full of psychological concepts. It will also deal with the people who think and act; the whole cognitive process will be considered in connection with the practical life of man and not as an idealized abstraction. The problem raised here is as follows: whether and when we can say that man acts rationally, if he believes conclusions drawn from true premises according to a fallible method, i.e. a method which may lead from true premises to false conclusions. So-called enumerative induction is one such fallible method of inference. Logicians and mathematicians have devoted much time to the question known as the problem of justification of induction. However, they have not been able so far to state clearly the nature of this problem: what should be done in order to justify induction? The aim of the present article is to give comprehensible meaning to the problem of justification of induction and, at the same time, to give a sample — unfortunately a sample that has no practical value — of solving this problem.