‘I come now to the definition of “knowledge.” As in the cases of “belief” and “truth,” there is a certain inevitable vagueness and inexactitude in the conception. Failure to realize this has led, it seems to me, to important errors in the theory of knowledge. Nevertheless, it is well to be as precise as possible about the unavoidable lack of precision in the definition of which we are in search.
It is clear that knowledge is a sub-class of true beliefs: every case of knowledge is a case of true belief, but not vice versa. It is very easy to give examples of true beliefs that are not knowledge. There is the man who looks at a clock which is not going, though he thinks it is, and who happens to look at it at the moment when it is right; this man acquires a true belief as to the time of day, but cannot be said to have knowledge. There is the man who believes, truly, that the last name of the Prime Minister in 1906 began with a B, but who believes this because he thinks that Balfour was Prime Minister then, whereas in fact it was Campbell-Bannerman. There is the lucky optimist who, having bought a ticket for a lottery, has an unshakeable conviction that he will win, and, being lucky, does win. Such instances can be multiplied indefinitely, and show that you cannot claim to have known merely because you turned out to be right.’
– Russell. B. (1912) The Problems of Philosophy