Randomness

Abstract

There is one kind of situation where the use of probability seems clear and uncontroversial: where we know a certain statistical statement; and where a certain object is ‘merely’ an instance of the reference class referred to in the statistical statement. For example, in the case of a well-balanced die, we know that the frequency of ones in the sequence of sets of tosses of the die is close to $\frac{1}{6}$. Furthermore, any toss of the die (other than one whose outcome we already know) is ‘merely’ another toss. There is nothing (ordinarily) we can know about it that will keep us from saying that the probability of its yielding a one is one sixth. This is particularly true when we refer to the toss by means of the indefinite article ‘a’. Almost everybody, not in the process of defending a philosophical position regarding the interpretation of probability, will agree that it is correct to say, of a well-balanced die, tossed in a normal fashion, that the probability of getting a one on a toss of the die is (practically) one sixth.