" is an undetermined value of a certain propositional function, it will be necessary if the function is always true, possible if it is sometimes true, and impossible if it is never true. This sort of situation arises in regard to probability, for example. Suppose a ball
is drawn from a bag which contains a number of balls: if all the balls are white, "
is white" is necessary; if some are white, it is possible; if none, it is impossible. Here all that is known about
is that it satisfies a certain propositional function, namely, "
was a ball in the bag." This is a situation which is general in probability problems and not uncommon in practical life—e.g. when a person calls of whom we know nothing except that he brings a letter of introduction from our friend so-and-so. In all such cases, as in regard to modality in general, the propositional function is relevant. For clear thinking, in many very diverse directions, the habit of keeping propositional functions sharply separated from propositions is of the utmost importance, and the failure to do so in the past has been a disgrace to philosophy.