 The principle of maximum entropy enjoins us to select from the family of all probability functions consistent with our background knowledge the function that maximizes this quantity. In the special case of choosing the most uninformative probability function over a finite set of possible outcomes, this is just the familiar ‘flat’ classical assignment discussed previously. Things get more complicated in the infinite case, since there cannot be a flat assignment over denumerably many outcomes, on pain of violating the standard probability calculus (with countable additivity). Rather, the best we can have are sequences of progressively flatter assignments, none of which is truly flat. We must then impose some further constraint that narrows the field to a smaller family in which there \(is\) an assignment of maximum  entropy.[3]  This constraint has to be imposed from outside as background knowledge, but there is no general theory of which external constraint should be applied when. 