Philosophers have long recognized that there is an important distinction within the class of true propositions: the distinction between those propositions that might have been false and those that could not have been false (those that must be true). Compare, for example, the proposition that Paris is the capital of France and the proposition that there is a prime between every number greater than 1 and its double. Both are true, but the former could have been false and the latter could not have been false. Likewise, there is a distinction to be made within the class of false propositions: between those that could have been true and those that could not have been true (those that had to be false).