Aristotle, in his work On Interpretation, had wrestled with the problem of future contingents. In particular whether one can meaningfully regard future contingents as true or false now, if the future is open, and if so, how?
In response, Diodorus maintained that possible was identical with necessary (e.g., not contingent); so that the future is as certain and defined as the past. Alexander of Aphrodisias tells us that Diodorus believed that that alone is possible which either is happening now, or will happen at some future time. When speaking about facts of an unrecorded past, we know well that a given fact either occurred or did not occur, yet without knowing which of the two is true—and therefore we affirm only that the fact may have occurred: so also about the future, either the assertion that a given fact will at some time occur, is positively true, or the assertion that it will never occur, is positively true: the assertion that it may or may not occur some time or other, represents only our ignorance, which of the two is true. That which will never at any time occur, is impossible.
Diodorus went on to formulate an argument that became known as the master argument (or ruling argument: ho kurieuôn logos /ὁ κυριεύων λόγος/). The most succinct description of it is provided by Epictetus:
The argument called the master argument appears to have been proposed from such principles as these: there is in fact a common contradiction between one another in these three propositions, each two being in contradiction to the third. The propositions are: (1) every past truth must be necessary; (2) that an impossibility does not follow a possibility; (3) something is possible which neither is nor will be true. Diodorus observing this contradiction employed the probative force of the first two for the demonstration of this proposition: That nothing is possible which is not true and never will be.
Epictetus' description of the master argument is not in the form as it would have been presented by Diodorus, which makes it difficult to know the precise nature of his argument. To modern logicians, it is not obvious why these three premises are inconsistent, or why the first two should lead to the rejection of the third. Modern interpretations therefore assume that there must have been extra premises in the argument tacitly assumed by Diodorus and his contemporaries.
One possible reconstruction is as follows: For Diodorus, if a future event is not going to happen, then it was true in the past that it would not happen. Since every past truth is necessary (proposition 1), it was necessary that in the past it would not happen. Since the impossible cannot follow from the possible (proposition 2), it must have always been impossible for the event to occur. Therefore if something will not be true, it will never be possible for it to be true, and thus proposition 3 is shown to be false.
Epictetus goes on to point out that Panthoides, Cleanthes, and Antipater of Tarsus made use of the second and third proposition to demonstrate that the first proposition was false. Chrysippus, on the other hand, agreed with Diodorus that everything true as an event in the past is necessary, but attacked Diodorus' view that the possible must be either what is true or what will be true. He thus made use of the first and third proposition to demonstrate that the second proposition was false.
Aristotle solved the problem by asserting that the principle of bivalence found its exception in this paradox of the sea battles: in this specific case, what is impossible is that both alternatives can be possible at the same time: either there will be a battle, or there won't. Both options can't be simultaneously taken. Today, they are neither true nor false; but if one is true, then the other becomes false. According to Aristotle, it is impossible to say today if the proposition is correct: we must wait for the contingent realization (or not) of the battle, logic realizes itself afterwards:
One of the two propositions in such instances must be true and the other false, but we cannot say determinately that this or that is false, but must leave the alternative undecided. One may indeed be more likely to be true than the other, but it cannot be either actually true or actually false. It is therefore plain that it is not necessary that of an affirmation and a denial, one should be true and the other false. For in the case of that which exists potentially, but not actually, the rule which applies to that which exists actually does not hold good. (§9)
For Diodorus, the future battle was either impossible or necessary. Aristotle added a third term, contingency, which saves logic while in the same time leaving place for indetermination in reality. What is necessary is not that there will or that there won't be a battle tomorrow, but the dichotomy itself is necessary:
A sea-fight must either take place tomorrow or not, but it is not necessary that it should take place tomorrow, neither is it necessary that it should not take place, yet it is necessary that it either should or should not take place tomorrow. (De Interpretatione, 9, 19 a 30.)