By the alethic openness of the future I mean that there is no complete, true, linear story of the future.
The main motivation for believing that the future is alethically open comes from future contingency. If the future is not alethically open but alethically settled, then there is a complete, true, linear story of the future. But, arguably—and the argument goes back as least as far as Aristotle (De Interpretatione 9)—if there is such a story, then the course of future events cannot deviate from it, otherwise the story would be false, contrary to hypothesis. If the course of future events and the complete, true, linear story of the future cannot deviate, then this must be either (1) because the truth of the story is settled by the course of future events, (2) because the course of future events is settled by the story, or (3) because both the story and the course of events are settled by something else (e.g., causal determinism). (2) can be ruled out because it gets the order of dependency between truth and reality backwards. Reality, which includes the actual occurrences of events, determines what’s true, not vice-versa. That leaves (1) and (3).
If (3), then there are no future contingents, no events that both might and might not happen such that their chance of occurrence is greater than zero and less than one. Hence, whatever the story says will happen must happen, and the future is fated.
If (1) then in a sense there is no real future. Because the story is true and because its truth is settled by events, those events must in some sense have already occurred and so they aren’t really future events. In other words, if (1) is right, then the course of “future” events is at most the course of relatively future events–they may be future in relation to a given temporal standpoint, but they are not future absolutely speaking. Hence, absolutely speaking, it follows that there are no future events and thus no future contingent events.
If the preceding argument or something akin to it is sound, then an alethically settled future is one lacking future contingents. If we suppose that there are future contingents—real, absolute future contingents—then the future must be alethically open.
Let us suppose, then, that there are future contingents. To be more concrete, let’s suppose that it is now a future contingent whether Admiral Smith will initiate a sea battle tomorrow against the dread pirate Jones. The question I want to pose is whether propositions like <Smith attacks Jones tomorrow> and <Smith will attack Jones tomorrow> are (a) false, or (b) neither true nor false.
The argument for (b) rests on the idea that <Smith attacks Jones tomorrow> and <Smith does not attack Jones tomorrow> are contradictories, meaning that they are mutually exclusive and jointly exhaustive of the possibilities. If so, then if one is true, the other is false, and if one is false, the other is true. Given bivalence, the principle that every proposition is either true or, if not true, then false, it follows that there is now a truth concerning how the future will unfold with respect to this sea battle. And since the reasoning here generalizes to all does/does not propositions about future contingents, it follows that there is a prior truth concerning how the future will unfold with respect to all future contingents, which brings us back to an alethically settled future and the fatalistic worry based on it. The only way to avoid this result given that the two propositions are contradictories is to deny bivalence and to say that neither <Smith attacks Jones tomorrow> nor <Smith does not attack Jones tomorrow> is true, and that neither is false. Such propositions, one must say, are neither true nor false.
The argument for (a) rests on the idea that <Smith attacks Jones tomorrow> and <Smith does not attack Jones tomorrow> are not contradictories, but merely contraries, meaning that they are mutually exclusive but not jointly exhaustive of the possibilities. If this is right, then even though the propositions cannot both be true, they can both be false. In answer to the question of how <Smith attacks Jones tomorrow> and <Smith does not attack Jones tomorrow> could both be false, the proponent of (a) answers that this is the case when a third type of proposition, one that is the contrary of both <Smith attacks Jones tomorrow> and <Smith does not attack Jones tomorrow>, is true instead. Thus, in addition to (i) it’s being now true that Smith attacks Jones tomorrow, (ii) it’s being now true that Smith does not attack Jones tomorrow, (iii) it could be now true that Smith might and might not attack Jones tomorrow. If any one of (i)–(iii) is true, then the other two are false. Hence, bivalence holds for propositions about future contingents. (Though it might still fail for other reasons, such as vagueness, on which see this book.)
In my published work I have defended (a), arguing that once one sees that in the case of future contingents there are in fact three possibilities—a future that is determinate with respect to one option, a future that is determinate with respect to the other option, and a future that is indeterminate with respect to both options—there is no longer any motivation for denying bivalence to avoid the fatalistic argument from alethic settledness.
But suppose we shift attention from thinking of tomorrow as future to imagining it as present. The past and present, unlike the future, are fully determinate. Hence, when tomorrow comes, it will be the case at any given moment either that Smith is attacking Jones or that Smith is not attacking Jones. (I’m setting the issue of vagueness aside.) In the present-tense case, the third, indeterminate option doesn’t seem to be available. So it seems like <Smith is attacking Jones> and <Smith is not attacking Jones> are contradictories. But if that’s right, then the corresponding tense-neutral propositions (I use uninflected verbs for these so as to distinguish them from present-tense propositions) <Smith attack Jones> and <Smith not attack Jones> also appear to be contradictories. And if we add temporal indices, e.g., <Smith attack Jones at T1> and <Smith not attack Jones at T1>, and range over all conceivable events and temporal indices, then it looks like we again arrive at a complete, true, linear, tense-neutral story of the future—unless we deny bivalence.
Does the proponent of (a) have an answer to this?
UPDATE (2014/05/19/): Edited for clarity and fixed some typos.