In Chapter 9 of On Interpretation, Aristotle argues that at least some statements about the future need to be exempted from the principle of Excluded Middle:
In the case of that which is or which has taken place, propositions, whether positive or negative, must be true or false. Again, in the case of a pair of contradictories, either when the subject is universal and the propositions are of a universal character, or when it is individual, as has been said,’ one of the two must be true and the other false; whereas when the subject is universal, but the propositions are not of a universal character, there is no such necessity. We have discussed this type also in a previous chapter.
When the subject, however, is individual, and that which is predicated of it relates to the future, the case is altered. For if all propositions whether positive or negative are either true or false, then any given predicate must either belong to the subject or not, so that if one man affirms that an event of a given character will take place and another denies it, it is plain that the statement of the one will correspond with reality and that of the other will not. For the predicate cannot both belong and not belong to the subject at one and the same time with regard to the future.
Thus, if it is true to say that a thing is white, it must necessarily be white; if the reverse proposition is true, it will of necessity not be white. Again, if it is white, the proposition stating that it is white was true; if it is not white, the proposition to the opposite effect was true. And if it is not white, the man who states that it is making a false statement; and if the man who states that it is white is making a false statement, it follows that it is not white. It may therefore be argued that it is necessary that affirmations or denials must be either true or false.
Now if this be so, nothing is or takes place fortuitously, either in the present or in the future, and there are no real alternatives; everything takes place of necessity and is fixed. For either he that affirms that it will take place or he that denies this is in correspondence with fact, whereas if things did not take place of necessity, an event might just as easily not happen as happen; for the meaning of the word ‘fortuitous’ with regard to present or future events is that reality is so constituted that it may issue in either of two opposite directions. Again, if a thing is white now, it was true before to say that it would be white, so that of anything that has taken place it was always true to say ‘it is’ or ‘it will be’. But if it was always true to say that a thing is or will be, it is not possible that it should not be or not be about to be, and when a thing cannot not come to be, it is impossible that it should not come to be, and when it is impossible that it should not come to be, it must come to be. All, then, that is about to be must of necessity take place. It results from this that nothing is uncertain or fortuitous, for if it were fortuitous it would not be necessary.
The argument here is that if it is already true, for example, that I will eat breakfast tomorrow, then I will necessarily eat breakfast tomorrow, and there is no option about this and no ability of anything to prevent it. Aristotle is here taking it for granted that some things about the future are uncertain, and is using this as a reductio against the position that such claims can be already true. He goes on to give additional reasons for the same thing:
Again, to say that neither the affirmation nor the denial is true, maintaining, let us say, that an event neither will take place nor will not take place, is to take up a position impossible to defend. In the first place, though facts should prove the one proposition false, the opposite would still be untrue. Secondly, if it was true to say that a thing was both white and large, both these qualities must necessarily belong to it; and if they will belong to it the next day, they must necessarily belong to it the next day. But if an event is neither to take place nor not to take place the next day, the element of chance will be eliminated. For example, it would be necessary that a sea-fight should neither take place nor fail to take place on the next day.
These awkward results and others of the same kind follow, if it is an irrefragable law that of every pair of contradictory propositions, whether they have regard to universals and are stated as universally applicable, or whether they have regard to individuals, one must be true and the other false, and that there are no real alternatives, but that all that is or takes place is the outcome of necessity. There would be no need to deliberate or to take trouble, on the supposition that if we should adopt a certain course, a certain result would follow, while, if we did not, the result would not follow. For a man may predict an event ten thousand years beforehand, and another may predict the reverse; that which was truly predicted at the moment in the past will of necessity take place in the fullness of time.
Further, it makes no difference whether people have or have not actually made the contradictory statements. For it is manifest that the circumstances are not influenced by the fact of an affirmation or denial on the part of anyone. For events will not take place or fail to take place because it was stated that they would or would not take place, nor is this any more the case if the prediction dates back ten thousand years or any other space of time. Wherefore, if through all time the nature of things was so constituted that a prediction about an event was true, then through all time it was necessary that that should find fulfillment; and with regard to all events, circumstances have always been such that their occurrence is a matter of necessity. For that of which someone has said truly that it will be, cannot fail to take place; and of that which takes place, it was always true to say that it would be.
Yet this view leads to an impossible conclusion; for we see that both deliberation and action are causative with regard to the future, and that, to speak more generally, in those things which are not continuously actual there is potentiality in either direction. Such things may either be or not be; events also therefore may either take place or not take place. There are many obvious instances of this. It is possible that this coat may be cut in half, and yet it may not be cut in half, but wear out first. In the same way, it is possible that it should not be cut in half; unless this were so, it would not be possible that it should wear out first. So it is therefore with all other events which possess this kind of potentiality. It is therefore plain that it is not of necessity that everything is or takes place; but in some instances there are real alternatives, in which case the affirmation is no more true and no more false than the denial; while some exhibit a predisposition and general tendency in one direction or the other, and yet can issue in the opposite direction by exception.
Now that which is must needs be when it is, and that which is not must needs not be when it is not. Yet it cannot be said without qualification that all existence and non-existence is the outcome of necessity. For there is a difference between saying that that which is, when it is, must needs be, and simply saying that all that is must needs be, and similarly in the case of that which is not. In the case, also, of two contradictory propositions this holds good. Everything must either be or not be, whether in the present or in the future, but it is not always possible to distinguish and state determinately which of these alternatives must necessarily come about.
Let me illustrate. A sea-fight must either take place to-morrow or not, but it is not necessary that it should take place to-morrow, neither is it necessary that it should not take place, yet it is necessary that it either should or should not take place to-morrow. Since propositions correspond with facts, it is evident that when in future events there is a real alternative, and a potentiality in contrary directions, the corresponding affirmation and denial have the same character.
This is the case with regard to that which is not always existent or not always nonexistent. 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. The case is rather as we have indicated.
Basically, then, there are two arguments. First there is the argument that if statements about the future are already true, the future is necessary. If a sea battle will take place tomorrow, it will necessarily take place. Second, there is the argument that this excludes deliberation. If a sea battle will take place tomorrow, then it will necessarily take place, and no place remains for deliberation and decision about whether to fight the sea battle. Whether you decide to fight or not, it will necessarily take place.
Unfortunately for Aristotle, both arguments fail. Consider the first argument about necessity. Aristotle’s example is that “if it is true to say that a thing is white, it must necessarily be white.” But this is hypothetical necessity, not absolute necessity. A thing must be white if it is true that is white, but that does not mean that “it must be white, period.” Thus for example I have a handkerchief, and it happens to be white. If it is true that it is white, then it must be white. But it would be false to simply say, “My handkerchief is necessarily white.” Since I can dye it other colors, obviously it is not simply necessary for it to be white.
In a similar way, of course it is true that if a sea battle will take place, it will take place. It does not follow at all that “it will necessarily take place, period.”
Again, consider the second argument, that deliberation would be unnecessary. Aristotle makes the point that deliberation is causative with respect to the future. But gravity is also causative with respect to the future, as for example when gravity causes a cup to fall from a desk. It does not follow either that the cup must be able not to fall, nor that gravity is unnecessary. In a similar way, a sea battle takes place because certain people deliberated and decided to fight. If it was already true that it was going to take place, then it also already true that they were going to decide to fight. It does not follow that their decision was unnecessary.
Consider the application to gravity. It is already true that if the cup is knocked from the desk, it will fall. It does not follow that gravity will not cause the fall: in fact, it is true precisely because gravity will cause the fall. In a similar way, if it true that the battle will take place, it is true because the decision will be made.
This earlier discussion about determinism is relevant to this point. Asserting that there is a definite outcome that our deliberations will arrive at, in each case, goes against our experience in no way. The feeling of “free will,” in any case, has a different explanation, whether or not determinism is true.
On the other hand, there is also no proof that there is such a determinate outcome, even if in some cases there are things that would suggest it. What happens if in fact there is nothing ensuring one outcome rather than another?
Here we could make a third argument on Aristotle’s behalf, although he did not make it himself. If the present is truly open to alternative outcomes, then it seems that nothing exists that could make it be true that “a sea battle will take place,” and false that “a sea battle will not take place.” Presumably if a statement is true, there must be something in reality which is the cause of the statement’s truth. Now there does not seem to be anything in reality, in this scenario, which could be a cause of truth. Therefore it does not seem that either alternative could be true, and Aristotle would seem to be right.
I will not attempt to refute this argument at this point, but I will raise two difficulties. First of all, it is not clear that his claim is even coherent. Aristotle says that “either there will be a sea battle or there will not be,” is true, but that “there will be a sea battle” is not true, and “there will not be a sea battle” is not true. This does not seem to be logically consistent, and it is not clear that we can even understand what is being said. I will not push this objection too hard, however, lest I be accused of throwing stones from a glass house.
Second, the argument that there is nothing in reality that could cause the truth of a statement might apply to the past as well as to the future. There is a tree outside my window right now. What was in that place exactly 100 million years ago to this moment? It is not obvious that there is anything in the present world which could be the cause of the truth of any statement about this. One might object that the past is far more determinate than the future. There are plenty of things in the present world that might be the cause of the truth of the statement, “World War II actually happened.” It is hard to see how you could possibly have arrived at the present world without it, and this “necessity” of World War II in order to arrive at the present world could be the cause of truth. The problem is that there is still no proof that this is universal. Once things are far enough in past, like 100 million years, perhaps minor details become indeterminate. Will Aristotle really want to conclude that some statements about the past are neither true nor false?
I will more or less leave things here without resolving them in this post, although I will give a hint (without proof at this time) regarding the truth of the matter. It turns out that quantum mechanics can be interpreted in two ways. In one way, it is a deterministic theory, and in this way it is basically time reversible. The present fully determines the past, but it equally fully determines the future. Interpreted in another way, it is an indeterministic theory which leaves the future uncertain. But understood in this way, it also leaves the past uncertain.