Susan Haack in her book Deviant Logic argues that Aristotle in his famous passage about future contingents commits a modal fallacy. Let’s look at Aristotle’s whole argument in Chapter 9 of de Interpretatione, paragraph by paragraph. He starts out saying:
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.
He is here presenting the assumption which is key to the entire affair. He assumes the principle of bi-valence (PB) and the law of non-contradiction (LNC) from the outset, but only to past and present events. He claims here that the LNC applies when the subject is universal and the propositions are universal or when the subject is individual and the propositions are universal; but if the subject of the proposition is universal and the proposition is not, there is no necessity for LNC to hold.
What does he mean by ‘universal’ and ‘individual’ here? In Chapter 7 he says, “By the term ‘universal’ I mean that which is of such a nature as to be predicated of many subjects, by ‘individual’ that which is not thus predicated. Thus ‘man’ is a universal, ‘Callias’ an individual.” So an example where the subject of a proposition is universal but the proposition overall is not would be what, exactly? Let’s try “There will be a sea fight tomorrow.” Here the subject is ‘sea fight’. Is this universal or individual? Well, let’s say that we are talking about a particular sea fight. So it is individual. Then is the whole proposition universal or individual? It would seem that the proposition “There will be a sea fight tomorrow” would also be individual in this case. So if this is true, then Aristotle is saying that this individual proposition would have an individual subject. But this would not be in the category where the PB would be specified by the above: Not very promising. Let’s assume that here that ‘sea fight’ is universal in Aristotle’s sense. Then whether a (universal) sea fight would take place tomorrow or not would be a case with a universal subject and but the proposition is individual (specific) and one of those cases where PB is not required to hold. This must be what he means. But he hasn’t proven anything yet, only asserted it.
His next paragraph in Chapter 9 is as follows:
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.
So here it seems that he really does mean that the subject is individual (a particular sea fight) but that the action of which the subject is predicated will take place in the future. Here the rule from paragraph one doesn’t apply. An individual sea fight is predicated true by one person and false by another. One must be right and the other wrong. Why? It seems that the law of the excluded middle (LEM) is assumed.
Let’s go on:
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.
The condition of being white is here assumed to be something that cannot change (no tanning salons in Athens). Here he asserts that this is the same as saying that being white is a necessary condition of a thing. He then says that affirmations or denials must be either true or false. But this is clearly wrong in general. It is true of ‘white’ but what about ‘angry’. In modern (Kantian) language, analytic qualities are necessary, but not synthetic qualities, qualities that can change. So let’s watch out for how this is used.
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.
Well, in this paragraph he shows that if all events were analytic, they would be necessary. But his apparent lack of appreciation for qualities that are not analytic looms as a caution.
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.
Here we have reached a conclusion to a reductio: we can’t say that a future event will take place because its affirmation or denial is either necessary or not, yet we know that it is contingent (there is an ‘element of chance’).
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.
He here concludes that the premise that the PB holds (or is it LEM?) for the future is reduced to absurdity by the outcome that fatalism is the result, and we know that this is not true! But this wasn’t the result of bivalence. It was a result of the assumption that all qualities are analytic. If we allow that some qualities are contingent, they are not necessary, and no reductio follows. So the problem seems to be not (just) a modal fallacy, but a failure to distinguish between analytic and synthetic qualities. But since Haack follows Quine in her avoidance of the distinction, she is quite content to rest her argument with the modal fallacy.
Now comes Aristotle’s own analysis of the modal fallacy.
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.
But is bivalence still in question here? Let’s try another reductio:
1) Future fact A is either true or false
2) Future fact A is a future contingent fact
3) How could we tell if A is either true or false?
In any case, it appears, Aristotle’s argument that PB implies fatalism seems to fail and with it his reductio that future contingents entail that PB is not true seems to fail. But the future contingents problem remains: How can we say that it is true or false that a future contingent event will take place. It is circular. It will be true or false only if true or false are the only values allowed in our logic. But if your logic specifically allows intermediate or value-less truth values from the beginning, then future contingents are surely indeterminate.