It must be added that none of the above distinctions purports to be an enlightening analysis of any modal concept. Indeed, I am sure that some senses of necessity cannot be analyzed at all without circularity; it is very doubtful, for instance, whether “cause” can be so analyzed, especially if causal statements be regarded as warranting counterfactual inferences. My only object, then, has been to distinguish these several senses sufficiently to prevent confusion in what follows.
Real and relative contingencies.—To speak of an event as contingent is to say, loosely, that it might or might not happen, that its occurrence is neither necessitated nor ruled out; but this, in the light of the foregoing distinctions, can mean any of several things.
It might mean (a) that a statement asserting its occurrence is logically contingent. But this is not remotely what Aristotle was thinking. In saying that the assumption of truth for a prediction requires necessarily the occurrence of what is predicated, he emphatically does not mean that such an assumption entails that the prediction is necessary or its denial self-contradictory—it is events, not statements, which are spoken of as necessary or contingent.26 Moreover, this interpretation would abolish any distinction between logically necessary and contingent statements, or between false and self-contradictory ones, which would be an absurdity, especially if ascribed to Aristotle.
Again, to speak of an event as contingent might mean (b) that it is uncertain, i.e., not known, whether the event has occurred, is occurring, or will occur.27 I have called this kind of contingency “epistemic”; it can also be called “relative,” being always relative to someone’s knowledge of things. If, for instance, an Athenian had said in 400 B.C. that Socrates might or might not die of poisoning, he would have meant in part at least that it was not known whether this would happen. Now being a very ordinary sense of contingency, it is exceedingly easy to force it upon Aristotle’s arguments; indeed, many philosophers have insisted that this is the only kind of “contingency,” other than logical, that is intelligible.28 But it would be absurdly incorrect to so interpret Aristotle: from the mere fact that this or that person may not know whether something is going to happen, it hardly follows that it is neither true nor false that it is going to happen,29 and Aristotle cannot be considered so dull as to have imagined that anything of this sort does follow.
Or again, one might mean by contingency (c) that natural causal processes are themselves ambiguous with respect to some outcome or other, that it is really undetermined by anything past or present whether an event of a given description is going to happen. This sort of contingency, which I have called “nomical,” might also be called “real” contingency, being not relative to this or that man’s powers of prediction but rather belonging to the very nature of things. And it is what our aforementioned Athenian could further have meant in saying that Socrates might or might not die of poisoning; that is, he might have meant, especially if he were philosophical, not only that he was uncertain about the outcome of things but that it was “uncertain,” i.e., as yet undetermined, by nature; that the state of the world was then causally compatible with either of at least two futures, the one containing that event and the other not. And it is in this sense that I would understand Aristotle, since (i) I believe that some things are contingent in this sense, (ii) we have good reasons to think that Aristotle thought so too, and (iii) this interpretation is absolutely required in order that Aristotle’s thesis can be rendered even plausible.
Finally, reference to an event as contingent might mean (d) that the outcome, i.e., its occurrence or nonoccurrence, has not already been decided one way or the other by the mere lapse of time—which is what I have called “temporal” contingency. One might, in short, simply be making the point that an event of a given description has not happened yet. Now one naturally wants to think that this is all Aristotle had in mind—else why should he have regarded contingencies as belonging to the future only, never to the past? But this, too, would be wrong. Aristotle did not hold that all statements having reference to the future are neither true nor false, though he can hardly have doubted that such statements do indeed have reference to things that have not happened yet.
Aristotle’s doctrine should, therefore, be construed as one concerning not merely contingent events, in the sense of real or nomical contingency—as this belongs to past events no less than to future ones—and not merely events of the future, or temporally contingents things—as some of these may be already determined—but as one concerning the combination of these. And it is this combination of modal notions which makes his arguments so enormously liable to confusion and at the same time so profound. His claim is, therefore, that (a) if an event of a given description is really contingent in the sense given, i.e., not yet nomically determined, and (b) if the outcome of things, i.e., the occurrence or nonoccurrence of the event in question, has not already been decided merely by the lapse of time, such that it irrevocably has happened or has failed to happen—in short, if the thing in question is a future contingency—then (c) any statement asserting or denying that it will happen is not (yet) true, but also not (yet) false.
Summary.—We can now summarize the argument in this fashion. Using the general notion “incapable of being otherwise” and “necessary” interchangeably, we may say:
If the statement “e has happened” is true, given a descriptive interpretation for “e,” then the event e is no longer capable of being otherwise; i.e., it is unalterable, with respect to its occurring, failing to occur, or occurring otherwise than as described, by anything that happens between the time of e and the present, (however nomically contingent e may be). Or, calling this statement “p,”
(1) (“p” is true) ⊃ (necessarily, e).
Note that this is not saying either (a) that since one proposition necessarily entails another, then it entails that that other is necessary, nor (b) that “e has happened” is logically necessary, nor (c) that a proposition can entail an event, nor (d) that the truth of “p” entails that e is nomically determined, nor (e) that p is the cause of e.
By identical reasoning, if the statement “e will happen” is true, given a descriptive interpretation for “e,” then the event e is henceforth incapable of being otherwise; i.e., it is unalterable, with respect to its occurring, failing to occur, or occurring otherwise than as described, by anything that happens between the time of e and the present (however nomically contingent e may be). Calling this statement “q,”
(2) (“q” is true) ⊃ (necessarily, e).
And note here, too, that this is not to be given an interpretation similar to any of the five just rejected.
Now one feels no inclination to deny the consequent of (1). That is, once an event has happened, it is incapable of being otherwise, i.e., it is now impossible that it should not have happened, however nomically contingent it may have been. Hence, one feels no inclination to deny the antecedent, viz., that the statement may be true.
But we do deny the consequent of (2), i.e., we deny that e is incapable of being otherwise—for instance, that it is incapable of not occurring at all—so long as it is as yet future, unless something else already exists nomically sufficient for its occurrence, i.e., unless e, though future, is already causally necessitated by what exists already, and hence is not a real contingency. Denying the consequent (with this important qualification), then, we deny also the antecedent, viz., that the statement “q” is true. By similar inference, we deny also that “q” is false.
III. ANSWERS TO OBJECTIONS
First objection.—The truth values of propositions are no function of time. More precisely, a correspondence theory of truth, such as Aristotle assumes, does not at all require the present existence of facts for propositions to agree or conflict with, but only the existence of such facts at some time or other.
C. A. Baylis directed this criticism at Lukawiewicz’ arguments,30 which are essentially those of Aristotle, and Donald Williams has on the same and other grounds rejected all theories wh
ich deny truth about the future.31 Baylis suggests that it is no better to argue that a proposition referring to the future cannot be true or false, on the ground that there is not yet any definite fact with which it can agree or conflict, than to argue that one referring to the past cannot be true or false, on the ground that there is no longer any fact to make it such; and both Aristotle and Lukasiewicz, like everyone else, admit that statements about the past are either true or are false. And Donald Williams, making the same point, says that “all these arguments are strangely selective ... in making much of supposed difficulties about the future which are quietly ignored as they equally affect the past and present.”32
Reply.—This criticism quite misses the point, for Aristotle’s argument is not to the effect that because some facts do not yet exist, propositions about them are neither true nor false. It was not just their temporal distance that bothered him, but their contingency, or rather, the contingency of some of them. There is thus in Aristotle’s philosophy no general denial of truth about the future. The motions of the heavenly bodies and the alterations of the seasons, for instance, are entirely “according to necessity,” he thought. Hence, being uniform and determined, nothing stands in the way of there being truths about them in advance of their occurring.33 We can thus see how little force there is in Williams’s remark that “even Aristotle, when he said ‘All men are mortal,’ did not mean merely that all men living at the moment were mortal,”34or his further comment that reference to an eclipse tomorrow, rather than to a sea fight, “would not find us half so receptive of the suggestion of its unreality.”35 Neither man’s mortality nor celestial motions are among those “things that can be otherwise.”
Second objection.—All temporal references in statements are in principle eliminable, if replaced by explicit references to dates; that is, variations of tense, and hence explicit or implicit references to nows and thens, can be eliminated from statements altogether without changing their meanings and hence without changing their truth values. The advantage in doing so is that there is removed any temptation to think of the truth values of tensed statements as changing with the lapse of time; any proposition, when so expressed with date or time, appears as an eternal truth if a truth at all. Instead, of instance, of saying, “Socrates was executed,” and thereby having on our hands a tensed statement which it might be tempting to think could not have been true during Socrates’ lifetime, but which became true immediately thereafter, one can just say, tenselessly, “Socrates is executed in 399 B.C.,” which amounts to the same thing. And this is fatal to Aristotle’s thesis, for if the statements, e.g., “There will be a sea fight tomorrow” and “There was a sea fight yesterday,” uttered on separate days with a day intervening and both referring to the same event, are equivalent to “There is a sea fight on—,” the date replacing the blank, then it is obviously impossible to say that some of these are true, or are false, while one of them is neither.
St. Thomas thought that what is essentially this view holds for all propositions, necessary or contingent, known to God, since “His knowledge is measured by eternity,”36 and logicians have tended to take the same view in order to facilitate logical analysis.37 Bertrand Russell,”38 A. J. Ayer,39 Nelson Goodman,40 and J. N. Findlay41 have all advocated the elimination of tense for certain purposes to achieve clarity and precision, the last declaring that “if we avoided the adverbs ‘here’ and ‘there,’ if we purged our language of tenses, and talked exclusively in terms of dates and tenseless participles, we should never be involved in difficulties.” Indeed, it has been persuasively argued that it was only by historical accident that variations ever came to be made on verbs to indicate temporal rather than spatial direction in the first place, and that such variations can, in any case, be eliminated, just as we avoid “spatial tenses” by explicit reference, when necessary, to locations.42 It is in terms of this view that Donald Williams is able to speak of “the totality of being, of facts, or of events as spread out eternally in the dimension of time as well as the dimensions of space”43 and to say that “there ‘exists’ an eternal world total in which past and future events are as determinately located, characterized, and truly describable as are southern events and western events.”44
Reply.—First, this argument begs the question by simply assuming that future contingency statements are already either true of false—precisely the thing at issue—and then offering those very statements, irrelevantly adorned with dates, as an argument.45
Secondly, the objection is mistaken anyway, for in fact one cannot convey the same information and avoid the systematic ambiguity of “now” and “then” just by substituting dates for tenses. This can be done only if an additional statement is supplied in order to complete the information so easily completed by the use of tense, and this additional statement must contain a temporal reference relative to now.46 That is, it must be a statement to the effect that the date mentioned is earlier than, contemporaneous with, or future to now—precisely the thing that the use of dates was intended to avoid. Upon being told, for instance, that “Socrates is executed in 399 B.C.,” I by no means get the idea that he has already been executed, unless I am also told, or happen somehow to know, that 399 B.C. is before now, that it is now past. Of course nearly everyone does know this, but only because we happen to have been taught how past and future times can be designated by numbers and what numbers designate, at various times, what is designated by “now.” An ignorant man might not know this at all; but he would have to be more than ignorant to have no sense of the difference between things past and things yet to come.
Third objection.—From the truth of a statement that an event of a given description has happened, there is no temptation to infer that it had to happen, or that its occurrence was in any way necessitated by this posterior truth. Indeed, it might be quite certain that it happened, or even that it happened contingently—from which it plainly follows, not that it was not contingent after all, but that it was. But similarly, from the truth of a statement that an event of a given description will happen, it does not at all follow that it must happen, or that its occurrence is somehow necessitated by this anterior truth, but only that it will in fact occur. Indeed, it might be quite certain that it will occur, or even that it will occur contingently—from which it plainly follows, not that it will not be contingent after all, but that it will. Aristotle’s confusion thus results from the feeling that if it is antecedently true that an event of a certain kind will happen, then that event is by that truth obliged to happen and that hence there is nothing anyone can do to prevent it—whereas all that follows is that nothing will in fact be done to prevent it, that no condition nomically sufficient to prevent it will arise.47
More precisely, let e be some event, such as my coughing tomorrow, which, let us assume, is going to happen, and f another event, such as my taking cough medicine meanwhile, which is not going to happen but which would be such that, if it did happen, it would prevent e. Consider, then, these four statements:1. e will occur.
2. If f were to occur, then e would not occur.
3. f will not occur.
4. f might occur.
Now it is evident (a) that the first two of these statements entail the third, and (b) all four may be true. Hence, (c) no combination of them can entail that the last is false. Therefore, the truth of (1) cannot entail that e must happen, or that it cannot be prevented, because (4), which we can assume is also true, entails the opposite, viz., that something might happen which would prevent it.
Reply.—This argument also begs the question, for it just assumes that our thesis is mistaken and conceals that assumption by applying it, not to the event e, to which our attention is mainly directed, but to another event, f, concerning which the very same difficulties that were initially raised concerning e now arise all over again.
For if, in the first place, f is a real and not a relative future contingency—that is, if nothing has yet occurred which is nomically sufficient either for the
occurrence of f or for its non-occurrence—then it is not already true that it will occur, on the basis of the arguments heretofore given. By the same token, it is not yet true that it will not. Therefore, if it is assumed that statement (4) is true, and “might” is given the sense of real contingency, then it cannot be simply assumed that (3) is true also without begging the question. If (4) is true, then (3), according to Aristotle’s and my arguments, is neither true nor false.
But if, on the other hand, f is not a real future contingency, then something already exists which is nomically sufficient either for its occurrence or for its nonoccurrence; i.e., either f or not-f is already nomically determined. But in that case, though (3) may indeed be true, (4) is no longer true, if “might” is given the sense of real contingency; for f is now by hypothesis not a contingency, whereas statement (4) asserts that it is.
So in either case, premise (b) of the argument, that all four statements may be true, must be rejected; or at any rate, it clearly cannot be used to refute our thesis but can be accepted only after our thesis has been refuted without using it.
Fourth objection.—One cannot find any general difference between past and forthcoming events, other than the difference in time, and Aristotle does not rest his thesis upon the mere futurity of future contingencies, this being something they have in common with future necessities. For when the various senses of “contingent” are examined, it is found that past and future events are contingent in the same ways and that the only difference left between them is a merely temporal one.
The same logical possibilities apply to both predictions and retrodictions, for instance, the only logical impossibility being, in either case, that an event of a given description both does and does not occur.48 Again, the same epistemic possibilities apply in both cases, there being ever so many things of the past concerning which we know nothing and can only say that, for all we know, they might have existed, or might not. Indeterminacy, again, belongs to past events no less than to future ones, if it belongs to anything at all, a causally undetermined event being no less so by the mere accident of being now past. So we are left with no way of distinguishing future contingencies from past ones other than by their temporal direction from us, which is by hypothesis irrelevant.