pronounced Aristotle’s reasoning “so swaggeringly invalid that the student can hardly believe he meant it,” and his conclusion “as nearly incredible as any proposition could be.”6
The prevailing opinion, then, is, and always has been, that Aristotle was muddled in these arguments and that his conclusion was false. I want to show, on the contrary, that he was exceptionally profound and that at least one important part of his doctrine is true. And if, as I believe, Aristotle was right, some far-reaching consequences follow. The conclusion yields, for instance, (1) in metaphysics, the view, much fought over lately, that time has not only an intrinsic order, as does space, but also an intrinsic sense or asymmetry, as space has not; (2) in logic, an area of applicability of a three-valued system, and (3) in theology, a revision of the traditional notion of divine omniscience.
I shall proceed as follows: In the first section, to set forth Aristotle’s thesis and three of the arguments for it which I regard as valid; in the second, to clarify these arguments and elicit their presuppositions; and finally, to defend Aristotle’s opinion against all the important objections I know of. The reader can thus probably find in this last section his own objection, if he has one, and satisfy himself whether it has been answered.
I. ARISTOTLE’S OPINION
The thesis.—Aristotle, as I understand him, maintains that all propositions are either true or are false, with the sole exception of a limited class of propositions about the future, viz., those that assert the occurrence, or nonoccurrence, of some future contingency. Concerning these (only) he held (a) that they are, antecedently, not true and yet not false, but (b) that any disjunction of such a proposition with its denial is necessarily true.7 And by a “future contingency” is meant any event which belongs not to the present or past, but which in the nature of things, and not merely in relation to our knowledge or ignorance of things, might or might not occur in the future.
The arguments.—There seem to be three distinct arguments for this, somewhat mixed together and admixed with other considerations. They are predicated on two assumptions, so I shall state first the assumptions and then, paraphrastically, the arguments.
The first assumption is a correspondence theory of truth, the minimum requirement of which is that in the case of any true proposition asserting some predicate of a particular individual, there is (tenselessly) a fact consisting of that individual having that predicate. This raises problems of its own, but we can ignore them. The second assumption is that there are genuine ambiguities in the future, i.e., that sometimes various mutually incompatible events are each of them future possibilities. We shall see what this means shortly.
(1) The first argument is this: Suppose all propositions, including those about future contingencies, are now either true or are false. Then, if one man says today that a particular event—e.g., a sea fight—will occur tomorrow, and another denies this, what one of them says must correspond to a fact forthcoming, positive or negative, and what the other says must fail to correspond. But in that case it must already be true that a sea fight definitely will take place, such that there is now no possibility that it might not, or else that it definitely will not take place, such that there is now no possibility that it nevertheless might. This, however, is false; for on such a view “nothing is or takes place fortuitously [ἀπὸ τύχης], either in the present or in the future, and there are no real alternatives; everything takes place of necessity and is fixed ... for the meaning of the word ‘fortuitous’ in regard to present or future events is that reality is so constituted that it may issue in either of two opposite directions.”8
Two qualifications are added to this and the following arguments. First, that it does not matter how far in advance a prediction is made: “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.”9 Second, that it is irrelevant whether such propositions about the future ever are actually stated or entertained, for “it is manifest that the circumstances are not influenced by the fact of an affirmation or denial on the part of anyone.”10
(2) The second argument concerns propositions about past contingencies considered in relation to the time when the event in question was as yet future, and unlike the first it is stated categorically rather than disjunctively. It is this: Consider an object which is now white, e.g., a table. Now on the supposition that every proposition is true, or if not true then false, it must have been true before the table became white, or even existed, that it would become white; indeed, it must have been true from all eternity. But if it was always true that it would become white, then it was never really possible that it might not, “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.” So again, “it results from this that nothing is uncertain or fortuitous,”11 that “there are no real alternatives, but that all that is or takes place is the outcome of necessity.”12 This, however, is false, forin those things which are not continuously actual there is a potentiality in either direction [τὸ δυνατὸν εἶναι καὶ μἠ]. Such things may either be or not be; events also therefore may either take place or not take place.... 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.13
(3) The third argument is exceedingly succinct and straightforward, being but a combination of the two aforementioned assumptions and a conclusion therefrom. It is simply this: “Since propositions correspond with facts, it is evident that when in future events there is a real alternative, and a potentiality in contrary directions [τὰ ἐνανία ἐνδέχεσθαι], the corresponding affirmation and denial have the same character.”14 We could express this otherwise, but no better, by saying that if the world is such that something which has not happened nevertheless might occur or might fail to occur in the future, and if this contingency or “potentiality in contrary directions” belongs to the nature of things and is not merely relative to our knowledge or ignorance of things, then it expresses the whole truth about such an event to say that it might happen, or it might not.
It will be noticed that the arguments I have summarized bear only on part (a) of Aristotle’s thesis, viz., that future contingency statements neither are true nor are false, and do nothing to prove part (b), viz., that any disjunction of one such proposition and its denial is nevertheless necessarily true; and it is, in fact, only the former that I shall consider. It may be that the truth of (a) would require a revision of (b), as I believe it would, but we shall have enough on our hands if we say what needs to be said concerning (a).
II. COMMENT
These arguments are valid, though terribly susceptible of misinterpretation. In this section I shall (a) formulate a more careful statement of the doctrine of real contingencies, upon which Aristotle’s and my own forthcoming arguments rest, and (b) indicate the senses in which the modal terms involved should be taken.
The doctrine of real contingencies.—Most critics have tended to treat Aristotle’s arguments simply as articles of logic, interpreting such key words as “necessary” as logical modalities, predictable of propositions, such that the question then becomes that of whether these arguments constitute logically valid inferences—as they plainly do not, unless further assumptions are introduced. From the mere fact that a statement is true, it hardly follows that it is logically necessary—unless one is prepared to abandon any distinction between contingent and necessary truths.15 I should maintain, then, that Aristotle’s arguments are derived from a metaphysical assumption: the assumption, namely, that there are real ambiguities in nature, i.e., from a doctrine of real contingencies.
This doctrine is best understood in
terms of what it denies, namely, universal causal determinism, which is to the effect that (as it has just recently been well put) “without exception ... the present (including the present character and behavior of human beings) is the only present that could exist, given the past that did exist, and the future will be the only future that could exist, given the particular present that now is.”16 Belief in determinism, that is, involves the belief that, for any event that ever happens, there are conditions given which nothing else could happen. And since the causal conditions of events, or the occurrences of such conditions, are themselves events, this proposition does entail that the past and present states of the world, in their totality, are compatible with only one future, that the future is unambiguous, save in reference to our powers of prediction.
The denial of this is simply that some events are not such as described. This view has sometimes—I think by Aristotle—been thought plausible only as applied to the choices or decisions of men. But however narrowly construed, if this view is true then determinism, as formulated above, is absolutely false, the past and the present states of the world are compatible with any of several alternative futures, and “future possibilities” are real ones, not just logical or relative possibilities.
I shall give no argument for this view of real contingencies; indeed, I think it can be neither proved nor disproved, though I happen to believe it. For the purpose of the present discussion, it may be regarded as an hypothesis only, such that our problem can be formulated as the following hypothetical one: If the doctrine of real contingencies is true, was Aristotle right in believing that some propositions—viz., those asserting or denying the existence in the future of contingent things—are neither true nor false?
That Aristotle believed in real contingencies is, I think, beyond doubt, but I shall not prove it here, it being an historical question. Two articles of his philosophy do, however, deserve to be mentioned, as clarifying somewhat the doctrine in question.
The first is his rarely formulated theory of the fortuitous. According to this, as I understand it, any causally connected series of events is such that each member is caused by its predecessor, if it has a predecessor, and in this sense comes about “of necessity.” The beginning of such a series, however—e.g., the ultimate cause of the choice or decision of a living being, or perhaps of a man—“no longer points to something further,” and thus, Aristotle says, is “the starting-point for the fortuitous, and will have nothing else as cause of its coming to be.”17 Such a conception involves an unusual conception of causation, according to which some things—e.g., men and other active things, in the strict sense of “active”—can be “originative sources of motion,” but Aristotle evidently did believe this (as I do), and whether it is unusual or not is in any case irrelevant.
The other doctrine, closely connected with the first, and alluded to in the arguments I have paraphrased, is that of rational and nonrational capacities (δυνάμεις μετὰ λόγου and δυνάμεις ἄλογοι).18 A nonrational capacity is the disposition of something toward a unique state under given conditions—which is, of course, what philosophers normally have in mind in speaking of capacities or dispositions. Sugar placed in warm water, for instance, can only dissolve; it cannot sometimes dissolve, sometimes ignite, and sometimes do nothing. Water, heated to a certain point, can only boil, it cannot solidify; the sun can only warm us, under given conditions, not sometimes warm and sometimes chill us. Rational capacities, on the other hand, are “capacities for opposites [δυνάμεις τῶν ἐναντίων],” and characterize (together with nonrational ones) only living things, perhaps only rational beings.19 These are dispositions to do any of two or more incompatible things under a given set of conditions, that is, dispositions that are really ambiguous. Such capacities are not utterly ambiguous—indeed, the states or acts to which a thing having such a capacity may tend, in given circumstances, may be as few as two—but the important thing is that such a disposition is not toward some unique state. Moreover, such capacities are not manifest “necessarily,” i.e., from ordinary causal processes; if they were, then being capacities for opposites, they would result in incompatible states at the same time, which is impossible. Something further is needed, then, to “decide,” and this is what Aristotle calls “desire or will [ὄρεξις ἤ προαίρεσις].”20 And this, again, is something which is not simply the actualization of another capacity, rational or nonrational, but is instead simply the act of an active being—i.e., of a being which acts and is not merely acted upon—considered as an “originative source of movement,” not itself entirely determined to one thing rather than another by any fixed causal connections.
Now either of these doctrines—which really amount to much the same thing—would yield a theory of real contingencies. And both, I submit, are plausible in the light of what we take ourselves, as active beings, to be, but I shall not prove them.
Modal predicates.—Nothing is so apt to mislead as Aristotle’s use of such concepts as “necessary” and “possible,” so I shall now clarify these.
Given a meaning for any one of the four modal terms—“necessary,” “possible,” “impossible,” and “contingent”—the others can forthwith be defined in terms of it. Given, for instance, a meaning for “necessary,” the remaining three predicates can be explicated as follows:x is possible ≡ ~(~x is necessary)
x is impossible ≡ ~x is necessary
x is contingent ≡ ~(x is necessary) . ~(~x is necessary),
substituting for “x” a statement, an event, or whatever the sense of the modal term requires, and letting “~x” designate, not simply the absence of x, but something not compossible with x, in the sense of the modality in question.
These definitions, which are of course empty until a meaning is given to the basic modal term, exhibit one important point that is easily overlooked, viz., that the possible and the contingent are not the same. Whatever is contingent is possible, but not vice versa; for if anything is necessary, then it is also possible, but not therefore contingent.21
In the light of these definitions four more or less familiar senses of necessity and hence also, derivatively, of contingency, can be distinguished in roughly the following way:
(1) Logical necessity is predicable of a statement or proposition and corresponds to analyticity. Thusnecessarily p ≡ “p” is analytic,
and a logically contingent statement is thus one which is neither analytic nor self-contradictory.22
(2) Epistemic necessity is predicable of events and states, though only in a derivative way, and corresponds to what is known to be. Thusnecessarily e ≡ e is known to exist,
and an epistemically contingent event is one concerning which it is not known whether it exists (has existed, will exist) or not—one which, “for all we know,” might exist, or might not. This is indeed a strange kind of contingency and is in fact no real contingency at all, being only a reflection of someone’s knowledge or ignorance of things, but it is nevertheless the commonest sense of contingency embodied in ordinary speech. If, for instance, someone says before opening a drawer that it might or might not contain his necktie, he only means that he does not yet know; if someone says it might rain a week hence, he ordinarily means only that he does not know that it will not. On the other hand, one who knows, says, that Mr. Jones is in New York cannot really consider it possible that he is not.23
(3) Nomical necessity, also called “causal” and “etiological,” is necessitation by causation and is predicable of an event. Thusnecessarily e ≡ there is (was, will be) a cause for e,
and a nomically contingent event is therefore one neither the occurrence nor nonoccurrence of which has a cause.24 Derivatively, an event causally dependent, remotely or proximately, upon a contingent event would itself be contingent, prior to the occurrence of any member of the causal series of which it was itself a member. Of course it is customary to deny that causation does involve necessitation, and this is correct if such n
ecessity be considered logical (and thus predicable only of statements or propositions), but on the other hand there is a fairly clear sense in which, for instance, water cannot but boil under certain conditions, or a man who is decapitated must die, and so forth, and it is simply the modality expressed by such words as “cannot but” or “must” in such uses which is here called “nomical.” Also, some would deny that there are any contingent events, in this sense, but I have only made it an hypothesis that there are, and I am in any case not trying to prove they exist by defining them.
(4) Temporal necessity, which might less misleadingly be called “irrevocability” or “unalterability,”25 applies to any event that has happened, and is thus relative to a date. Thusnecessarily e ≡ e has already occurred,
and a temporally contingent event is thus simply one which has not yet occurred, an event temporally incompatible with it having likewise not yet occurred. This is perhaps the strangest kind of contingency yet, but no questions are begged by introducing it. What this notion calls attention to is just this obvious, and in other contexts trivial, fact: that nothing that may be in the past is in any way revocable or alterable by what might happen now, whereas this is plainly not the case with such things as may be yet to come. The lapse of time by itself thus imposes a kind of necessity on things; things once capable of being otherwise, or of not existing at all, are no longer so. Until an event has happened, it is sometimes possible that it might not, but once it has happened, it is no longer possible that it did not—and this, despite the fact that it is still possible that it did not happen in any or all of the three foregoing senses of “possible.” All this is surely a truism of sorts, but it does indicate an indubitable sense in which past things, but not future things, are by now “of necessity.”