If, accordingly, statements about future contingencies are neither true nor false, then we should accept the same conclusion as applied to past ones, or else say, as Aristotle did not, that the mere futurity of an event, unlike pastness, renders statements about it neither true nor false. Or else, conversely—and this is what most philosophers believe—if there are truths about past events, including contingent ones, there is no reason for doubting that there are truths about future ones too.49
Reply.—It is not the futurity of future contingencies, nor the nomical contingency of them, upon which our thesis rests, but the combination of the two. When something has happened, then however contingent it may have been, its occurring excludes the possibility of something incompatible with it happening at the same time, whereas in the case of some (not all) ostensibly future things, nothing has happened to exclude the possibility of something else happening then instead. In Aristotelian concepts, this is to say that when a potentiality in opposite directions has become actualized in one of these directions, there ceases to be any potentiality for the opposite, the antecedent alternative possibilities having been forever foreclosed by the one that has now become actual.50 Nothing, however, now excludes any real contingency for the future and nothing will, until it is excluded by the realization of its opposite or of something nomically sufficient for the realization of its opposite; that is, until it has ceased to be a future contingency.
Putting this another way, we can say that there is only one possible past but many possible futures. There are, indeed, ordinary interpretations according to which this is absurd, but there is another according to which it is true. It is part of what people mean in saying, as Aristotle said, that the past cannot be “undone,” no matter what indeterminism or haphazardness there may be in it.51 The past consists of everything that has happened, and even if we should suppose that any or all of these things might easily have been otherwise, the fact that they have happened renders impossible forever after the occurrence of anything else in their place. The future, too, consists of everything that will happen; but here, nothing has happened to preclude the occurrence of either of two or more incompatible events. Concerning a future contingency, we can say only if it occurs then the occurrence of anything incompatible with it is excluded; but concerning a past contingency, we express the fact by saying since it occurred everything incompatible with its occurring is excluded.52 The future is alterable, and not merely in the trivial sense of being alterable by our own forthcoming efforts but by the mere lapse of time, which itself reduces to zero what were once many alternative future possibilities.53 One may indeed say that when tomorrow comes, we shall find its contents as fully determinate and exclusive of things incompatible with those contents as we now find the contents of yesterday, and this is true; but it only means that with the lapse of time, what were once alternative possibilities have dwindled until reduced to zero by those which have become actual.54
If, then, in the sense explained, there is no longer any real contingency in things past, we do not express the whole truth in any statement about the past other than by saying of an event of this or that description that it did happen or that it did not. In the case of future contingencies, however, it expresses the whole truth to say of one of them that it might happen or it might not.55 It cannot be true now that it will, for this means more than “might,” nor can it be true now that it will not, for this means more than “might not.” The lapse of time, and not merely the increase of our knowledge and experience, can confute our statement that it will happen as well as our statement that it will not, whereas only the increase of knowledge, and not merely the lapse of time can confute our beliefs about things past and done.56
Fifth objection.—Aristotle’s arguments rest on a common amphiboly, treating as equivalent certain statements which can indeed be expressed in the same way but which are really quite different in what they assert. One isnecessarily, p or not-p
understood in the first place as meaning that the whole disjunction is necessary (which is true) but then understood to mean that one or other of the disjuncts by itself is necessary (which hardly follows). Another isif p, then necessarily p,
understood first as meaning that the whole hypothetical statement is necessary (which is true) and then to mean that the consequent, by itself, is necessary (which is by no means the same).
Moreover, if every true proposition is in some sense necessary, then every false one must in a similar sense be impossible; indeed, Aristotle says as much: “That which is must needs be when it is, and that which is not must needs not be when it is not.”57 But if we combine these suppositions with his further claim that a proposition may be contingent, we can, by elementary rules of logical inference, get the absurd result that if a proposition is contingent, then it is false and hence impossible, but also that it is true and hence necessary. Thus, in obvious notation:(1) p ⊃ Np
(2) ∼(Np) ⊃ ∼p
(3) Cp ⊃ ∼p,
and so on. And:(4) ∼p ⊃ Ip
(5) ∼(Ip) ⊃ p
(6) Cp ⊃ p,
and so on. And this is absurd.
Reply.—If Aristotle had argued (1) that it is necessary that every proposition or its denial is true, and that therefore every proposition is itself necessarily true, or its denial necessarily true, or (2) that a proposition necessarily entails itself, and therefore necessarily entails that it is itself a necessary proposition, then his arguments would be as “swaggeringly invalid” as Donald Williams, who ascribes them to Aristotle, has claimed.58 But in fact he says nothing like this. Someone might be tempted to adopt Aristotle’s thesis on the basis of such amphibolies, but Aristotle did not,59 and neither do I.
The reductio ad absurdum of the second part of this criticism is question begging, for it simply assumes that if a proposition is not true, then it is false, and if not false, then true—precisely the point at issue. Thus, the transposition of step 2 is sufficient for asserting “∼p” only if this is read “not-p.” This cannot be equated with “p is false” without begging the question. Again, step 5 is not even correctly symbolized; the consequent must read “~(~p),” meaning “it is not the case that not-p”—which does not mean that p is true. Moreover, step 3 is accomplished only by substituting “contingent” for “not necessary,” and step 6 by substituting the same for “not impossible.” But “contingent” means “not necessary and not impossible”; it does not mean “not necessary or not impossible.” A thing which is impossible is indeed not necessary—but not therefore contingent; similarly, a thing which is necessary is indeed not impossible—but again, not therefore contingent. These distinctions are simply obliterated by this kind of criticism.
Sixth objection.—Whether or not there is any omniscient being, the conception of one involves no evident absurdity. But an omniscient being would by definition know everything, and hence everything that is going to happen, and being less than omniscient can know something of the future. And if any man or god might know which of various alternative contingent things are going to happen, then it must already be true, though not therefore necessary, that those things will happen, and that things incompatible with them, while not impossible, will not happen.60
Reply.—An omniscient being would not be one who knows everything, simply, but one who knows everything that is knowable.61 If there is anything that cannot be known—and of course there are infinitely many such things, for example, all false propositions—then even an omniscient being cannot be expected to know it. This kind of qualification was presupposed by the Scholastics when God’s omnipotence was considered, the view of St. Thomas being, for example, that God can do only whatever is metaphysically capable of being done; if anything is inherently impossible, then it is idle to expect that God should do it.62
With this qualification, the question becomes whether things that are future and contingent are knowable. Now of course they are not knowable by inductive inference, but that is not the question. The question is whe
ther any degree of prescient or sapient power would enable one to know which of several alternative contingencies will in time come about, assuming there are real contingencies.
It seems evident that it would not. For in the first place, knowledge can be only knowledge of what is true, and it has been our main point to prove that statements about future contingencies are neither true nor false. To argue, then, that such statements must be true, since they are known to God, if there is a God, is plainly circular.
Secondly, if the future is partially undetermined and in its very nature ambiguous, an omniscient being would have to comprehend it just that way. This alone would be knowledge of the future; to see it as otherwise, to comprehend it as already determinate and to judge exactly what is going to happen, is not knowledge but only the obscurity of guesswork and error.63 Of course on this view an omniscient being would know more at one time than at another, but this need not be inconsistent with the idea of omniscience; at any time such a being would know all there is to know, and this ought surely to suffice.64
I think the only rejoinder that can be made to this is that, as Boethius and many others after him put it, “foreknowledge is not the cause of any necessity in things to come.”65 This point is iterated often, as if it left nothing more to be settled. Gilbert Ryle, for instance, observing that neither an “anterior truth” nor the knowledge of it could cause any event to happen, adds the similar point that propositions can never entail events but only other propositions.66 Now all this is true, but it is irrelevant to what is here being asserted. I am not saying, nor did Aristotle, that foreknowledge would cause this thing or that to happen,67 or that propositions, known or unknown, entail events, all of which is surely nonsense, but rather that the supposition of foreknowledge is inconsistent with the claim that any of several alternative futures might become real, using “might” in the sense of real and not relative contingency. For the assumption that any one of these futures, no matter which, is already known, and hence will in fact come into being, is incompatible with the theory of real contingency, viz., that some other future is no less likely to come into being than that one.
Seventh objection.—Suppose someone, “A,” indulged in prophecy, asserting, “Henry will sneeze tomorrow,” and another person, “B,” following Aristotle’s principles, replied, “No, he might, or he might not; it cannot yet be true either that he will or that he will not, this being in the realm of contingencies.” Tomorrow comes, and Henry sneezes. A, it would seem, can now say, “I said he would sneeze, and he did, so what I said was true, while you, in denying that what I said was true, are now shown to have been wrong.” This comment by A seems reasonable, for it certainly seems that yesterday A had something that B did not have—namely, a true opinion. Of course, B did not say Henry would not sneeze, but still, his opinion was not as good as A’s—for A’s opinion, we now discover, was true, while B’s was just noncommittal.
Reply.—The most this argument can be claimed to prove is that either A’s prophecy was true or that it became true, just as it became fulfilled,68 through the lapse of time and the reduction to zero of alternative possibilities. There is nothing in it to show that it was antecedently true, any more than that it was antecedently fulfilled. Or, to put it otherwise, all the argument shows is the trivial fact that when “tomorrow” had ceased to be tomorrow and had become today, it contained just those events which then happened; it does not show that, on the day before, it was going to contain those rather than alternative ones.69 No advantage, in the way of true opinion, can be claimed by A as having obtained when he first made his prediction, for all he can claim is that it was fulfilled—which suffices for any wagers that were made. The apparent advantage of his opinion over B’s is only an ex post facto sort of one—much like the advantage one might have who, by taking one path rather than another, stumbles upon a fortune. B, on the other hand, has had from the beginning a real advantage, for he claimed the future to be ambiguous and unsettled—as in fact it then was. His opinion, unlike A’s, did not have to wait to become true but was true from the start. It only became an inadequate opinion, but not disconfirmed, when A’s prediction came true, that is, when the event in question ceased to be a future contingency and to admit of any possibility of being otherwise.
It might be said that if we allow B’s opinion to have been true in advance, then nothing prevents A’s opinion from having been true as well. But this overlooks the fact that A’s statement concerns a future contingency, whereas there is nothing of contingency in B’s proposition that Henry might sneeze or he might not. We need not wait upon anything to see whether this is so.
Again, it might be said that A’s statement can be reformulated to say, “The belief that Henry will sneeze, while perhaps not true now, will become true” and that this assertion is about a future contingency no less than the first. But this complication introduces nothing new into the original argument; for B could reply that it might become true or it might not, the rest of the argument then proceeding exactly as before, only with more words.
NOTES
1 De Int., ch. ix.
2 See C. A. Baylis, “Are Some Propositions neither True nor False?” Philosophy of Science, III (1936), 156-166; Donald Williams, “The Sea Fight Tomorrow,” in Structure, Method and Meaning, ed. P. Henle, H. M. Kallen, and S. K. Langer (New York, 1951), pp. 280-306; A. N. Prior, “Three-valued Logic and Future Contingents,” Philosophical Quarterly, III (1953), 317-326; Leonard Linsky, “Professor Donald Williams on Aristotle,” Philosophical Review, LXIII (1954), 250-252; Donald Williams, “Professor Linsky on Aristotle,” ibid., 253-255; Gilbert Ryle, “It Was to Be,” in Dilemmas (Cambridge, 1954), pp. 15-35; R. J. Butler, “Aristotle’s Sea Fight and Three-valued Logic,” Philosophical Review, LXIV (1955), 264-274; G. E. M. Anscombe, “Aristotle and the Sea Battle,” Mind, n.s., LXV (1956), 1-15.
3 Op. cit.
4 “On a So-called Paradox,” Mind, n.s., LXII (1953), 65.
5 Op. cit. Cf. the introductory lecture of this collection.
6 “The Sea Fight Tomorrow,” pp. 284, 291.
7 Aristotle believed that “p ∨ ∼p,” is true for any interpretation of “p” including statements of future contingencies, if understood in the sensus compositionis . Neither “true” nor “false” can be predicated of the constituents of an interpretation of that law, however, if “p” is a statement about a future contingency. Aristotle could accordingly accept the first but not the other two of the following formulations as applying to any statements whatever, including future contingency statements: (1) “If a statement is true, its denial is false, and if false, its denial is true”; (2) “Each statement is true, or, if not true, then false”; (3) “If two propositions contradict each other, one must be true.”
8 De. Int. 18b 5-9. All quotations are from the Oxford translation of E. M. Edghill, ed. by W. D. Ross.
9 Ibid., 18b 33-36.
10 Ibid., 18b 36-38. Cf. Ryle, op. cit., pp. 16-17.
11 De Int. 18b 13-16.
12 Ibid., 18b 30-31.
13 Ibid., 19a 9-20.
14 Ibid., 19a 32-35.
15 Linsky, op. cit., p. 252, interprets Aristotle as abolishing this distinction, comparing his philosophy to that of Leibniz in this respect. Cf. Butler, op. cit., pp. 267-268.
16 H. Van Rensselaer Wilson, “Causal Discontinuity in Fatalism and Indeterminism,” Journal of Philosophy, LII (1955), 70.
17 Met., bk. VI, ch. iii. Cf. De Gen. et Corr., 337a 34 ff.; also, W. D. Ross, Aristotle (London, 1949), p. 164.
18 See Met. 1046a 38-1046b 25; Phys. 251a 28.
19 Met. 1047b 1-1048a 16. See also H. H. Joachim, The Nicomachean Ethics (Oxford, 1951), pp. 108-110. This distinction is not consistently maintained, for Aristotle sometimes connects contingency with matter as such. See also Met. 1050b 6-14: “Every potency is at one and the same time a potency of the opposite.”
20 Met. 1047b 35-1048a 11. Cf. Joachim, op. cit., p. 109.
21 See De. Int., ch. x
iii; also Yehoshua Bar-Hillel, “Mr. Weiss on the Paradox of Necessary Truth,” Philosophical Studies, VI (1955), 92-93.
22 Cf. W. V. Quine, “Notes on Existence and Necessity,” Journal of Philosophy, XL (1943), 121.
23 Cf. Nelson Goodman, “On Likeness of Meaning,” in Semantics and the Philosophy of Language, ed. by Leonard Linsky (Urbana, Ill., 1952), p. 68.
24 “Nomic necessity” has been used by R. B. Braithwaite and W. E. Johnson. “Etiological necessity” has been used by C. J. Ducasse.
25 Cf. Butler, op. cit., p. 269.
26 Prior, op. cit., p. 324, has shown that Aristotle was not thinking of logical necessity in these arguments.
27 Cf. Anscombe, op. cit., p. 12.
28 Hobbes is an excellent example: “All propositions concerning future things, contingent or not contingent ... are either necessarily true, or necessarily false; but we call them contingent because we do not yet know whether they be true or false; whereas their verity depends not upon our knowledge, but upon the foregoing of their causes” (The Metaphysical System of Hobbes, Open Court edition, ed. by M. W. Calkins, pp. 78-79). Cf. C. J. Ducasse, “Truth, Verifiability, and Propositions about the Future,” Philosophy of Science, VIII (1941), 331-333.
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