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The Future and the Truth-Value Links: an Ockhamist and Common Sense View
My topic is a seemingly large one, and a very old and well-known one. It concerns two desires which as I see it are both perfectly reasonable, but which might be thought to be incompatible.
The first desire is for realism with respect to the semantics of propositions expressed by future-tense sentences. I want to try to understand how the concept of the future works, in such a way that typical propositions about the future come out true or false, in perfect accordance with bivalence. So if someone had said on June 5th 1944, ‘The invasion will take place tomorrow’, it might have been a reasonable thing for someone else to say, “True,” adding perhaps, and I add the continuation to give verisimilitude to the original remark and its setting, ‘But it won’t be easy.’ There you have two true propositions about the future, as it then was, uttered before the events that would make them true had occurred. At that point both propositions were about the future, and both, it seems reasonable to think, were true, simply because both were borne out by the subsequent facts.
My second desire concerns the metaphysics of realism. Here I am perhaps closer to the anti-realists. In order for propositions about the future to be true, or false, they must correspond to or fail to correspond to facts, if there is any truth to the correspondence theory. But how can there be any facts corresponding to propositions expressed by future-tense sentences, or rather, how can there be any now? For if there are future facts now, would they not already be present facts of some sort, rather than future facts?
I wish to argue that although there are not now any facts corresponding to propositions expressed by future-tense sentences, yet in the future there will be such facts, and that it is these yet-to-be facts which are the “truth-makers” for the propositions expressed by future-tense sentences uttered now. Propositions about the future are true because there will be facts to go along with them, not because there now are. And that is at the heart of the concept of the future. Semantic realism requires nothing except these yet-to-be facts, and an understanding of the logical requirements of the use of the future tense, rather than any empty theory of facts already existing in the ontological mode of futurity or whatever. And realism about the future in the metaphysical sense is false, if it means that there are in any sense at all some future factsright now.
How then can semantic realism be true? What must the yet-to-be-present facts be like, in order for there to be truths about the future? The short answer is that they must be exactly like other present facts, when their time comes. ‘The weather will improve tomorrow’, said today, is not true because it is now the case that, in the future, it is improving, but because it will improve, when the time comes. “The weather will improve” is made true by the fact that it improves, when it does, so to speak, which has exactly the same character as any other present fact. Today’s fact that there is a fox in the garden and tomorrow’s fact that there is a fox in the garden may have exactly the same character - it may even be the same reappearing fox that constitutes both facts.
To summarize things so far, as I see it the fact that the weather will improve tomorrow is a fact not about what is the case, but what about will be the case, and to me that seems good enough to underwrite bivalence.
There is an objection to my Ockhamist view[1], suggested by my colleague Jim Hardy. According to me, he points out, ‘The weather will improve tomorrow’ (let us refer to the sentence ‘The weather will improve tomorrow’as W) is made true by the fact of tomorrow’s improvement in the weather. This fact will not exist until tomorrow. However, on my view the proposition expressed by W is true even before the weather improves. But if the proposition expressed by W is true today, then so is the proposition expressed by W*, the sentence ‘W is true today.’ W* is a sentence which expresses a proposition about the present semantic status of W, not about tomorrow’s weather. Since the proposition expressed by W* is true, there must be a fact to which it corresponds. And since the proposition expressed by W* is about the present, because the sentence which expresses it is a present-tense sentence, it is reasonable to suppose that F*, its truth-maker, is a present fact. Furthermore, since W* implies W, if F* is sufficient for the truth of the proposition expressed by W*, then it is also sufficient for the truth of W. If so, there is a present fact F* which is the truth-maker for the proposition expressed by W. Hence future facts are not needed for future-tense sentences to express true propositions.
It seems to me that Hardy’s objection is in an interesting way question-begging. For it is not quite right to say that the proposition which W* expresses is “about the present”, whatever exactly this means. It is true that W* is a sentence in the present tense (‘W is true’). But W is itself is a sentence “about” the future and on my view the proposition that it expresses has a future truth-maker. So a proposition declaring the existence of this truth-maker, and relating it to W (if truth is the correspondence of a proposition to a fact), must be partially “about” the future, in the sense that it asserts that there is a relation, a so-called semantic relation, between the proposition expressed by apresent-tense sentence uttered now and the future fact which makes it true.
The argument I have been discussing is valid. It can be set out in the following form, in which A is a proposition about the future, and F is a future or yet-to-be fact expressed by A.
(1)If a fact is a yet-to-be fact, then it does not now exist.
(2)F is a yet-to-be fact.
So(3)F does not now exist [from (1) and (2)].
But (4)If A corresponds to F, then F exists now.
But(5)If A is true, then it corresponds to F (the Correspondence
Theory).
So (6)A is not true [from (3) and (4), and then (5)].
So(7)A is false (Bivalence).
The whole idea of facts “existing” is obscure at the very best, but, leaving this aside, (7) is in any case false, from a common sense and unAristotelian point of view, so the argument is unsound. My Ockhamistexplanation is that it is (4) which is false, and that what is really true is that if A is true, then F exists or existed or will exist.[2] I will call this proposition (4*). It is interesting that given that (7) is false, the only real choice is whether to deny (1) or to deny (4). For my part, I reject as at best interestingly creative and at worst bad grammar the way of speaking which says that events predicted by propositions expressed by future-tense propositions do exist in the future. Nor do the idioms in which we say today things such as ‘The invasion takes place tomorrow’ offer any firm support to this view. This is not because they express or describe a definite intention (an obvious counterexample is ‘Tomorrow, which is December 21st, is the longest night of the year’) but merely because they are entirely neutral with respect to the metaphysical facts.
Michael Dummett describes four possible metaphysical models about the reality of the past and the future.
Model (1) Only the present is real.
Model (2) The future is real but the past is not.
Model (3) The past is part of reality, the future is not.
Model (4) Past and future are both real.[3]
In fact there are altogether eight possible models. Letting P represent the proposition that the past is real, N (for “now”) represent the proposition that the present is real, and F represent the proposition that the future is real, we have:
1. P N FDummett Model (4)a
2. P N~FDummett Model (3)a
3. P~N FDummett Model (4)b
4. P ~N~FDummett Model (3)b
5.~P N FDummett Model (2)a
6.~P N~FDummett Model (1)
7.~P~N FDummett Model (2)b
8.~P~N~FTime is unreal
Dummett does not distinguish the a and the b versions of his Models (2), (3) and (4), and he does not mention the Model given in line 8., which is McTaggart’s view that time is unreal, or any of the other ~N lines (3., 4., and 7.). His discussion of Model (1), line 6, usually now called “presentism”, invites comment. He writes,
Furthermore, the thesis that only the present is real denies any truth-value to statements about the past and future; for, if it were correct, there would be nothing in virtue of which a statement of either type could be true or false, whereas a proposition can be true only if there is something in virtue of which it is true.[4]
I must make two remarks about this argument.
Remark 1: One has only to appreciate the reasonableness of the Ockhamist view - the distinction between premise (4) in the argument set out above, and (4*) - to see that it is not the case that if it were true that only the present is real, then there would be nothing in virtue of which a statement about the future could be true or false. For it is almost analytic that only the present is(present tense, nota bene) now real.[5] But the future will be real, and the whole functionality of future-tense sentences is to express propositions whose truth depends only on whether what they predict will be the case.
Remark 2: ‘A proposition can be true only if there is something in virtue of which it is true.’ As we have seen, the Ockhamist will wish to amend this to read instead, ‘A proposition can be true only if there is something in virtue of which it is true or something in virtue of which it will be true.’
This is also perhaps the moment to say, I believe with Ockham, that I do not believe for an instant that his (and my) view that contingent future-tense sentences express propositions which obey bivalence (and therefore express genuine propositions) implies any form of determinism. Why should it? Nobody accepts fatalism, the ancient trick argument from the antecedent truth of a proposition to the necessity of the future events it predicts, for the very good reason that Dummett gives:
[T]he argument for the indefiniteness of the future lacks all cogency. The illusion derives from the idea that present truth must compel the future action. The efficacy is in the reverse direction: a proposition about what I am going to do is true in virtue of my later future action. Christ’s prediction that Peter would deny him did not compel Peter to do so: it was true because he did.[6]
The Ockhamist view might seem to throw up an irritating and excessively familiar little problem about the logic of tenses. This toy problem, as I shall call it, has to do with the fact that when as predicted the weather improves, what happens is not that the weather will improve, but that it does. How can the improvement in the weather which is present when it occurs tomorrow make true the prediction uttered today that it will improve? When the weather improves, this present fact is to be described in a sentenceusingthe present tense (‘The weather is improving’), and not,using the future tense, as the fact that ‘The weather will improve.’ How can the fact described by the sentence that the weather is improving make true the apparently quite different proposition, uttered on an earlier occasion, that the weather will improve? It seems that a sentence expressing the proposition that the weather will improve tomorrow (call this sentence W, as before) is made true, when the time comes, by the fact that the weather is improving(call the sentence expressing this proposition P, for “present”). The truth of P corresponds to the fact that the weatheris improving. The truth of Wsurely corresponds to the fact that the weather will improve, not to the fact that it is improving. So what we have to verify when we verify the proposition that the weather will improve is that the weather will improve. Why then should we set about verifying it by observing, when the time comes, that the weather is improving?
In itself my toy problem is of no particular depth or importance, and its sole interest for us is to prepare the ground for the question what the function of the concept of the future is. There are any number of different ways of solving it, which relate it to different areas in the philosophy of language. The simplest one is to distinguish the proposition from the sentence. W and P are different sentences, but they both express a just one proposition which is made true by just one fact. ‘The weather will improve’ and ‘Theweather is improving’ are very different sentences, but they express one and the same proposition.[7]
How is it that propositions about the future have the characteristics that I have attributed to them and which, I believe, Ockham also attributed to them? And how does this view explain the connection the two differently tensed sentences which express them, beyond saying that they express the same proposition? Put another way, if they express the same proposition, why then do we use different sentences for them? Put yet another way, what is the point of using the two different sentences in this way?
Put still another way, what is the explanation of what Dummett calls the “truth-value links”?
Such a truth-value link requires that if a statement in the present tense, uttered now, of the form “An event of type K is occurring,” is true, then the corresponding statement in the past tense, “An event of type K occurred a year ago,” uttered a year hence, must perforce also be true.[8]
Similarly, to generalize Dummett’s point to a more controversial case, if a statement in the present tense, uttered a year from now, of the form “An event of type K is occurring,” is true a year hence, then the corresponding statement in the future tense, “An event of type K will occur a year hence,” must perforce also be true now. The truth-value links, then, are obviously not accidental features of sentences expressing propositions about the future; they are the essence of the functioning of these sentences.
The case Dummett gives can be represented as follows.
Time of UtteranceTruth-Value Links
Utterance
Now (tn)“An event of type K is now occurring” T
One Year
Waiting “perforce”
Period (+1 year)
tn+1“An event of type K occurred a year ago” T
The more controversial case involving the truth of propositions expressed by future-tense sentences is this.
Time of UtteranceTruth-Value Links
Utterance
tn“An event of type K is now occurring” T
One year
Retrospective “perforce”
Period (-1 year)
tn-1“An event of type K will occur a year hence” T
It is a remarkable and interesting fact that the truth-value links do generalize from the indisputable single case that Dummett gives. His claim is that if someone says now, with truth, that ‘The weather is improving’, he is logically committed now to the truth of ‘The weather was improving’, uttered a year from now. The point generalizes to dual cases, however, such as (to take a controversial example) one in which someone says, a year from now, with truth, that the weather is improving, and is thereby logically committed to the truth of ‘The weather will improve’, said by someone now.
Here are two further but entirelyunproblematiccases of the same sort which involve different tenses. With the first, there is some sort of inconsistency in claiming that it is true that an event of type K occurred a year ago, but that the present-tense sentence expressing the proposition that the event was occurring, uttered a year ago, did not express a true proposition.
Time of UtteranceTruth-Value Links
Utterance
tn“An event of type K occurred a year ago.” T
One year
Retrospective “perforce”
Period (-1 year)
tn-1“An event of type K is now occurring.” T
With the second of these two new cases, there is exactly the same sort of inconsistency as in the first. Note that the philosophical claim here is conditional. If Aristotle’s view is false, and future-tense sentences can express true propositions, then after the appropriate time has elapsed, a certain present-tense sentence expressing the corresponding proposition must “perforce” also be true. What positively gives the lie to Aristotle’s view is not just the existence of truth-value links between today’s utterance and the fact of tomorrow’s sea-battle, but the whole pattern of the truth-value links across all the different times and tenses. Here is another example.
Time of UtteranceTruth-Value Links
Utterance
tn“An event of type K will occur a year hence.” T
One year
Waiting “perforce”
Period (+1 year)
tn+1“An event of type K is now occurring.” T
On my view propositions about the future work in exactly the same way as propositions about the present, though with one extra and important difference. In order to connect the present-tense sentence expressing the proposition that the weather is improving with what makes it true, all we have do is: to observe the weather, noting the fact that it is improving. The same thing is true of future-tense sentences. In order to connect the future-tense sentence expressing the proposition that the weather will improve with what makes that proposition true, what we have to do is, first: to wait. And then, when we have waited long enough, all we have to do is: to observe the weather, noting the fact that it is improving. That is the reason the truth-value links exist for propositions expressed with future-tense sentences. We have to wait for the future; and it is clearly possible to do this. (The realization of the fact that it is possible is what gives the toy problem the only importance that it has.) While we are waiting, time passes, and the future comes, in the B-series sense that what has not yet happened does happen. And that is enough to make the proposition expressed by a future-tense sentence just as true at the time of its utterance as any regular proposition expressed by its corresponding present-tense sentence. Dummett’s delineation of the notion of a truth-value link does us a great service because it shows that this feature of the logic of tenses is not peculiar to the future tense, but links sentences of no matter what tense which express propositions about the occurrence of events at different times into a single logical network.[9]