Alethic Openness and Bivalence (Part 1 of 2)

By | September 24, 2013

By the alethic openness of the future I mean that there is no complete, true, linear story of the future.

The main motivation for believing that the future is alethically open comes from future contingency. If the future is not alethically open but alethically settled, then there is a complete, true, linear story of the future. But, arguably—and the argument goes back as least as far as Aristotle (De Interpretatione 9)—if there is such a story, then the course of future events cannot deviate from it, otherwise the story would be false, contrary to hypothesis. If the course of future events and the complete, true, linear story of the future cannot deviate, then this must be either (1) because the truth of the story is settled by the course of future events, (2) because the course of future events is settled by the story, or (3) because both the story and the course of events are settled by something else (e.g., causal determinism). (2) can be ruled out because it gets the order of dependency between truth and reality backwards. Reality, which includes the actual occurrences of events, determines what’s true, not vice-versa. That leaves (1) and (3).

If (3), then there are no future contingents, no events that both might and might not happen such that their chance of occurrence is greater than zero and less than one. Hence, whatever the story says will happen must happen, and the future is fated.

If (1) then in a sense there is no real future. Because the story is true and because its truth is settled by events, those events must in some sense have already occurred and so they aren’t really future events. In other words, if (1) is right, then the course of “future” events is at most the course of relatively future events–they may be future in relation to a given temporal standpoint, but they are not future absolutely speaking. Hence, absolutely speaking, it follows that there are no future events and thus no future contingent events.

If the preceding argument or something akin to it is sound, then an alethically settled future is one lacking future contingents. If we suppose that there are future contingents—real, absolute future contingents—then the future must be alethically open.

Let us suppose, then, that there are future contingents. To be more concrete, let’s suppose that it is now a future contingent whether Admiral Smith will initiate a sea battle tomorrow against the dread pirate Jones. The question I want to pose is whether propositions like <Smith attacks Jones tomorrow> and <Smith will attack Jones tomorrow> are (a) false, or (b) neither true nor false.

The argument for (b) rests on the idea that <Smith attacks Jones tomorrow> and <Smith does not attack Jones tomorrow> are contradictories, meaning that they are mutually exclusive and jointly exhaustive of the possibilities. If so, then if one is true, the other is false, and if one is false, the other is true. Given bivalence, the principle that every proposition is either true or, if not true, then false, it follows that there is now a truth concerning how the future will unfold with respect to this sea battle. And since the reasoning here generalizes to all does/does not propositions about future contingents, it follows that there is a prior truth concerning how the future will unfold with respect to all future contingents, which brings us back to an alethically settled future and the fatalistic worry based on it. The only way to avoid this result given that the two propositions are contradictories is to deny bivalence and to say that neither <Smith attacks Jones tomorrow> nor <Smith does not attack Jones tomorrow> is true, and that neither is false. Such propositions, one must say, are neither true nor false.

The argument for (a) rests on the idea that <Smith attacks Jones tomorrow> and <Smith does not attack Jones tomorrow> are not contradictories, but merely contraries, meaning that they are mutually exclusive but not jointly exhaustive of the possibilities. If this is right, then even though the propositions cannot both be true, they can both be false. In answer to the question of how <Smith attacks Jones tomorrow> and <Smith does not attack Jones tomorrow> could both be false, the proponent of (a) answers that this is the case when a third type of proposition, one that is the contrary of both <Smith attacks Jones tomorrow> and <Smith does not attack Jones tomorrow>, is true instead. Thus, in addition to (i) it’s being now true that Smith attacks Jones tomorrow, (ii) it’s being now true that Smith does not attack Jones tomorrow, (iii) it could be now true that Smith might and might not attack Jones tomorrow. If any one of (i)–(iii) is true, then the other two are false. Hence, bivalence holds for propositions about future contingents. (Though it might still fail for other reasons, such as vagueness, on which see this book.)

In my published work I have defended (a), arguing that once one sees that in the case of future contingents there are in fact three possibilities—a future that is determinate with respect to one option, a future that is determinate with respect to the other option, and a future that is indeterminate with respect to both options—there is no longer any motivation for denying bivalence to avoid the fatalistic argument from alethic settledness.

But suppose we shift attention from thinking of tomorrow as future to imagining it as present. The past and present, unlike the future, are fully determinate. Hence, when tomorrow comes, it will be the case at any given moment either that Smith is attacking Jones or that Smith is not attacking Jones. (I’m setting the issue of vagueness aside.) In the present-tense case, the third, indeterminate option doesn’t seem to be available. So it seems like <Smith is attacking Jones> and <Smith is not attacking Jones> are contradictories. But if that’s right, then the corresponding tense-neutral propositions (I use uninflected verbs for these so as to distinguish them from present-tense propositions) <Smith attack Jones> and <Smith not attack Jones> also appear to be contradictories. And if we add temporal indices, e.g., <Smith attack Jones at T1> and <Smith not attack Jones at T1>, and range over all conceivable events and temporal indices, then it looks like we again arrive at a complete, true, linear, tense-neutral story of the future—unless we deny bivalence.

Does the proponent of (a) have an answer to this?

UPDATE (2014/05/19/): Edited for clarity and fixed some typos.

6 thoughts on “Alethic Openness and Bivalence (Part 1 of 2)

      1. Jacob

        Good deal. I’m particularly interested in “will” props about future contingents, and how we talk about what I’m thinking of in terms of temporally indexed tokens vs. temporally indexed types.

        Consider the proposition expressed by “I will take a shower February 3rd 2014.”

        A token of this type specifies a relation between causes at the time the sentence was uttered and the future contingent it is/was about. Such props seem to me alethically invariant.

        The type is not indexed to a particular time, so doesn’t specify a relation between any causes and the future contingent it is about. It would be alethically variant depending on when it is uttered, as only then would it specify a causal relation.

        The latter seems to me what you were addressing the the FB post… and I’m curious if you would make sense out of them in the same way… that is… by specifying that they are proposition types and not tokens.

        Reply
        1. Alan Rhoda Post author

          Hi Jacob,

          Sorry for the much delayed reply. I’m not *finished* with the dual masters degrees I was working on, and so I finally have some time to be back into blogging.

          Anyways, as to your question, in my post I try to avoid type/token complications by speaking directly about propositions like instead of statements (sentential expressions of propositions) like “Smith will attack Jones tomorrow.” The type/token distinction is very applicable to sentences. As a type, a given sentence can be uttered on multiple occasions. As a token, it has a specific time/place of utterance. But when it comes to propositions, the token is the type. is what it is, and has the semantic content it does, regardless of when, how, or even whether it is expressed.

          Make sense?

          Reply
  1. Jeff

    How can we tell what “Smith not attack Jones” even means? Without tense, the law of non-contradiction has no discernible application does it? The LNC is typically articulated with the phrase “at the same time.” Tense is thus seemingly relevant to the LNC and the Law of Identity. And the Law of Identity is just another way of saying we interpret elements of our conscious states as attributes of extra-self beings such that we can consistently distinguish multiple beings from one another in time, right? In short, without tense, are we really saying anything specific enough to apply logic to yet? I don’t see how.

    Reply
    1. Alan Rhoda Post author

      Good question, Jeff. There is something decidely odd about using an unconjugated verb as I do, but I think it can be seen to make sense.

      is to be understood from an absolute perspective. This is the same as a “God’s eye” perspective, but where we stay neutral on the question of divine temporality. So is true just in case from such a perspective God “sees” (presently, if God is temporal, or timelessly, if God is not) Smith attacking Jones. On a linear B-theory of time, for example, the static block of events is always eternally *there* and available for divine inspection. So if *at any point in the block* God sees Smith attacking Jones, then is true.

      Regarding LNC, we adequately express LNC by saying that for all propositions, p, necessarily, not-(p and not-p). Hence, the “at the same time” clause is strictly unnecessary. In colloquial presentations of LNC it is commonly added so that application of LNC to sentences is more straightforward. Thus, we might say that it is not the case that “Smith is attacking Jones” and “It is not the case that Smith is attacking Jones” are true “at the same time.” But all we mean by that is that they can’t be *jointly* true. That’s why LNC still holds even if, as Quine thought, all propositions have their truth values timelessly so that it makes no sense to say that p is *true now* or *true at time t*. (For the record, I think Quine is seriously mistaken on this point, but I wouldn’t accuse him of rejecting LNC.)

      Regarding the Law of Identity, I wouldn’t explain this, as you do, by saying that it “is just another way of saying we interpret elements of our conscious states as attributes of extra-self beings such that we can consistently distinguish multiple beings from one another in time.” Strictly speaking, the Law doesn’t have any necessary relation to us or our conscious states. It would still be a law even if no creatures ever existed. For the record, the “Law of Identity” is more precisely called the “Indiscernibility of Identicals”. It says that, necessarily, for any X and Y, if X=Y then X and Y have exactly the same (non-Cambridge) properties.

      Reply

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