Todd (ch.6) – Part 1: Betting on the Open Future

This is part 6 of my ongoing series on Patrick Todd’s recently published book The Open Future: Why Future Contingents are All False (Oxford, 2021). (Previous installments: part 1, part 2, part 3, part 4, and part 5.)

Chapter 6 is a long chapter that arguably should have been split into two parts—at the very least, I shall be splitting my commentary on the chapter into two parts. The whole chapter is concerned with responding to practical objections to open futurism. Roughly the first third of the chapter (pp. 119–129) concerns the common argument that betting practices support the idea of retro-closure (i.e., the idea that if something happens then it was previously true that it was going to happen), which conflicts with the kind of open futurism that most open futurists want to defend. This is the part of the chapter that I will cover in this post. The balance of the chapter (pp. 129–147) is concerned with arguments to the effect that open futurists can’t make sense of probabilities about the future. I will discuss that part of the chapter in a follow-up post.

I. What are we doing when we bet?

Suppose that you and I have made a wager: I wager (today) that it will rain tomorrow, whereas you take the complementary wager (no rain tomorrow). Now suppose that tomorrow it rains. That means you need to pay up, right? Well, maybe not. Suppose we both agree that reality is (almost certainly) now indeterministic with respect to rain tomorrow. And suppose, further, that you are an open futurist who believes that if it is now indeterministic whether there is rain tomorrow then it is now not true that there will be rain tomorrow. Could you respond as follows: “I don’t need to pay up. When we placed our bets, you bet on the current truth of the proposition <It will rain tomorrow>, but even though it did rain, it wasn’t true then because the future was still open in that respect.”

Obviously your refusal to pay up is ludicrous. As Todd points out, quoting A.N. Prior, “that just isn’t the way the game is played” (p. 120). But why is it ludicrous? There are two possibilities:

1. Retro-closure is true and open futurism is false. You did indeed bet on the then-current truth of <It will rain tomorrow>, but you are wrong in thinking that it wasn’t true then. The mere fact that it is now raining shows that it was true yesterday that it would rain today. So you lost the bet. Pay up.
2. You weren’t betting on the then-current truth of <It will not rain tomorrow>, nor was I betting on the then-current truth of <It will rain tomorrow>; rather, you and I were simply agreeing to an outcome-based payoff scheme. It doesn’t matter what was or was not true yesterday. All that matters is that my designated outcome eventuated and yours didn’t and we agreed that you would pay me if that happened. So pay up.

Todd contends that (2) is right way to think about our betting practices. They are nothing more than outcome-based payoff arrangements and so have no implications one way or the other about whether the propositional target of the bet was true when the bet was made. I think Todd is exactly right about this. Here’s how he puts it:

One bets that it will be that p iff one does something that brings it about that any p future is a future in which one is owed the [contextually specified] betting response. … Suppose we bet £5 on rain tomorrow. I bet on rain; you bet on no rain. But the matter is indeterministic. Nevertheless, having now bet, the causally possible futures are divided between the rain futures in which I win, and no-rain futures in which you win. … We didn’t agree that any rain future in which there had been going to be rain is a future in which I win. We simply agreed that any rain future is one in which I win. And we are, now, in a scenario with rain. So I win. It wasn’t the case that I was going to win—but … that simply doesn’t matter. (pp. 121–122, underlining reflects Todd’s emphasis)

II. Extending Todd’s argument

I think the point can be made more forcefully than Todd puts it. Betting on the current truth of <It will rain tomorrow> is actually very odd because it amounts to betting on something that we cannot empirically verify, at least not directly. We know how to verify whether it is raining now—just look outside—but we don’t how to verify, at least not directly, whether it was true yesterday that it would rain today. So suppose you and I bet yesterday on the then-current truth of <It will rain tomorrow>. And suppose that today it is in fact raining. In order to adjudicate the bet it wouldn’t be enough for us to observe today’s rain. We would also need a way to infer <it was true yesterday that it was going to rain today> from <it is raining today>. In other words, we would need to invoke a non-empirical bridge principle, namely, retro-closure:

retro-closure (RC): p → HFp (i.e., if p is the case then it has always been the case that p will be the case)

But if we have to assume RC in order to adjudicate bets on the current truth of propositions about the future, then we can’t turn around and appeal to those same betting practices to support RC, for that would be to reason in a circle. We thus arrive at a dilemma:

Dilemma: On the one hand, if our betting practices are understood along the lines of (1), i.e., as bets on the present truth of claims about the future, then the adjudication of those bets presupposes RC and so cannot support it. On the other hand, if our betting practices are understood along the lines of (2), i.e., as agreements to some outcome-based payoff scheme, then the adjudication of those bets has no implications for the present truth of claims about the future. Either way, our betting practices provide no support for RC and thus pose no problem for open futurism.

If this is right, then the much-discussed “prediction problem” for open futurism is nothing more than a question-begging exercise.

III. “You were right”

But then why, upon someone’s winning a bet, do we sometimes say things like “you were right”? Superficially that may look like a retrospective endorsement of the idea that the proposition bet upon was right (i.e., true) when the person made the bet. But in light of the argument I just gave that our betting practices provide zero support for RC, I don’t think it’s right to construe the retrospective “you were right” as an endorsement of RC. How then should we construe it? Todd doesn’t address this question directly in Ch. 5, but he does return to the prediction problem in the appendix to Ch. 7. Skipping ahead a bit, here’s what he says there:

Note that, if I make a given prediction, and then things turn out as I predicted, saying, “See, I was right” seems most natural in cases in which I take myself to have had strong warrant for making the prediction that I made. (If someone rashly predicts that the ball will land in slot 17, and then, miraculously, it does, and the person says, in a cock-sure manner, “See! I was right!”, we might be inclined to reply that you got it right, but that you weren’t right.) In “this” sense of “was right”, however, someone saying, “See, I was right” is not implying the truth of Retro-closure; they are instead claiming that they had warrant for their prediction, and implying that the fact that their prediction came true is good evidence that it was likely to come true, precisely as they predicted. … When an expert makes an entirely warranted projection of a major hurricane next weekend, and then, when that hurricane comes to pass, says, “See, I was right”, no open futurist needs to think that he speaks falsely, even if it is maintained that “There will be a hurricane next weekend” was not true at the time of his projection. For in saying that he was right, he may simply be saying that he was right to make that projection—and he was, given the probabilities that obtained at the relevant time, and would have been right to do so even if the improbable happened and no hurricane came to pass. (p. 178, underlining reflects Todd’s emphasis)

This seems right to me. Upon winning an improbable bet it seems quite out of place to say, “I was right” or “I knew it”. If the event really was improbable and/or you believed it to be so, then you didn’t know it was going to happen, and you are in no position to take credit for having been “right”. A more natural and modest response would be to say, “Wow, I got it right” or “Wow, I got lucky”, neither of which even hints at RC. On the other hand, if you had (or think you had) strong reasons for believing a certain outcome to be probable, and it subsequently pans out, then you might have some justification for saying “I was right” or “I knew it”. But here, as Todd says, the utterance is plausibly understood as “I was right to have made that projection” or “I knew I had good grounds for making that projection”. Again, neither of those latter utterances even hints at RC, as they could be true and justifiably uttered even if the projection hadn’t panned out.

IV. Conclusion

In sum, our betting practices and related utterances do not, and cannot, support retro-closure. They cannot support it because we have no direct way to verify the past truth of propositions about the future. If we assume RC then we can retrospectively project present truth back into the past as something that always has been true about what will happen. But that’s only one possible interpretation of things. An equally plausible idea, in terms of what we can presently verify, is that the bet-upon proposition (e.g., that it rains tomorrow) subsequently becomes true (or false) at the relevant time in question (i.e., tomorrow). Because we can’t directly verify (or falsify) either of these theories, it makes much more sense to interpret our betting practices as in (2), i.e., as agreements to some sort of outcome-based payoff scheme.

Another moral of this discussion is that it’s a serious mistake to base a philosophical theory like RC merely on colloquial turns of phrase like “See, I was right”. Colloquial language does not aim at theoretical precision and clarity the way philosophy talk does (or should). Vagueness, ambiguity, idiomatic and figurative expressions, and “loose use” are pervasive features of colloquial language. Its aims are generally very concrete and practical (e.g., to convey just enough information quickly and without excess nuance) and it often consists of speech acts that are less locutionary (i.e., about what is uttered or said) than illocutionary (i.e., about the intent behind what is said) or perlocutionary (i.e., about the actual effect of what is said).