The Open Future

In an apparent attempt to interpret Aristotle, Jan Łukasiewicz proposed that the idea that the future is open carries a semantic shadow: future contingents are neither true nor false, and connectives are governed by three-valued truth-tables. The view is suspicious, among other things, because it introduces violations of the law of excluded middle (LEM) that do not track intuition (when A is neither true nor false, so is A ∨¬A). Thomason's application of the method of supervaluations offered a way to salvage the truth-value gap insight while holding on to the validity of LEM. For supervaluationists, future contingents are neither supertrue nor superfalse, but instances of LEM are supertrue—since every way the future will unfold is bound to support one disjunct or the other.In The Open Future, Patrick Todd also maintains that the openness hypothesis carries a semantic shadow. For him, if the future is open, all future contingents are false. Evidently, this view does not need supervaluationism to validate LEM. If A is guaranteed false and negation is classical, A ∨¬A is guaranteed true. The foundation of Todd's proposal is a twist on what Prior called the Peircean view of future discourse. Peirceanism:Sentences of the form In the future A, Will A, and so on are true if and only if A is true in all causally possible futures. (Todd emphasizes he's a smidgen non-Peircean: the exact difference won't matter here.) Pick a canonical future contingent sentence—say,(1) It will rain.If the future is open with respect to (1), there are open possibilities in which it does not rain that are compatible with all the currently settled facts. It follows that (1) is false, that its wide-scope negation It is not the case that it will rain is true, and that LEM is not threatened.Peirceanism is simple and distinguished by a history of high-profile endorsements. It is also not credible, and the incredulous stares it generates do not stem from some hard-to-express bellyaches but from well-known objections. These objections play a structuring role in Todd's discussion:The core of the book is an energetic rejoinder to these arguments. Todd should be credited for running the gauntlet, and for doing so with creativity and ingenuity. Since, like Todd, I recently spent a few years writing a book on future-directed language (Cariani 2021), and since I have come to diametrically opposed conclusions, you should expect me to believe that Todd's responses fail. Indeed, I think they do. I will flag the major points of disagreement and then note a way in which the most creative and interesting aspects of the book can be preserved.In response to the negation argument, Todd argues that will belongs to a category of expressions linguists call 'neg-raisers'. These are expressions that are typically interpreted as scoping over negation, regardless of where negation seems to appear superficially. So, the reason why we do not detect a reading of It won't rain on which not scopes over will resembles the reason why we interpret I don't think it's raining as roughly equivalent to I think it's not raining.1 The idea of will as a neg-raiser was originally advocated by the linguist Lauren Winans (2016). Given some additional assumptions, it is also related to Bridget Copley's (2009) proposal that It will rain presupposes that it rains in either all or none of the relevant futures—in other words, that will carries a "homogeneity" presupposition. Indeed, one of the leading accounts of neg-raising—due to Jon Gajewski (2017)—is that it arises because the relevant expressions demand homogeneity.Todd tries to address challenges to the neg-raising thesis. For example, Winans herself worries that the excluded middle inference of ordinary neg-raisers does not project out of questions, whereas WEM does. Contrast:(2a) Does John think Mary is home?(2b) Will Mary be home?A "no" answer to (2a) does not entail that John thinks Mary is not home. A "no" answer to (2b) entails she won't be. Todd would disagree with this last judgment. He emphatically thinks that, if the future is open, WEM is not valid. He claims that in ordinary contexts in which we utter It will rain, we do not have in mind the open future model. For him, there is something called semantics-cum-metaphysical competence that supplies us linguistic judgments that are informed both by meaning and by some assumptions about the world. In particular, when we do zero in on the open future model, we stop judging the relevant claims as logically true. Try as I might, I could not find any of Todd's alleged judgments convincing—except as restatements of the Peircean predictions. And the idea of "semantics-cum-metaphysical competence" seems mythical.On this issue, Todd is also at variance with Gajewski's prominent presuppositional analysis of neg-raisers. Traditionally, the homogeneity presupposition is instrumental to predict the perceived validity of WEM. The idea is that It will rain presupposes that either all relevant futures are rain futures or none are, and for that very reason It will rain or it won't can be classified as a logical truth. Its status is the same as that of Either the King of France is bald or he isn't: it cannot be false as long as its presupposition that France has a King is satisfied. This is as close as logically true as a sentence can get if it carries a nontrivial presupposition. If Todd adopted this view, there would be fewer bullets for him to bite.The real heart of the book's argument is the pragmatic error theory that is mobilized to answer the credences and practices objections. A major reason to care about semantic content is that it feeds into a broader story about communication, inquiry, knowledge, and rational belief. The book faces the important difficulties in this arena head on. Todd's response to the credence problem is that when we ascribe a probability to It will rain tomorrow, we are not making claims about the probability of the truth of a proposition. Instead, we express an estimate of the world's tendency to produce a certain outcome. This error theory generalizes to the "practices" objection: promising that it will rain is not a matter of standing in a relation to the proposition that it will rain; and betting that it will rain is not betting on the truth of that proposition either. (Presumably, however, present- and past-directed promises and bets are still propositional.)I doubt that these practices can be splintered in this way. Suppose you promise that you will pick up your friend on August 1, 2025, but you have lost track of where you are in time: for all you know, that date might have passed, and it might not have. Then it won't be transparent to you whether your promise is directed at a proposition or at a production tendency. Moreover, the object of your promises will change as you pass through time. That seems problematic.Furthermore, it is not clear what to say about bets or promises in the contents of mixed sentences like It rained yesterday and it will rain again tomorrow. This is one of those points that ought to be on the agenda of any error theorist but gets no mention at all in the book. Finally, all of these objections become even more biting if Todd's view were extended to attitudes like hopes and wonders that are typically future-directed. Todd does not explicitly do this, but that appears to be at best a lacuna in his treatment.In section 6.10, Todd discusses a devastating objection against his own view. The view predicts the consistency of:(3) # It is not the case that it will rain but it probably will.Given Todd's view, this should be perfectly acceptable whenever rain is open, but the future has the right tendency to produce it. After acknowledging that the problem might be insurmountable, Todd goes on to try to explore what it would be like to bite this bullet. I'll be blunt: there is no there there. This prediction is as bad as a semantic theory's predictions can get, and there is no massaging it into acceptability.The good news is that there is no shame in not doing natural language semantics. Todd's development of the open future thesis is more interesting if it is construed as specifying a canonical language in which the commitments of a certain metaphysical outlook might be formulated. Some of the most interesting parts of the book are the two chapters that connect the metaphysics with the theory of divine omniscience—one being a reprint of an excellent essay that Todd recently coauthored with Brian Rabern. Nothing in these chapters requires the bridge principles connecting truth and divine belief to be about truth in some language people actually speak. In fact, it is a bad idea to advance a dialectic in which views about divine omniscience require the empirical commitment to Peirceanism. Surely some people—perhaps some actual people—could speak a non-Peircean language, and absolutely nothing would follow about divine omniscience.The argumentative development in The Open Future is interesting. It might, in fact, be one of the better ways of supporting its overarching premise. But that premise is itself dubious as a hypothesis about natural language—in fact, more dubious if this is the best one can do to make it plausible.I thank Simon Goldstein, John MacFarlane, Paolo Santorio, and Patrick Todd for feedback on earlier drafts.