I explore the motivation and logical consequences of the idea that we have some (limited) ability to know contingent facts about the future, even in presence of the assumption that the future is objectively unsettled or indeterminate. I start by formally characterizing skepticism about the future. This analysis nudges the anti-skeptic towards the idea that if some propositions about the future are objectively indeterminate, then it may be indeterminate whether a suitably positioned agent knows them. -/- Philosophical Perspectives, Volume 35, (...) Issue 1, Page 50-69, December 2021. (shrink)

This book launches a sustained defense of a radical interpretation of the doctrine of the open future. Patrick Todd argues that all claims about undetermined aspects of the future are simply false.

Provisional draft, pre-production copy of my book “The Modal Future” (forthcoming with Cambridge University Press).

We care not only about what experiences we have, but when we have them too. However, on the B-theory of time, something’s timing isn’t an intrinsic way for that thing to be or become. Given B-theory, should we be rationally indifferent about the timing per se of an experience? In this paper, I argue that B-theorists can justify time-biased preferences for pains to be past rather than present and for pleasures to be present rather than past. In support of this (...) argument, I appeal to the doctrine of temporal parts or “four-dimensionalism” for short. When held in conjunction with a certain evaluative principle about whose experiences matter, four-dimensionalism reconciles B-theory with some time-biased preferences. (shrink)

Various philosophers have long since been attracted to the doctrine that future contingent propositions systematically fail to be true—what is sometimes called the doctrine of the open future. However, open futurists have always struggled to articulate how their view interacts with standard principles of classical logic—most notably, with the Law of Excluded Middle. For consider the following two claims: Trump will be impeached tomorrow; Trump will not be impeached tomorrow. According to the kind of open futurist at issue, both of (...) these claims may well fail to be true. According to many, however, the disjunction of these claims can be represented as p ∨ ~p—that is, as an instance of LEM. In this essay, however, I wish to defend the view that the disjunction these claims cannot be represented as an instance of p ∨ ~p. And this is for the following reason: the latter claim is not, in fact, the strict negation of the former. More particularly, there is an important semantic distinction between the strict negation of the first claim [~] and the latter claim. However, the viability of this approach has been denied by Thomason, and more recently by MacFarlane and Cariani and Santorio, the latter of whom call the denial of the given semantic distinction “scopelessness”. According to these authors, that is, will is “scopeless” with respect to negation; whereas there is perhaps a syntactic distinction between ‘~Will p’ and ‘Will ~p’, there is no corresponding semantic distinction. And if this is so, the approach in question fails. In this paper, then, I criticize the claim that will is “scopeless” with respect to negation. I argue that will is a so-called “neg-raising” predicate—and that, in this light, we can see that the requisite scope distinctions aren’t missing, but are simply being masked. The result: a under-appreciated solution to the problem of future contingents that sees and as contraries, not contradictories. (shrink)

There is a familiar debate between Russell and Strawson concerning bivalence and ‘the present King of France’. According to the Strawsonian view, ‘The present King of France is bald’ is neither true nor false, whereas, on the Russellian view, that proposition is simply false. In this paper, I develop what I take to be a crucial connection between this debate and a different domain where bivalence has been at stake: future contingents. On the familiar ‘Aristotelian’ view, future contingent propositions are (...) neither true nor false. However, I argue that, just as there is a Russellian alternative to the Strawsonian view concerning ‘the present King of France’, according to which the relevant class of propositions all turn out false, so there is a Russellian alternative to the Aristotelian view, according to which future contingents all turn out false, not neither true nor false. The result: contrary to millennia of philosophical tradition, we can be open futurists without denying bivalence. (shrink)

This paper investigates the logic of Ockhamism, a view according to which future contingents are either true or false. Several attempts have been made to give rigorous shape to this view by defining a suitable formal semantics, but arguably none of them is fully satisfactory. The paper draws attention to some problems that beset such attempts, and suggests that these problems are different symptoms of the same initial confusion, in that they stem from the unjustified assumption that the actual course (...) of events must be represented in the semantics as a distinguished history, the Thin Red Line. (shrink)

There is a long-standing disagreement among Branching-Time theorists. Even though they all believe that the branching representation accurately grasps the idea that the future, contrary to the past, is open, they argue whether this representation is compatible with the claim that one among many possible futures is distinguished—the single future that will come to be. This disagreement is paralleled in an argument about the bivalence of future contingents. The single, privileged future is often called the Thin Red Line. I reconstruct (...) the history of the arguments for and against this idea. Then, I propose my own version of the Thin Red Line theory which is immune to the major objections found in the literature. I argue that the semantic disagreement is grounded in distinct metaphysical presuppositions. My solution is expressed in a conceptual framework proposed by John MacFarlane, who distinguishes semantics from postsemantics. I extend his distinction and introduce a new notion of presemantics to elucidate my idea. (shrink)

These are my materials (a short precis, and replies to John MacFarlane, Mitchell Green, Ryan Wasserman, and Anthony Bigg and Kristie Miller) for a symposium on my book, _The Open Future: Why Future Contingents are All False_ (OUP, 2021) in *Analytic Philosophy*. [The contribution from MacFarlane is available on his website, those from Wasserman and Green are on their Academia profiles, and the contribution from Bigg and Miller is on Miller's PhilPapers profile.].

This book discusses fundamental topics on contemporary Ockhamism. The collected essays show how contemporary Ockhamism can impact areas of research such as semantics, metaphysics and also the philosophy of science. In addition, the volume hosts one historian of Medieval philosophy who investigates the way in which William of Ockham “in flesh and bone” construed time and, more generally, future contingency. The essays explore the different meanings of this theory. They cover three main topics, in particular. The first examines the thesis (...) that sentences and propositions about the future have a definite truth value, without any ensuing commitment to determinism or fatalism. The second topic looks at the problem whether the branching-time model needs to countenance a privileged branch (the so-called Thin Red Line). Finally, the third topic considers the idea that there are so-called soft facts. These would be the subject matter of sentences and propositions verbally about the present or the past, but metaphysically about a later time, and which might change in the future. Overall, the book provides an updated and rigorous idea of the debate about Ockhamism. It gives readers a deeper understanding into this philosophical approach influenced by William of Ockham, characterized by the rejection of the Aristotelian idea that, in order to preserve the contingency of the future, future contingents must be deemed neither true nor false. (shrink)

This volume seeks to further the use of formal methods in clarifying one of the central problems of philosophy: that of our free human agency and its place in our indeterministic world. It celebrates the important contributions made in this area by Nuel Belnap, American logician and philosopher. Philosophically, indeterminism and free action can seem far apart, but in Belnap’s work, they are intimately linked. This book explores their philosophical interconnectedness through a selection of original research papers that build forth (...) on Belnap’s logical and philosophical work. Some contributions take the form of critical discussions of Belnap's published work, some develop points made in his publications in new directions, and others provide additional insights on the topics of indeterminism and free action. In Nuel Belnap’s work on indeterminism and free action, three formal frameworks figure prominently: the simple branching histories framework known as "branching time;" its relativistic spatio-temporal extension, branching space-times; and the “seeing to it that” logic of agency. As those frameworks provide the formal background for the contributed papers, the volume introduction gives an overview of the current state of their development. It also introduces case-intensional first order logic, a general intensional logic offering resources for a first-order extension of the mentioned frameworks and a recent research focus of Belnap’s. The volume also contains an extended biographical interview with Nuel Belnap. (shrink)

According to an influential line of thought, from the assumption that indeterminism makes future contingents neither true nor false, one can conclude that assertions of future contingents are never permissible. This conclusion, however, fails to recognize that we ordinarily assert future contingents even when we take the future to be unsettled. Several attempts have been made to solve this puzzle, either by arguing that, albeit truth-valueless, future contingents can be correctly assertable, or by rejecting the claim that future contingents are (...) truth-valueless. The paper examines three of most representative accounts in line with the first attempt, and concludes that none of them succeed in providing a persuasive answer as to why we felicitously assert future contingents. (shrink)

In the presented article, I have analyzed the famous Saul Kripke statement that some a priori truths are contingent. I show, that despite Kripke’s thesis, in the historical understanding of contingency, the notions of contingency and apriority are in deep conflict with each other. In this understanding of contingency, the past, which can be known a priori, is not contingent, and the future, which is contingent, has difficulty acquiring a priori knowledge. Having stated Kripke’s thesis more precisely, I propose three (...) means in order to defend it in the historical understanding of possibility: by introducing the notion of “factual” future, by replacing the notion of apriority with the notion of apriority-in-the-future; by replacing the notion of apriority with the notion of historical apriority, and the notion of contingency with the notion of once-apriority. In the annex of the article, I present the formal analysis of the problem that I have introduced and three solutions which I have proposed in the language of temporal-modal logic of predicates for models of indeterministic time. (shrink)

In a recently published paper, Patrick Todd (2016, 'Future contingents are all false! On behalf of a Russellian open future') advocates a novel treatment of future contingents. On his view, all statements concerning the contingent future are false. He motivates his semantic postulates by considerations in philosophy of time and modality, in particular by the claim that there is no actual future. I present a number of highly controversial consequences of Todd’s theory. Inadequacy of his semantics might indirectly serve as (...) an argument against the philosophical view underpinning his proposal. (shrink)

Este artículo se centra en un argumento presentado por Fara (2010) en contra del supervaluacionismo en el contexto de la vaguedad. Muestro cómo dicho argumento es igualmente aplicable al supervaluacionismo de tiempo ramificado (presentado por primera vez por Thomason 1970), pero no a la semántica 'STRL' de Malpass y Wawer (2012), que está estrechamente relacionada.

Non-bivalent semantics of the future tense assert that propositions regarding future contingents are neither true nor false. One of the most relevant non-bivalent semantics is supervaluationism :264–281, 1970; Thomason, in: Gabbay, Guenthner Handbook of philosophical logic, Springer, Berlin, 1984), which preserves important logical principles. Recently, non-bivalent semantics are under attack from some pragmatics arguments: these semantics would be incompatible with our practices of asserting future contingents and with the probability we ascribe to such assertions :251–271, 2014; Cariani and Santorio in (...) Mind 127:129–165, 2018). The aim of this paper is to defend supervaluationism against this kind of criticism. We argue that, if probability is interpreted as the subjective belief in a proposition and if a semantic contextualism is adopted, supervaluationism makes correct predictions concerning the norms that govern our practices of asserting future contingents. Obviously, other arguments can be proposed against supervaluationism, but they must be of a different kind, such as metaphysical arguments. (shrink)

The purpose of the paper is to rethink the role of actuality in the branching model of possibilities. We investigate the idea that the model should be enriched with an additional factor—the so-called Thin Red Line—which is supposed to represent the single possible course of events that gets actualized in time. We believe that this idea was often misconceived which prompted some unfortunate reactions. On the one hand, it suggested problematic semantic models of future tense and and on the other, (...) it provoked questionable lines of criticism. We reassess the debate and point to potential pitfalls, focusing on the semantic dimension of the Thin Red Line theory. Our agenda transcends the semantics, however. We conclude that semantic considerations do not threaten the Thin Red Line theory and that the proper debate should be carried in the domain of metaphysics. (shrink)

This paper gives an overview of logico-philosophical issues of time and determinism. After a brief review of historical roots and 20th century developments, three current research areas are discussed: the definition of determinism, space-time indeterminism, and the temporality of individual things and their possibilities.

In this article, we take into consideration two semantics of the future tense: linearism, according to which future-tense sentences are interpreted on a single history, and universalism, according to which they are evaluated by universally quantifying on the plurality of future histories that radiate from the present instant. Specifically, we focus on a objection advanced against universalism: if universalism were correct semantics of _will_, negated future-tense sentences of natural language should have two readings, depending on the scope of negation with (...) respect to the universal quantifier on histories. However, since natural language does not show this difference, one may conclude that there is no universal quantifier in the interpretation of these sentences. We show that this conclusion is premature. First, _will_ has clear scope interactions with indefinite nouns phrases, contrary to what linearism predicts. Second, it is possible to extend the treatment of vague predicates as partial predicates to _will_: Since partial predicates have no scope interactions with negation, this can account for the scopelessness of _will_. The partiality of truth conditions is not restricted to _will_ but also pertains to counterfactuals and generics and probably is part of a general tendency to maximize contraries. (shrink)

This paper establishes two facts. The first is that a recently presented problem for supervaluationism applies equally to the branching-time cousin of the theory. The second fact is that a new version of branching-time supervaluationism avoids this and related problems.

In addressing the problem of the (in)compatibility of divine foreknowledge and human freedom, philosophers of religion encounter problems regarding the metaphysics and structure of time. Some models of temporal logic developed for completely independent reasons have proved especially appropriate for representing the temporal structure of the world as Molinism conceives it. In particular, some models of the Thin Red Line ( $$\mathsf {TRL}$$ ) seem to imply that conditionals of freedom are true or false, as Molinists maintain. Noting the resemblance (...) between Molinism and $$\mathsf {TRL}$$ models, Restall (Molinism and the thin red line. In: Perszyk K (ed) Molinism: the contemporary debate, pp 227–239, 2011) has advanced some criticisms of Molinism that have also been leveled against $$\mathsf {TRL}$$ models. In particular, Restall believes that the implication $$p \rightarrow \mathbf {HF}p$$ is not true in $$\mathsf {TRL}$$ models. Because Molinists must also accept that this implication is not true, this is a problem for them. We will show that Restall’s criticism is wide of the mark. Firstly, it will be demonstrated that in many open future models (not just $$\mathsf {TRL}$$ ) the implication $$p \rightarrow \mathbf {HF}p$$ is invalid. Secondly, while it is possible to account for this implication, some modifications are required in respect of the branching time semantics. In proposing one such modification, we show that this new semantics can be adopted by advocates of the $$\mathsf {TRL}$$ and, as a consequence, by Molinists as well. We conclude that the principle stated by Restall is either a problem for many open future models (not just for Molinists) or can be accounted for by these models and so is not a problem for Molinists either. (shrink)

Tense logic is a branch of contemporary logic which includes formal devices that allow us to deal with the temporal relations between propositions. The aim of our paper is threefold: 1) to reveal how Aristotelian philosophical ideas about time, truth, possibility and necessity were reinterpreted by the founder of contemporay tense logic Arthur Prior; 2) to discuss what novel solutions to the classical problem of future contingents are available using Priorean invention; 3) to describe how the tools of tense logic (...) have transcended their original theoretical purposes. (shrink)

Open futurism is the indeterministic position according to which the future is ‘open’, i.e., there is now no fact of the matter as to what future contingent events will actually obtain. Many open futurists hold a branching conception of time, in which a variety of possible futures exist. This paper introduces two challenges to branching-time open futurism, which are similar in spirit to a challenge posed by Fine to tense realism. The paper argues that, to address the new challenges, open (...) futurists must adopt an objective, non-perspectival notion of actuality and subscribe to an A-theoretic, dynamic conception of reality. Moreover, given a natural understanding of “actual future”, it is perfectly sensible for open futurists to hold that a unique, objectively actual future exists, contrary to a common assumption in the current debate. The paper also contends that recognising the existence of a unique actual future helps open futurists to avoid potential misconceptions. (shrink)

The thin red line theory is a form of branching indeterminism. It entails that, among the many possible developments that reality might take, one is privileged: the actual history. The thin red line theory is naturally paired off with a semantic thesis that may be called ‘the actuality principle’: a statement is true as used at a moment if and only if it is true at that moment on the actual history. The actuality principle has been challenged, for it would (...) be wrong about several counterfactual reasonings. On the one hand, the actuality principle should entail that any statement uttered at a merely possible moment is untrue. On the other hand, the actuality principle should be at odds with the way we use subjunctive conditionals. This paper argues that both objections rely on an inadequate understanding of the notion of the history of use. As for the first objection, the paper argues that to assume the actuality principle amounts to taking the actual history as the history of use. As a consequence, one cannot consistently take the actual history as the history of use and, at the same time, a merely possible moment as the moment of use. As for the second objection, the paper shows that the actuality principle is consistent with any reasonable treatment of subjunctive conditionals. (shrink)

According to an influential line of thought, from the assumption that indeterminism makes future contingents neither true nor false, one can conclude that assertions of future contingents are never permissible. This conclusion, however, fails to recognize that we ordinarily assert future contingents even when we take the future to be unsettled. Several attempts have been made to solve this puzzle, either by arguing that, albeit truth-valueless, future contingents can be correctly assertable, or by rejecting the claim that future contingents are (...) truth-valueless. The paper examines three of most representative accounts in line with the first attempt, and concludes that none of them succeed in providing a persuasive answer as to why we felicitously assert future contingents. (shrink)

This paper follows Part I of our essay on case-intensional first-order logic ). We introduce a framework of branching histories to take account of indeterminism. Our system BH-CIFOL adds structure to the cases, which in Part I formed just a set: a case in BH-CIFOL is a moment/history pair, specifying both an element of a partial ordering of moments and one of the total courses of events that that moment is part of. This framework allows us to define the familiar (...) Ockhamist temporal/modal connectives, most notably for past, future, and settledness. The novelty of our framework becomes visible in our discussion of substances in branching histories, i.e., in its first-order part. That discussion shows how the basic idea of tracing an individual thing from case to case via an absolute property is applicable in a branching histories framework. We stress the importance of keeping apart extensionality and moment-definiteness, and give a formal account of how the specification of natural sortals and natural qualities turns out to be a coordination task in BH-CIFOL. We also provide a detailed answer to Lewis’s well-known argument against branching histories, exposing the fallacy in that argument. (shrink)

Supervaluationism is one of the most discussed approaches to the semantics of future tense sentences in a branching time. In this paper, we consider the criticism advanced by Malpass against Supervaluationism. This criticism relies on the fact that supervaluationists must accept as supertrue disjunctions whose disjuncts are not only supertrue—which supervaluationists are ready to acknowledge—but also not satisfiable. In order to show this, Malpass proposes a formula, F F 1, which shows the existence of a satisfiable disjunction with unsatisfiable disjuncts (...) in supervaluationist models. In reply, we show that formula F F 1 cannot be expressed within a model (whether Ockhamist or supervaluationist) because it quantifies on models. It can be correctly characterised only within a meta-model that has the resources to quantify on various models. However, once that is done, F F 1 is, for the advocates of Supervaluationism, no more demanding than other disjunctions because it just generalises at the meta-theoretical level what supervaluationists already acknowledge at the theoretical level. (shrink)

This paper follows Part I of our essay on case-intensional first-order logic (CIFOL; Belnap and Müller (2013)). We introduce a framework of branching histories to take account of indeterminism. Our system BH-CIFOL adds structure to the cases, which in Part I formed just a set: a case in BH-CIFOL is a moment/history pair, specifying both an element of a partial ordering of moments and one of the total courses of events (extending all the way into the future) that that moment (...) is part of. This framework allows us to define the familiar Ockhamist temporal/modal connectives, most notably for past, future, and settledness. The novelty of our framework becomes visible in our discussion of substances in branching histories, i.e., in its first-order part. That discussion shows how the basic idea of tracing an individual thing from case to case via an absolute property is applicable in a branching histories framework. We stress the importance of keeping apart extensionality and moment-definiteness, and give a formal account of how the specification of natural sortals and natural qualities turns out to be a coordination task in BH-CIFOL. We also provide a detailed answer to Lewis’s well-known argument against branching histories, exposing the fallacy in that argument. (shrink)