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)

Many languages have past-and-counterfactuality markers such as English simple past. There have been various attempts to find a common definition for both uses, but I will argue in this paper that they all have problems with ruling out unacceptable interpretations, or accounting for the contrary-to-fact implicature of counterfactual conditionals, or predicting the observed cross-linguistic variation, or a combination thereof. By combining insights from two basic lines of reasoning, I will propose a simple and transparent approach that solves all the observed (...) problems and offers a new understanding of the concept of counterfactuality. (shrink)

D. M. Armstrong, Michael Tooley, and Fred Dretske have recently proposed a new realist account of laws of nature, according to which laws of nature are objective relations between universals. After criticizing this account, I develop an alternative realist account, according to which (1) the nomic structure of a world is a relation between initial world-histories and world-histories, and (2) a law of nature is a fact that holds solely in virtue of nomic structure (and not, for example, in virtue (...) of past history). (shrink)

I argue that a counterexample proposed by donald nute shows only that past tenses involve indexical restriction to a limited domain of times. The purpose of this note is to defend the thesis that there is a single conditional connective figuring in both indicative and 'had'--'would' connectives, And that the differences in logical form between the two sorts of english conditional expressions have to do with tense.

Many languages have past-and-counterfactuality markers such as English simple past. There have been various attempts to find a common definition for both uses, but I will argue in this paper that they all have problems with (a) ruling out unacceptable interpretations, or (b) accounting for the contrary-to-fact implicature of counterfactual conditionals, or (c) predicting the observed cross-linguistic variation, or a combination thereof. By combining insights from two basic lines of reasoning, I will propose a simple and transparent approach that solves (...) all the observed problems and offers a new understanding of the concept of counterfactuality. (shrink)

We show that truth conditions for counterfactuals need not always be given in terms of a vague notion of similarity. To this end, we single out the important class of historical counterfactuals and give formally rigorous truth conditions for these counterfactuals, employing a partial ordering relation called "comparative closeness" that is defined in the framework of branching space-times. Among other applications, we provide a detailed analysis of counterfactuals uttered in the context of lost bets. In an appendix we compare our (...) theory with the branching space-times based reading of counterfactuals recently proposed by Belnap. (shrink)

The thin red line ( TRL ) is a theory about the semantics of future-contingents. The central idea is that there is such a thing as the ‘actual future’, even in the presence of indeterminism. It is inspired by a famous solution to the problem of divine foreknowledge associated with William of Ockham, in which the freedom of agents is argued to be compatible with God’s omniscience. In the modern branching time setting, the theory of the TRL is widely regarded (...) to suffer from several fundamental problems. In this paper we propose several new TRL semantics, each with differing degrees of success. This leads up to our final semantics, which is a cross between the TRL and supervaluationism. We discuss the notions of truth, validity and semantic consequence which result from our final semantics, and demonstrate some of its pleasing results. This account, we believe, answers the main objection in the literature, and thus places the TRL on the same level as any other competing semantics for future contingents. (shrink)

Possible worlds semantics for conditionals leave open the problem of how to construct models for realistic domains. In this paper, we show how to adapt logics of action and change such as John McCarthy’s Situation Calculus to conditional logics. We illustrate the idea by presenting models for conditionals whose antecedents combine a declarative condition with a hypothetical action.

This is part A of a paper in which we defend a semantics for counterfactuals which is probabilistic in the sense that the truth condition for counterfactuals refers to a probability measure. Because of its probabilistic nature, it allows a counterfactual ‘ifAthenB’ to be true even in the presence of relevant ‘Aand notB’-worlds, as long such exceptions are not too widely spread. The semantics is made precise and studied in different versions which are related to each other by representation theorems. (...) Despite its probabilistic nature, we show that the semantics and the resulting system of logic may be regarded as a naturalistically vindicated variant of David Lewis’ truth-conditional semantics and logic of counterfactuals. At the same time, the semantics overlaps in various ways with the non-truth-conditional suppositional theory for conditionals that derives from Ernest Adams’ work. We argue that counterfactuals have two kinds of pragmatic meanings and come attached with two types of degrees of acceptability or belief, one being suppositional, the other one being truth based as determined by our probabilistic semantics; these degrees could not always coincide due to a new triviality result for counterfactuals, and they should not be identified in the light of their different interpretation and pragmatic purpose. However, for plain assertability the difference between them does not matter. Hence, if the suppositional theory of counterfactuals is formulated with sufficient care, our truth-conditional theory of counterfactuals is consistent with it. The results of our investigation are used to assess a claim considered by Hawthorne and Hájek, that is, the thesis that most ordinary counterfactuals are false. (shrink)

Open future is incompatible with realism about possible worlds. Since realistically conceived (concrete or abstract) possible worlds are maximal in the sense that they contain/represent the full history of a possible spacetime, past and future included, if such a world is actual now, the future is fully settled now, which rules out openness. The kind of metaphysical indeterminacy required for open future is incompatible with the kind of maximality which is built into the concept of possible worlds. The paper discusses (...) various modal realist responses and argues that they provide ersatz openness only, or they lead to incoherence, or they render the resulting theory inadequate as a theory of modality. The paper also considers various accounts of the open future, including rejection of bivalence, supervaluationism, and the ‘thin red line’ view (TRL), and claims that a version of (TRL) can avoid the incompatibility problem, but only at the cost of deflating the notion of openness. (shrink)

A middle fact is a true proposition about what would have happened had A been true (where A is in fact false), whose truth isn't entailed by any non-counterfactual facts. I argue that there are no middle facts; if there were, we wouldn't know them, and our ignorance of them would result in ignorance about whether regret is fitting in cases where we clearly know it is. But there's a problem. Consider an unflipped fair coin which is such that no (...) non-counterfactual fact determines that it would have landed heads had it been flipped (or tails had it been flipped). If there are no middle facts, it's not true that it would have landed heads had it been flipped nor that it would have landed tails had it been flipped. Yet each counterfactual is still possibly true for all we know. I argue that we can resolve this tension in the anti-middle fact position, further strengthening the case against middle facts. (shrink)

I discuss three observations about backtracking counterfactuals not predicted by existing theories, and then motivate a theory of counterfactuals that does predict them. On my theory, counterfactuals quantify over a suitably restricted set of historical possibilities from some contextually relevant past time. I motivate each feature of the theory relevant to predicting our three observations about backtracking counterfactuals. The paper concludes with replies to three potential objections.

This paper is predicated on the idea that some modal operators are better understood as quantificational expressions over worlds that determine not only first-order facts but modal facts also. In what follows, we will present a framework in which these two types of facts are brought closer together. Structural features will be located in the worlds themselves. This result will be achieved by decomposing worlds into parts, where some of these parts will have “modal import” in the sense that they (...) will determine structure on other worldly parts. The main upshot of this will be a clearer grasp of the interaction between modal notions. (shrink)

The connection between the probabilities of conditionals and the corresponding conditional probabilities has long been explored in the philosophical literature, but its implementation faces both technical obstacles and objections on empirical grounds. In this paper I ?rst outline the motivation for the probabilistic turn and Lewis’ triviality results, which stand in the way of what would seem to be its most straightforward implementation. I then focus on Richard Jeffrey’s ’random-variable’ approach, which circumvents these problems by giving up the notion that (...) conditionals denote propositions in the usual sense. Even so, however, the random-variable approach makes counterintuitive predictions in simple cases of embedded conditionals. I propose to address this problem by enriching the model with an explicit representation of causal dependencies. The addition of such causal information not only remedies the shortcomings of Jeffrey’s conditional, but also opens up the possibility of a uni?ed probabilistic account of indicative and counterfactual conditionals. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

Standard proofs of generalized Bell theorems, aiming to restrict stochastic, local hidden-variable theories for quantum correlation phenomena, employ as a locality condition the requirement of conditional stochastic independence. The connection between this and the no-superluminary-action requirement of the special theory of relativity has been a topic of controversy. In this paper, we introduce an alternative locality condition for stochastic theories, framed in terms of the models of such a theory (§2). It is a natural generalization of a light-cone determination condition (...) that is essentially equivalent to mathematical conditions that have been used to derive Bell inequalities in the deterministic case. Further, it is roughly equivalent to a condition proposed by Bell that, in one investigation, needed to be supplemented with a much stronger assumption in order to yield an inequality violated by some quantum mechanical predictions. It is shown here that this reflects a very general situation: from the proposed locality condition, even adding the strict anticorrelation condition and the auxiliary hypotheses needed to derive experimentally useful (and theoretically telling) inequalities, no Bell-type inequality is derivable. (These independence claims are the burden of §4.) A certain limitation on the scope of the proposed stochastic locality condition is exposed (§5), but it is found to be rather minor. The conclusion is thus supported that conditional stochastic independence, however reasonable on other grounds, is essentially stronger than what is required by the special theory.Our results stand in apparent contradiction with a class of derivations purporting to obtain generalized Bell inequalities from locality alone. It is shown in Appendix (B) that such proofs do not achieve their goal. This fits with our conclusion that generalized Bell theorems are not straightforward generalizations of theorems restricting deterministic hidden-variable theories, and that, in fact, such generalizations do not exist. This leaves open the possibility that a satisfactory, non-deterministic account of the quantum correlation phenomena can be given within the framework of the special theory. (shrink)

In his (1981) paper, Stalnaker has revised his old theory of conditionals and has given the revision an interesting defense. Indeed, Stalnaker shows that this new theory meets the standard objections put to the old. However, I argue that the revision runs into difficulties in the context of quantum mechanics: If Stalnaker's theory of the conditional is assumed, then from plausible assumptions certain Bell-like conflicts with experiment can be derived. This result, I go on to argue, is a good reason (...) to reject Stalnaker's theory, at least for the quantum mechanical context. (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)

In this paper I shall be concerned primarily with contingent subjunctive conditionals, not to analyze them, but to argue that those who attempt such an analysis employing the concept of law--an approach which I confess seems promising--are at best providing logically sufficient conditions for the truth of contingent subjunctive conditionals and are not providing a correct analysis. My argument will have two parts. I shall first argue that the more plausible attempts to analyze our concept of law without subjunctive conditionals (...) seem to fall prey to counter-examples. Secondly, I shall argue that even if we had an independent understanding of law, it is at least questionable that such an analysis could be employed in explicating conditions which are both logically necessary and sufficient for the truth of a subjunctive conditional. (shrink)

In addressing the problem of the 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 ) seem to imply that conditionals of freedom are true or false, as Molinists maintain. Noting the resemblance between Molinism and (...) \ models, Restall Molinism: the contemporary debate, pp 227–239, 2011) has advanced some criticisms of Molinism that have also been leveled against \ models. In particular, Restall believes that the implication \ is not true in \ 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 ) the implication \ 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 \ 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 or can be accounted for by these models and so is not a problem for Molinists either. (shrink)

I present and discuss two logical results. The first shows that a non-trivial counterfactual analysis exists for any contingent proposition that is false in at least two possible worlds. The second result identifies a set of conditions that are individually necessary and jointly sufficient for the success of a counterfactual analysis. I use these results to shed light on the question whether disposition ascribing propositions can be analyzed as Stalnaker-Lewis conditional propositions. The answer is that they can, but, in order (...) for a counterfactual analysis to work, the antecedent and consequent must be related in a particular way, and David Lewis’s Time’s Arrow constraints on comparative world similarity must be relaxed. The upshot is that counterfactual analyses are easy to come by, in principle, even if not in practice. In that sense, it’s easy to be iffy. (shrink)

Statements about the future are central in everyday conversation and reasoning. How should we understand their meaning? The received view among philosophers treats will as a tense: in ‘Cynthia will pass her exam’, will shifts the reference time forward. Linguists, however, have produced substantial evidence for the view that will is a modal, on a par with must and would. The different accounts are designed to satisfy different theoretical constraints, apparently pulling in opposite directions. We show that these constraints are (...) jointly satisfied by a novel modal account of will. On this account, will is a modal but doesn't work as a quantifier over worlds. Rather, the meaning of will involves a selection function similar to the one used by Stalnaker in his semantics for conditionals. The resulting theory yields a plausible semantics and logic for will and vindicates our intuitive views about the attitudes that rational agents should have towards future-directed contents. (shrink)

This paper explores the possibility that causal decision theory can be formulated in terms of probabilities of conditionals. It is argued that a generalized Stalnaker semantics in combination with an underlying branching time structure not only provides the basis for a plausible account of the semantics of indicative conditionals, but also that the resulting conditionals have properties that make them well-suited as a basis for formulating causal decision theory. Decision theory (at least if we omit the frills) is not an (...) esoteric science, however unfamiliar it may seem to an outsider. Rather it is a systematic exposition of the consequences of certain well-chosen platitudes about belief, desire, preference and choice. It is the very core of our common-sense theory of persons, dissected out and elegantly systematized. (David Lewis, Synthese 23:331–344, 1974, p. 337). A small distortion in the analysis of the conditional may create spurious problems with the analysis of other concepts. So if the facts about usage favor one among a number of subtly different theories, it may be important to determine which one it is. (Robert Stalnaker, A Defense of Conditional Excluded Middle, pp. 87–104, 1980, p. 87). (shrink)

In this paper, we investigate the semantics and logic of choice-driven counterfactuals, that is, of counterfactuals whose evaluation relies on auxiliary premises about how agents are expected to act, i.e., about their default choice behavior. To do this, we merge one of the most prominent logics of agency in the philosophical literature, namely stit logic, with the well-known logic of counterfactuals due to Stalnaker and Lewis. A key component of our semantics for counterfactuals is to distinguish between deviant and non-deviant (...) actions at a moment, where an action available to an agent at a moment is deviant when its performance does not agree with the agent’s default choice behavior at that moment. After developing and axiomatizing a stit logic with action types, instants, and deviant actions, we study the philosophical implications and logical properties of two candidate semantics for choice-driven counterfactuals, one called rewind models inspired by Lewis, 455–476 1979) and the other called independence models motivated by well-known counterexamples to Lewis’s proposal Slote, 3–27 1978). In the last part of the paper we consider how to evaluate choice-driven counterfactuals at moments arrived at by some agents performing a deviant action. (shrink)

We show that five important elements of the ‘nomological package’— laws, counterfactuals, chances, dispositions, and counterfactuals—needn’t be a problem for the Growing-Block view. We begin with the framework given in Briggs and Forbes (in The real truth about the unreal future. Oxford studies in metaphysics. Oxford University Press, Oxford, 2012 ), and, taking laws as primitive, we show that the Growing-Block view has the resources to provide an account of possibility, and a natural semantics for non-backtracking causal counterfactuals. We show (...) how objective chances might ground a more fine-grained concept of feasibility, and furnished a places in the structure where causation and dispositions might fit. The Growing-Block view, thus understood, provides the resources to explain the close link between modality and tense, so that it predicts modal change as time passes. This account lets us capture not only what the future might hold for us, and also what might have been. (shrink)

A structure is described that can serve as a foundation for a semantics for a modal agentive construction such as sees to it that Q ([ stit: Q]). The primitives are Tree,,Instant, Agent, choice. Eleven simple postulates governing this structure are set forth and motivated. Tree and encode a picture of branching time consisting of moments gathered into maximal chains called histories. Instant imposes a time-like ordering. Agent consists of agents, and choice assigns to each agent and each moment in (...) Tree a set of possible choices, where each possible choice is a set of histories. All of these ingredients are referred to in the semantics suggested for [ stit: Q]. The most complex part of the discussion is the motivation for the definition of what it means for a typically non-terminating chain of moments jointly to witness the truth of [ stit: Q] at a moment.The paper begins with an informal account of the Refref conjecture, which says that the only way to refrain from refraining from seeing to something is to see to it. The paper ends with a consideration of an argument of Prior's that in a certain sense contemplation and action are inconsistent. (shrink)

If we seek to analyse causation in terms of counterfactual conditionals then we must assume that there is a class of counterfactuals whose members (i) are all and only those we need to support our judgements of causation, (ii) have truth-conditions specifiable without any irreducible appeal to causation. I argue that (i) and (ii) are unlikely to be met by any counterfactual analysis of causation. I demonstrate this by isolating a class of counterfactuals called non-projective counterfactuals, or NP-counterfactuals, and indicate (...) how counterfactual analyses of causation must appeal to them to account for the correct causal judgements we make. I show that the truth-conditions of NP-counterfactuals are specifiable only by irreducible appeal to causation. A dilemma then holds: if counterfactual analyses of causation eschew appeal to NP-counterfactuals they are empirically inadequate, but if they appeal to NP-counterfactuals they are circular and thus conceptually inadequate. (shrink)

In this paper I would like to offer a new framework for hypothetical reasoning, with the goal of predicting what scenarios we consider when we interpret a conditional or causal claim (such as a sentence containing the word ‘because‘). The idea is that when we interpret a conditional or causal claim, we identify a part of the world to change and imagine changing that. Sentences are about parts of the world: when we interpret a conditional antecedent or because clause, we (...) allow the part of the world it is about to vary. -/- My main evidence for this approach is that it gives just the right range of hypothetical scenarios to account for how we interpret both conditionals and causal claims. Some approaches (such as Stalnaker and Lewis’s semantics of conditionals based on similarity, and Kratzer’s premise semantics) consider too few scenarios, while others (such as Fine’s truthmaker semantics of conditionals) consider too many. The present approach inhabits a Goldilocks zone between these extremes: not too restrictive, not too permissive, but just right. (shrink)

We investigate the semantics of historical counterfactuals in indeterministic contexts. We claim that "plain" and "necessitated" counterfactuals differ in meaning. To substantiate this claim, we propose a new semantic treatment of historical counterfactuals in the Branching Time framework. We supplement our semantics with supervaluationist postsemantics, thanks to which we can explain away the intuitions which seem to talk in favor of the identification of "would" with "would necessarily".