Williamson has claimed that we assess counterfactuals 'If it were/had been that A, it would be/have been that C' primarily using a combination of two heuristics, both inconsistent: one for the indicative 'if' – essentially, a Ramsey Test for indicatives; one for 'would'. A better candidate for our primary way of assessing counterfactuals has been known for decades. Mathematical results guarantee that it doesn't have certain troubles of the heuristics invoked by Williamson; on some ways of fine-tuning, it (...) may even be rationally ideal. So calling it a 'heuristic' may be uncharitable. (shrink)

If the laws are deterministic, then standard theories of counterfactuals are forced to reject at least one of the following conditionals: 1) had you chosen differently, there would not have been a violation of the laws of nature; and 2) had you chosen differently, the initial conditions of the universe would not have been different. On the relevant readings—where we hold fixed factors causally independent of your choice—both of these conditionals appear true. And rejecting either one leads to trouble (...) for philosophical theories which rely upon counterfactual conditionals—like, for instance, causal decision theory. Here, I outline a semantics for counterfactual conditionals which allows us to accept both (1) and (2). And I discuss how this semantics deals with objections to causal decision theory from Arif Ahmed. (shrink)

Recent literature on non-causal explanation raises the question as to whether explanatory monism, the thesis that all explanations submit to the same analysis, is true. The leading monist proposal holds that all explanations support change-relating counterfactuals. We provide several objections to this monist position. 1Introduction 2Change-Relating Monism's Three Problems 3Dependency and Monism: Unhappy Together 4Another Challenge: Counterfactual Incidentalism 4.1High-grade necessity 4.2Unity in diversity 5Conclusion.

Recently, von Fintel (2001) and Gillies (2007) have argued that certain sequences of counterfactuals, namely reverse Sobel sequences, should motivate us to abandon standard truth conditional theories of counterfactuals for dynamic semantic theories. I argue that we can give a pragmatic account of our judgments about counterfactuals without giving up the standard semantics. In particular, I introduce a pragmatic principle governing assertability, and I use this principle to explain a variety of subtle data concerning reverse Sobel sequences.

To an unusual extent, philosophers agree that counterfactuals have truth conditions involving the most similar possible worlds where their antecedents are true, in the style of the celebrated and path‐breaking Stalnaker/Lewis accounts. Roughly, these accounts say that the counterfactual if A were the case, C would be the case is true if and only if at the most similar A‐worlds, C is true. I will argue that there are general structural problems with the appeals to both “the most” and (...) “similar”. I will challenge any fixation on ‘the most __ worlds’, however we fill in the blank with a non‐trivial ordering of worlds: in ignoring worlds that are later in the ordering, it adjudicates various implausibly specific counterfactuals to be true. I will then raise foundational problems for appealing to ‘similarity’—from consequents that are chancy, disjunctive antecedents, and unspecific antecedents more generally. I will also raise further problems for a number of specific proposals for understanding ‘similarity’. A recurring theme will be the tension that may arise between probability and similarity considerations. I will end by arguing for a paradigm shift, replacing ‘the most similar worlds’ approach with one based on conditional chances. (shrink)

How precisely to understand and evaluate counterfactuals can be an intricate issue. The aim of this article is to examine a new set of difficulties for evaluating counterfactuals that arise in the context of the dynamical spacetimes described by the theory of general relativity (GR). The initial value formulation provides us with a methodology to pin down the specific combination of features of the theory at the origin of the difficulties, namely, non-linearity and certain non-local aspects (typically captured (...) by ellipticity at the analytical level), in particular when combined with the global and/or quasi-local character of physical quantities in GR. Finally, we connect the philosophical question about counterfactuals with concrete applied physical issues in GR about extracting meaningful predictions by constructing appropriate initial data sets, leading us to question the very suitability of the Cauchy approach to fully account for the explanatory power of the theory. (shrink)

In this paper we propose a semantic analysis of Lewis' counterfactuals. By exploiting the structural properties of the recently introduced boolean algebras of conditionals, we show that counterfactuals can be expressed as formal combinations of a conditional object and a normal necessity modal operator. Specifically, we introduce a class of algebras that serve as modal expansions of boolean algebras of conditionals, together with their dual relational structures. Moreover, we show that Lewis' semantics based on sphere models can be (...) reconstructed in this framework. As a consequence, we establish the soundness and completeness of a slightly stronger variant of Lewis' logic for counterfactuals with respect to our algebraic models. In the second part of the paper, we present a novel approach to the probability of counterfactuals showing that it aligns with the uncertainty degree assigned by a belief function, as per Dempster-Shafer theory, to its associated conditional formula. Furthermore, we characterize the probability of a counterfactual in terms of Gärdenfors' imaging rule for the probabilistic update. (shrink)

In this paper two paradoxes of infinity are considered through the lens of counterfactual logic, drawing heavily on a result of Fine (2012b). I will argue that a satisfactory resolution of these paradoxes will have wide ranging implications for the logic of counterfactuals. I then situate these puzzles in the context of the wider role of counterfactuals, connecting them to indicative conditionals, probabilities, rationality and the direction of causation, and compare my own resolution of the paradoxes to alternatives (...) inspired by the theories of Lewis and Fine. Here is a quick overview of the paper. Sections 17.1 and 17.2 introduce two paradoxes of infinity that rest on certain principals concerning the logic of counterfactuals. Section 17.3 considers three possible ways to weaken the counterfactual logic that would resolve these paradoxes, and examines three concrete theories of conditionals which make those weakenings — Lewis (1973), Fine (2012a) and Bacon (2015). With the first two theories found wanting, Sect. 17.4 develops my preferred solution in (Bacon, 2015) a little further, and provides some simple models to show that the paradoxes can indeed be resolved in that framework. (shrink)

This paper investigates the interpretation of counterfactual conditionals. The main goal of the paper is to provide an account of the semantic role of similarity in the evaluation of counterfactuals. The paper proposes an analysis according to which counterfactuals are treated as predications “ de re ” over past situations in the actual world. The relevant situations enter semantic composition via the interpretation of tense. Counterfactuals are treated as law-like conditionals with de re predication over particular facts. (...) Similarity with respect to particular facts is ensured by the semantics of tense in interaction with the modal, while the modal itself is responsible for invoking laws. In the paper, various arguments are provided to support a local view of similarity over the global approach found in semantics along the line of Lewis’s and Stalnaker’s. Arguments are also provided tying the evaluation of similarity to the interpretation of tense. Finally, arguments are provided to show that in key cases, the approaches make comparable predictions. (shrink)

Is A & C sufficient for the truth of ‘if A were the case, C would be the case’? Jonathan Bennett thinks not, although the counterexample he gives is inconsistent with his own account of counterfactuals. In any case, I argue that anyone who accepts the case of Morgenbesser's coin, as Bennett does, should reject Bennett’s counterexample. Moreover, I show that the principle underlying his counterexample is unmotivated and indeed false. More generally, I argue that Morgenbesser’s coin commits us (...) to the sufficiency of A & C for the truth of the corresponding counterfactual. (shrink)

Alan Hájek (2024) argues for counterfactual skepticism, the view that many (or “most”) counterfactuals are false. In this paper, I consider what Hájek's semantic position looks like when we pair it with a MacFarlane (2008, 2014)‐style relativist postsemantics. On this view, a counterfactual utterance may start out false, but later come to be assessed as true—even if the counterfactual's antecedent and consequent express eternalist propositions. The package view, which I call chancy relativism, preserves Hájek's metaphysical commitments but pairs smoothly (...) with speakers' intuitions about retrospective assessments. (shrink)

I argue that there are three different sorts of counterfactuals involved in causal investigation and counterfactual history and that these counterfactuals range from the relatively unproblematic to the hopelessly speculative. This threefold distinction undermines a central argument in support of counterfactual history and supports the critics’ contention that counterfactual history involves speculative leaps not found in ordinary historical investigations. I conclude, however, by proposing an alternative methodology for counterfactual history, one that avoids counterfactuals of the hopelessly speculative (...) variety. (shrink)

On the standard analysis, a counterfactual conditional such as “If P had been the case, then Q would have been the case” is true in the actual world if, in all nearest possible worlds in which its antecedent (P) is true, its consequent (Q) is also true. Despite its elegance, this analysis faces a difficulty if the laws of nature are deterministic. Then the antecedent could not have been true, given prior conditions. So, it is unclear what the relevant “nearest (...) possible worlds” are. David Lewis suggested that they are ones in which a local breach of the laws occurred: a “small miracle”. Others have suggested that they are ones in which the initial conditions were different (“backtracking”). I propose another response. It builds on the idea that the special sciences, where counterfactual reasoning is most common, operate at a higher level of description from fundamental physics, and that the world may behave indeterministically at higher levels even if it behaves deterministically at the fundamental physical one. The challenge from determinism can then be bypassed for many special-science counterfactuals. (shrink)

How do people attribute responsibility in situations where the contributions of multiple agents combine to produce a joint outcome? The prevalence of over-determination in such cases makes this a difficult problem for counterfactual theories of causal responsibility. In this article, we explore a general framework for assigning responsibility in multiple agent contexts. We draw on the structural model account of actual causation (e.g., Halpern & Pearl, 2005) and its extension to responsibility judgments (Chockler & Halpern, 2004). We review the main (...) theoretical and empirical issues that arise from this literature and propose a novel model of intuitive judgments of responsibility. This model is a function of both pivotality (whether an agent made a difference to the outcome) and criticality (how important the agent is perceived to be for the outcome, before any actions are taken). The model explains empirical results from previous studies and is supported by a new experiment that manipulates both pivotality and criticality. We also discuss possible extensions of this model to deal with a broader range of causal situations. Overall, our approach emphasizes the close interrelations between causality, counterfactuals, and responsibility attributions. (shrink)

This paper supplies a computational model, via Logic Programming (LP), of counterfactual reasoning of autonomous agents with application to morality. Counterfactuals are conjectures about what would have happened had an alternative event occurred. The first contribution of the paper is showing how counterfactual reasoning is modeled using LP, benefiting from LP abduction and updating. The approach is inspired by Pearl’s structural causal model of counterfactuals, where causal direction and conditional reasoning are captured by inferential arrows of rules in (...) LP. Herein, LP abduction hypothesizes background conditions from given evidence or observations, whereas LP updating frame these background conditions as a counterfactual’s context, and then imposes causal interventions on the program through defeasible LP rules. The second contribution it to apply counterfactuals to agent morality using this LP-based approach. We demonstrate its potential for specifying and querying moral issues, by examining viewpoints on moral permissibility via classic moral principles and examples taken from the literature. Application results were validated on a prototype implementing the approach on top of an integrated LP abduction and updating system supporting tabling. (shrink)

von Fintel and Gillies : 329–360, 2007) have proposed a dynamic strict conditional account of counterfactuals as an alternative to the standard variably strict account due to Stalnaker and Lewis. Von Fintel’s view is motivated largely by so-called reverse Sobel sequences, about which the standard view seems to make the wrong predictions. More recently Moss :561–586, 2012) has offered a pragmatic/epistemic explanation that purports to explain the data without requiring abandonment of the standard view. So far the small amount (...) of subsequent literature has focused primarily on the original class of cases motivating the strict conditional view. What is needed in the debate is an examination of the predictions of the dynamic strict conditional account for a broader range of data. I undertake this task here, presenting a slew of cases that are problematic for the strict conditional view but not for Moss’s view, and considering some possible responses. Ultimately I take my contribution to constitute a significant blow to the dynamic strict conditional view, though not a decisive verdict against it. (shrink)

Probabilities figure centrally in much of the literature on the semantics of conditionals. I find this surprising: it accords a special status to conditionals that other parts of language apparently do not share. I critically discuss two notable ‘probabilities first’ accounts of counterfactuals, due to Edgington and Leitgeb. According to Edgington, counterfactuals lack truth values but have probabilities. I argue that this combination gives rise to a number of problems. According to Leitgeb, counterfactuals have truth conditions-roughly, a (...) counterfactual is true when the corresponding conditional chance is sufficiently high. I argue that problems arise from the disparity between truth and high chance, between approximate truth and high chance, and from counterfactuals for which the corresponding conditional chances are undefined. However, Edgington, Leitgeb and I can unite in opposition to Stalnaker and Lewis-style ‘similarity’ accounts of counterfactuals. (shrink)

This paper offers two novel conceptual tools: one concerning the semantics of counterfactuals and what should be held fixed when assessing them (the modal moat), and the other concerning the pragmatics of counterfactual assertions and how to avoid the potential pitfalls of meaning more than we say (antecedent gluttony). These allow us to address existing issues with the assessment of backwards counterfactuals within a framework that applies equally to forwards cases. In addition to solving a thorny problem from (...) the time travel literature, what we learn teaches us something quite general about our evaluation of counterfactuals. (shrink)

Philosophers typically rely on intuitions when providing a semantics for counterfactual conditionals. However, intuitions regarding counterfactual conditionals are notoriously shaky. The aim of this paper is to provide a principled account of the semantics of counterfactual conditionals. This principled account is provided by what I dub the Royal Rule, a deterministic analogue of the Principal Principle relating chance and credence. The Royal Rule says that an ideal doxastic agent’s initial grade of disbelief in a proposition \(A\) , given that the (...) counterfactual distance in a given context to the closest \(A\) -worlds equals \(n\) , and no further information that is not admissible in this context, should equal \(n\) . Under the two assumptions that the presuppositions of a given context are admissible in this context, and that the theory of deterministic alethic or metaphysical modality is admissible in any context, it follows that the counterfactual distance distribution in a given context has the structure of a ranking function. The basic conditional logic V is shown to be sound and complete with respect to the resulting rank-theoretic semantics of counterfactuals. (shrink)

How are causal judgements such as 'The ice on the road caused the traffic accident' connected with counterfactual judgements such as 'If there had not been any ice on the road, the traffic accident would not have happened'? This volume throws new light on this question by uniting, for the first time, psychological and philosophical approaches to causation and counterfactuals. Traditionally, philosophers have primarily been interested in connections between causal and counterfactual claims on the level of meaning or truth-conditions. (...) More recently, however, they have also increasingly turned their attention to psychological connections between causal and counterfactual understanding or reasoning. At the same time, there has been a surge in interest in empirical work on causal and counterfactual cognition amongst developmental, cognitive, and social psychologists--much of it inspired by work in philosophy. In this volume, twelve original contributions from leading philosophers and psychologists explore in detail what bearing empirical findings might have on philosophical concerns about counterfactuals and causation, and how, in turn, work in philosophy might help clarify the issues at stake in empirical work on the cognitive underpinnings of, and relationships between, causal and counterfactual thought. (shrink)

This paper extends Fine’s truthmaker semantics for counterfactuals along two dimensions: first, while Fine’s semantics is only positive, this paper also provides falsification conditions for counterfactuals; second, this paper also deals with non-vacuous counterpossibles, i.e., counterfactuals with a necessarily false antecedent, from within the truthmaker semantics perspective.

I assess the thesis that counterfactual asymmetries are explained by an asymmetry of the global entropy at the temporal boundaries of the universe, by developing a method of evaluating counterfactuals that includes, as a background assumption, the low entropy of the early universe. The resulting theory attempts to vindicate the common practice of holding the past mostly fixed under counterfactual supposition while at the same time allowing the counterfactual's antecedent to obtain by a natural physical development. Although the theory (...) has some success in evaluating a wide variety of ordinary counterfactuals, it fails as an explanation of counterfactual asymmetry. (shrink)

The paper proposes a solution to the problem of counterfactuals, building on both Rescher’s epistemic and Tichý’s semantic approaches. The core of the proposed solution is the thesis that when expressing a true counterfactual, the speaker assumes a set of background indicative premises as an implicit parameter. When added tacitly to an unreal antecedent, these premises entail the consequent logically or analytically. We draw a distinction between a potentially unreal and an absolutely unreal condition expressed in the antecedent. We (...) view counterfactuals with a positive time vector and an absolute unreal condition as abbreviated deductive retrodictions. Similarly, we consider counterfactuals with a potentially unreal condition to be abbreviated deductive predictions. In a similar manner, we also explain the truth (falsity) of vacuously true counterpossibles or counterpossible conditionals. In the second part, we discuss the enigmatic backtracking counterfactuals. We propose that their negative time direction is due to their being abductive retrodictions, i.e., explanations of unreal effects based on possible causes in which the conditions remain tacit or unexpressed. The backtracking temporal direction of counterfactual abductive retrodictions is in accordance with the thesis on the positive temporal direction from cause to effect. Thus, we demonstrate that in order to explain backtracking counterfactuals, there is no need to assume violations of laws of nature or a special logic. What we need to do is to take into account the third parameter, i.e., a set of tacit or unexpressed additional propositions, as well as the principle of ceteris paribus as the background. (shrink)

This chapter starts with Goodman's project, saying what his aim was, spelling out the resources that he allowed himself to use in order to accomplish this aim, and explaining why the aim could not be accomplished with these resources. The author considers Goodman's response to the acknowledged failure of his initial attempt at analysis: how he proposed to redefine his Humean project. The chapter sketches David Lewis's project, which has two parts: an abstract formal semantic analysis of conditionals, and an (...) attempt to explain the primitive parameters of the semantic models in a way that is austere enough to satisfy the Humean structures. The author argues that Lewis does not succeed in identifying a suitable base for a reduction of counterfactuals and other causal notions. The chapter concludes with a brief remark on the problems that remain if we reject the project of Humean reduction. (shrink)

If one flips an unbiased coin a million times, there are 2 1,000,000 series of possible heads/tails sequences, any one of which might be the sequence that obtains, and each of which is equally likely to obtain. So it seems (1) 'If I had tossed a fair coin one million times, it might have landed heads every time' is true. But as several authors have pointed out, (2) 'If I had tossed a fair coin a million times, it wouldn't have (...) come up heads every time' will be counted as true in everyday contexts. And according to David Lewis' influential semantics for counterfactuals, (1) and (2) are contradictories. We have a puzzle. We must either (A) deny that (2) is true, (B) deny that (1) is true, or (C) deny that (1) and (2) are contradictories, thus rejecting Lewis' semantics. In this paper I discuss and criticize the proposals of David Lewis and more recently J. Robert G. Williams which solve the puzzle by taking option (B). I argue that we should opt for either (A) or (C). (shrink)

One stark difference between the past and the future lies in our ability to shape the future in a way in which we are unable to shape the past. This paper investigates what kind of beliefs about the future serve as premises in our reasoning about how to act. If we think about belief in terms of agents representing the world, we cannot lose sight of the fact that agents are part of, and shape, the same world they represent. Beliefs (...) about the future appear to have a circularity about them: on the one hand, they serve as premises for deciding what we will do. On the other hand, what we decide we will do determines what we believe about the future. I argue that beliefs in future-directed counterfactuals play a central role in our practical reasoning and in how we conceptualize the actual future. I defend a robust distinction between future-directed counterfactuals and future-directed indicatives, and, contra Keith DeRose (2010), argue that it is future-directed counterfactuals that we use in deliberation about how to act. I argue that we construe the actual future in hypothetical terms and dependent on what we do now, in contrast to how we construe the actual past. This asymmetry in our belief content about the past versus the future fits well with an account of the open future in terms of counterfactual dependence. (shrink)

This paper strengthens a triviality result by Santorio (2022, Analysis) for the probability of counterfactuals. The best response may be to drop the idea that the probability of counterfactuals behaves classically.

Counterfactuals is David Lewis' forceful presentation of and sustained argument for a particular view about propositions which express contrary to fact conditionals, including his famous defense of realism about possible worlds and his theory of laws of nature.

When patients are in vegetative states and their lives are maintained by medical devices, their surrogates might offer proxy consents on their behalf in order to terminate the use of the devices. The so-called ’substituted judgment thesis’ has been adopted by the courts regularly in order to determine the validity of such proxy consents. The thesis purports to evaluate proxy consents by appealing to putative counterfactual truths about what the patients would choose, were they to be competent. The aim of (...) this paper is to reveal a significant limitation of the thesis, which has hitherto been recognised only vaguely and intuitively. By appealing to the metaphysics of counterfactuals I explain how the thesis fails to determine the validity of proxy consents in a number of actual cases. (shrink)

One of the most popular answers to the grue puzzle appeals to counterfactual dependence. An observed green emerald is grue. But while it still would have been green even if unobserved, if unobserved it would not have been grue. Because of this, or something like it, we can project ‘green’ but not ‘grue’ to the unobserved emeralds. Counterfactual theories have been offered by Frank Jackson and Peter Godfrey-Smith, among others. But there is a worry that all counterfactual approaches to grue (...) fail for the same reason—counterfactual symmetry. The grue theorist can endorse symmetrical counterfactuals: an observed green emerald would have been grue but not green if unobserved. It then seems that counterfactual responses to grue beg the question. Here I argue that there are two ways to understand this challenge and that they both fail, but for different reasons. I close by drawing some general lessons about philosophical fair play regarding the twentieth century’s many broadly semantic, broadly skeptical challenges—grue, quus, gavagai, and the like. (shrink)

In this paper we study selected argument forms involving counterfactuals and indicative conditionals under uncertainty. We selected argument forms to explore whether people with an Eastern cultural background reason differently about conditionals compared to Westerners, because of the differences in the location of negations. In a 2x2 between-participants design, 63 Japanese university students were allocated to four groups, crossing indicative conditionals and counterfactuals, and each presented in two random task orders. The data show close agreement between the responses (...) of Easterners and Westerners. The modal responses provide strong support for the hypothesis that conditional probability is the best predictor for counterfactuals and indicative conditionals. Finally, the grand majority of the responses are probabilistically coherent, which endorses the psychological plausibility of choosing coherence-based probability logic as a rationality framework for psychological reasoning research. (shrink)

A criticism of Dorothy Edgington's attempt to make Gibbard's problem for indicative conditionals apply to counterfactuals.

The history of how philosophers have dealt with thought experiments in science is the main focus of this special issue. Counterfactual analysis is an interesting subset of thought experiments because it requires the imagination of alternative states of the world (cf also Fearon (1996), Lebow & Stein (1996), Reiss (2009), Tetlock and Belkin (1996) who suggest the same). In historical analysis, the use of imagination is often the focus of criticisms of such counterfactual analysis. In this paper I consider three (...) strategies for constraining imagination; making limited counterfactual changes, limiting counterfactual changes to decisions of important figures, and using evidence to restrict the scope for imagination. Given the focus of this special issue, I will relate this discussion to Lewis’ and Woodward’s analysis of counterfactuals in the philosophy of science. I show that counterfactual analysis in historical cases has some resemblance to Lewis’ and Woodward’s analysis, but that what Lewis calls “transition periods” cannot be left entirely vague, as Lewis suggests, nor can counterfactual changes be seen simply as interventions, as Woodward suggests. I propose that efforts to limit imagination in historical counterfactuals are ultimately problematic, but that imagination can nevertheless play a useful role in counterfactual analysis. (shrink)

It is widely held that, as Morgenbesser’s case is usually taken to show, considerations of causal or probabilistic dependence should enter into the evaluation of counterfactuals. This paper challenges that idea. I present a modified version of Morgenbesser’s case and show how probabilistic approaches to counterfactuals are in serious trouble. Specifically, I show how probabilistic approaches run into a dilemma in characterizing probabilistic independence. The modified case also illustrates a difficulty in defining causal independence. I close with a (...) suggestion for a strategy to handle this difficulty. (shrink)

Book synopsis: Philosophers have long been fascinated by the connection between cause and effect: are 'causes' things we can experience, or are they concepts provided by our minds? The study of causation goes back to Aristotle, but resurged with David Hume and Immanuel Kant, and is now one of the most important topics in metaphysics. Most of the recent work done in this area has attempted to place causation in a deterministic, scientific, worldview. But what about the unpredictable and chancey (...) world we actually live in: can one theory of causation cover all instances of cause and effect? (shrink)

Review of Kment, "*Modality and Explanatory Reasoning*, with an emphasis on counterfactuals.

We define a formal semantics of conditionals based on _normatively ideal worlds_. Such worlds are described informally by Armgardt (Gabbay D, Magnani L, Park W, Pietarinen A-V (eds) Natural arguments: a tribute to john woods, College Publications, London, pp 699–708, 2018) to address well-known problems of the counterfactual approach to causation. Drawing on Armgardt’s proposal, we use iterated conditionals in order to analyse causal relations in scenarios of multi-agent interaction. This results in a refined counterfactual approach to causal responsibility in (...) legal contexts, which solves overdetermination problems in an intuitively accessible manner. (shrink)

What is offered here is an interpretation of Hume’s views on causation. While it might not be literally Hume’s view, it is certainly consistent with Hume, and is probably what Hume should say on causation, in light of recent developments in science and logic. As a way in, it is argued that the considerations that Hume brings against rationalist theories of causation can be applied to counterfactual theories of causation. Since, counterfactuals, possible worlds and modality were not ideas that (...) would have been overly familiar to Hume, some supplementation of Hume’s arguments will be necessary. (shrink)