In this note I discuss what seems to be a new kind of counterexample to Lewis’s account of counterfactuals. A coin is to be tossed twice. I bet on ‘Two heads’, and I win. Common sense says that (1) is false. But Lewis’s theory says that it is true. (1) If at least one head had come up, I would have won.

Any counterfactual with a true antecedent and a true consequent is invariably predicted to be true by the standard Stalnaker–Lewis semantics. But many such true–true counterfactuals appear false to ordinary speakers, which is considered by many authors as evidence that the standard semantics should be revised. However, Walters and Williams prove that allowing true–true counterfactuals to be false would unacceptably invalidate some very plausible logical principles. The objective of this paper (...) is to provide a pragmatic account of seemingly false true–true counterfactuals, which explains why such counterfactuals seem false to ordinary speakers while being true semantically. In particular, a pluralistic pragmatic account is pursued: I argue that some true–trues seem false because they conversationally implicate some falsehood, and some others seem false because the focus (intonation stress) involved in them invokes some pragmatic re‐interpretation that affects speakers' truth‐value judgments. (shrink)

The standard semantics for counterfactuals ensures that any counterfactual with a true antecedent and true consequent is itself true. There have been many recent attempts to amend the standard semantics to avoid this result. I show that these proposals invalidate a number of further principles of the standard logic of counterfactuals. The case against the automatic truth of counterfactuals with true components does not extend to these further principles, however, so it is (...) not clear that rejecting the latter should be a consequence of rejecting the former. Instead I consider how one might defuse putative counterexamples to the truth of true-true counterfactuals. (shrink)

I have argued for a kind of ‘counterfactual scepticism’: most counterfactuals ever uttered or thought in human history are false. I briefly rehearse my main arguments. Yet common sense recoils. Ordinary speakers judge most counterfactuals that they utter and think to be true. A common defence of such judgments regards counterfactuals as context-dependent: the proposition expressed by a given counterfactual can vary according to the context in which it is uttered. In normal contexts, the counterfactuals (...) that we utter are typically true, the defence insists, while granting that there may be more rarefied contexts in which they are false. I give a taxonomy of such contextualist replies. One could be a contextualist about the counterfactual connective, about its antecedent, or about its consequent. I offer some general concerns about all these varieties of contextualism. I then focus especially on antecedent-contextualism, as I call it. I firstly raise some high-level objections to it. Then, I look at such a contextualist account due to Sandgren and Steele. I think it has many virtues, but also some problems. I conclude with some avenues for future research. (shrink)

In the article I discuss possible amendments and corrections to Lewis’s semantics for counterfactuals that are necessary in order to account for the indeterministic and non-local character of the quantum world. I argue that Lewis’s criteria of similarity between possible worlds produce incorrect valuations for alternate-outcome counterfactuals in the EPR case. Later I discuss an alternative semantics which rejects the notion of miraculous events and relies entirely on the comparison of the agreement with respect to individual facts. However, (...) a controversy exists whether to include future indeterministic events in the criteria of similarity. J. Bennett has suggested that an indeterministic event count toward similarity only if it is a result of the same causal chain as in the actual world. I claim that a much better agreement with the demands of the quantum-mechanical indeterminism can be achieved when we stipulate that possible worlds which differ only with respect to indeterministic facts that take place after the antecedent-event should always be treated as equally similar to the actual world. In the article I analyze and dismiss some common-sense counterexamples to this claim. Finally, I critically evaluate Bennett’s proposal regarding the truth-conditions for true-antecedent counterfactuals. (shrink)

In this paper I explore the ambiguity that arises between two readings of the counterfactual construction, then–d and thel–p, analyzed in my bookA Theory of Counterfactuals. I then extend the analysis I offered there to counterfactuals with true antecedents, and offer a more precise formulation of the conception of temporal divergence points used in thel–p interpretation. Finally, I discuss some ramifications of these issues for counterfactual analyses of knowledge.

Early commentators on David Lewis's account of counterfactuals noted that certain examples suggest that some counterfactuals with true antecedents and true consequents are false. Lewis's account has the consequence that all such counterfactuals are true, leaving us to choose between explaining away our intuitions about the examples in question or offering an alternative to Lewis's account. Here I argue that a simple modification of the familiar Lewisian truth conditions yields the intuitively correct verdicts about (...) these examples, and so we can take our intuitions about these examples at face value without any major departure from Lewis's approach to counterfactuals. (shrink)

One criticism of David Lewis's account of counterfactuals is that it sometimes assigns the wrong truth-value to a counterfactual when both antecedent and consequent happen to be true. Lewis has suggested a possible remedy to this situation, but commentators have found this to be unsatisfactory. I suggest an alternative solution which involves a modification of Lewis's truth conditions, but which confines itself to the resources already present in his account. This modification involves the device of embedding one (...) counterfactual within another. On the revised set of truth conditions, counterfactuals with true components are sometimes true and sometimes false, in a way that is more in keeping with our intuitive judgments about such statements. (shrink)

Are counterfactuals with true antecedents and consequents automatically true? That is, is Conjunction Conditionalization: if (X & Y), then (X > Y) valid? Stalnaker and Lewis think so, but many others disagree. We note here that the extant arguments for Conjunction Conditionalization are unpersuasive, before presenting a family of more compelling arguments. These arguments rely on some standard theorems of the logic of counterfactuals as well as a plausible and popular semantic claim about certain semifactuals. Denying (...) Conjunction Conditionalization, then, requires rejecting other aspects of the standard logic of counterfactuals, or else our intuitive picture of semifactuals. (shrink)

Counterfactuals abound in science, especially when reasoning about and with models. This often requires entertaining counterfactual conditionals with nomologically or metaphysically impossible antecedents, namely, counternomics or counterpossibles. In this paper I defend the make-believe view of scientific counterfactuals, a naturalised fiction-based account of counterfactuals in science which provides a means to evaluate their meanings independently of the possibility of the states of affairs their antecedents describe, and under which they have non-trivial truth-values. Fiction is here understood as (...) imagination (in contrast with its most typical association with falsity), characterised as a propositional attitude of pretense or ‘make-believe’ (Walton 1990). The application of this theory to scientific counterfactuals makes their evaluation a game of make-believe: a counterfactual is (fictionally) true iff its antecedent and the rules of the game prescribe the imagining of its consequent (Kimpton-Nye 2020). The result is a practice-based account of counterfactuals and counterfactual reasoning in science which incorporates insights from theoretical and experimental analytic philosophy as well as cognitive science. This way, the make-believe view of scientific counterfactuals shows that the evaluation of scientific counterfactuals is none other than a question of scientific representation in disguise. (shrink)

As the opening line of Dickens' classic novel suggests, it is very often the case that people can imagine both better and worse alternatives to their present reality. Although Dickens was writing about events that occurred over two centuries ago, it remains just as true today that we clearly live in neither the best nor the worst of possible worlds. For instance, we can wish for the amelioration of present difficulties in the Middle East yet still take comfort in (...) the fact that the threat of nuclear war has been greatly reduced since the end of the Cold War. On a more mundane level, it is easy for us to imagine how various aspects of our lives, such as our jobs, marriages, or physical fitness, could be both better and worse. Undoubtedly due to the pervasiveness and intrinsically fascinating qualities of this phenomenon of imagining alternatives to reality, there has been a veritable explosion of research in recent years on what have been termed mental simulation and counterfactual thinking processes. This chapter speculates upon and provides evidence for the antecedents and consequences of two types of counterfactuals: upward (it could have been better) and downward (it could have been worse). The importance of studying the antecedents and consequences of counterfactual direction lie in the differential structures, emotions, intentions, inferences, and behavioral consequences of upward versus downward counterfactual thinking. (shrink)

We present an analysis of counterfactuals in terms of stories and combine it with an account similar to Walton’s account of truth in fiction to yield truth conditions for counterfactuals. We discuss unusual features of this account, and compare it to other main approaches. In particular, we argue that our analysis succeeds in accounting for counterpossibles and counterfactuals with true antecedents while the other two main approaches fail, and we give reasons for thinking that it is (...) important to have an adequate account of these two areas. (shrink)

Kit Fine (1994. “Essence and Modality”, Philosophical Perspectives 8: 1-16) argues that the standard modal account of essence as de re modality is ‘fundamentally misguided’ (p. 3). We agree with his critique and suggest an alternative counterfactual analysis of essence. As a corollary, our counterfactual account lends support to non-vacuism the thesis that counterpossibles (i.e., counterfactual conditionals with impossible antecedents) are not always vacuously true.

Counterfactual Entailment is the view that a counterfactual conditional is true just in case its antecedent entails its consequent. I present an argument for Counterfactual Entailment, and I develop a strategy for explaining away apparent counterexamples to the view. The strategy appeals to the suppositional view of counterfactuals, on which a counterfactual is essentially a statement, made relative to the supposition of its antecedent, of its consequent.

The present thesis focuses on counterfactuals. Specifically, we will address new questions and open problems that arise for the standard semantic accounts of counterfactual conditionals. The first four chapters deal with the Lewisian semantic account of counterfactuals. On a technical level, we contribute by providing an equivalent algebraic semantics for Lewis' variably strict conditional logics, which is notably absent in the literature. We introduce a new kind of algebra and differentiate between local and global versions of each of (...) Lewis' variably strict conditional logics. We study the algebraic properties of Lewis' logics and the structure theory of our newly introduced algebras. Additionally, we employ a new algebraic construction, based on the framework of Boolean algebras of conditionals, to provide an alternative semantics for Lewisian counterfactual conditionals. This semantic account allows us to establish new truth conditions for Lewisian counterfactuals, implying that Lewisian counterfactuals are definable conditionals, and each counterfactual can be characterized as a modality of a corresponding probabilistic conditional. We further extend these results by demonstrating that each Lewisian counterfactual can also be characterized as a modality of the corresponding Stalnaker conditional. The resulting formal semantic framework is much more expressive than the standard one and, in addition to providing new truth conditions for counterfactuals, it also allows us to define a new class of conditional logics falling into the broader framework of weak logics. On the philosophical side, we argue that our results shed new light on the understanding of Lewisian counterfactuals and prompt a conceptual shift in this field: Lewisian counterfactual dependence can be understood as a modality of probabilistic conditional dependence or Stalnakerian conditional dependence. In other words, whether a counterfactual connection occurs between A and B depends on whether it is "necessary" for a Stalnakerian/probabilistic dependence to occur between A and B. We also propose some ways to interpret the kind of necessity involved in this interpretation. The remaining two chapters deal with the probability of counterfactuals. We provide an answer to the question of how we can characterize the probability that a Lewisian counterfactual is true, which is an open problem in the literature. We show that the probability of a Lewisian counterfactual can be characterized in terms of belief functions from Dempster-Shafer theory of evidence, which are a super-additive generalization of standard probability. We define an updating procedure for belief functions based on the imaging procedure and show that the probability of a counterfactual A > B amounts to the belief function of B imaged on A. This characterization strongly relies on the logical results we proved in the previous chapters. Moreover, we also solve an open problem concerning the procedure to assign a probability to complex counterfactuals in the framework of causal modelling semantics. A limitation of causal modelling semantics is that it cannot account for the probability of counterfactuals with disjunctive antecedents. Drawing on the same previous works, we define a new procedure to assign a probability to counterfactuals with disjunctive antecedents in the framework of causal modelling semantics. We also argue that our procedure is satisfactory in that it yields meaningful results and adheres to some conceptually intuitive constraints one may want to impose when computing the probability of counterfactuals. (shrink)

"My argument is as follows. In the first section, I sketch briefly the ways in which intentionalism might provide a solution to the problem of vagueness. The second section describes the different areas in which counterfactuals must be invoked by intentionalism. In the third section I point out that on a classic analysis of counterfactuals - that of David Lewis and Robert Stalnaker - the truth conditions of counterfactuals depend on relations of similarity among possible worlds. Since (...) similarity is vague, so are counterfactuals. Finally, I show that there is no unique solution to the problem of vagueness for the specific types of counterfactuals required by intentionalists - those referring to authors' or legislators' mental states, and those attempting to transport historical authors into the present. Although some counterfactuals are relatively 'insensitive' - in Lewis's sense -- those required in intentionalist interpretation are at least moderately sensitive. This means taht different contexts will resolve the vagueness in different ways. The choice among contexts must be made by the interpreter and is not determined by author's intentions. Hence the vagueness due to counterfactual reasoning about author's intention leads to indeterminacies that cannot be resolved by intentionalism itself. Intentionalism is a solution neither to the problem of vagueness nor to the problem of indeterminacy." Distinguishes between strict intentionalism and moderate intentionalism. Both are often seen as a means for reducing vagueness in legal language. However, counterfactual intentions are needed to resolve certain problems. First, in combining actual intentions, e.g. in a legislature, where different combinations may result in different legislation. Second, it is needed to resolve conflicts between intentions, particularly between different levels of abstraction. Third, reducing vagueness, which will be necessary even with enactment intentions. Fourth, there may be no determinate intention that would even, in principle, resolve a borderline case - e.g. when intentions are conflated. [For discussion of application and enactment intentions, see Goldsworthy, "Originalism in Constitutional Interpretation," Federal Law Review 25: 1.] Lastly, counterfactuals may be necessary to distinguish between application and enactment intentions. Lewis on counterfactuals: "For Lewis and Stalnaker, the key idea in the explication of truth conditions of counterfactuals is that of 'comparative overall similarity' of possible worlds. A counterfactual is true if and only if in the closest, most similar world to the actual in which the antecedent of the conditional is true, the consequent of the conditional is also true." Thus, there may be a determinate relevant world for some cases - i.e. there may be a counterfactual that determines the answer to a counterfactual question. This, however, will not always be the case. For example, counterfactuals concerning Caesar being the leader of N. Korea. Here, for Lewis, where there are ties of closeness of counterfactuals, all tied CFs will be false. When considering counterfactual intentions for the sake of interpretation, some may be determinate or insensitive. Normally, however, this will not be the case. "For intentionalism to resolve the matter of whether the regulation prohibiting vehicles prohibits toy cars as well, one of these counterfactuals must be true and the other false. Imagine a possible world in which the oncsideration of the borderline case is added to the authors' mental states. It is likely that connected belief will be affected as well. For example consideration of the aim of the regulation will occur as a consequence of the consideration of whether the regulation applies to the borderline case: Is ensuring peace and quiet in the park overriding, or are there exceptions to accommodate children's games? When there are changes in a constellation of men tal states, we will have to imagine a situation in whichh the legislators' beleifs are very different from what they in fact were. This creates at least a profound epistemological problem, because, as Dworkin puts it: "[it] has the effect of sharply reducing the amount of historical evidence that is relevant to answering the counterfactual." More important, however, in some worlds in which the legislators consider the case of a child's toy car, they will treat the peace and quiet purpose as overriding, whereas in others they will treat the children's play purpose as overriding. This means that different worlds will resolve the truth-value of the counterfactuals differently." "If I am right that counterfactual reasoning is ubiquitous in intentionalism, intentionalism suffers from an extra dimension of vagueness and is therefore at a disadvantage when measured against theories that do not rely on counterfactuals.". (shrink)

That all subjunctive conditionals with true antecedents and trueconsequents are themselves also true is implied by every plausibleand popularly endorsed account. But I am wary of endorsing thisimplication. I argue that all presently endorsed accounts fail tocapture the nature of certain subjunctive conditionals in contextsof consequentialist reasoning. I attempt to show that we must allowfor the possibility that some subjunctive conditionals with trueantecedents and true consequents are false, if we are to believethat certain types of straightforward consequentialist (...) reasoningare coherent. I begin by evaluating a pair of morally releventcounterfactuals in a case via David Lewis's account. I then turnto a slight modification of the case, arguing that Lewis'ssemantics fails to generate the correct truth values of thesubjunctive conditionals in the modified case. Finally, I presenta modified version of Lewis's semantics that generates the correctresults in all of the cases. (shrink)

The following semantics for counterfactuals is fairly standard: for a counterfactual to be true, the closest antecedent worlds have to be consequent worlds. Closeness is measured by overall similarity of worlds to an evaluation world. There is a range of interrelated challenges to this account: counterfactual scepticism, ‘Hegel’-, ‘Sobel’-, and ‘Heim’-sequences. So far there is no unified solution to these challenges. I discuss a solution that preserves the standard semantics by writing the shifty parameter into pragmatics. The (...) solution has been suggested by Križ for Sobel- and Heim-sequences, yet I argue that it can be generalized to counterfactual scepticism. Conditionals are subject to a pattern which is familiar from descriptions. Everyday counterfactuals are semantically homogeneous and pragmatically non-maximal. Homogeneity: a counterfactual is neither true nor false if only some but not all closest antecedent worlds are consequent worlds. Non-maximality: in many contexts, not all but only practically all closest antecedent worlds have to be consequent worlds for the utterance of a counterfactual to say something true if the difference does not matter for the purposes of conversation. (shrink)

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)

Standard accounts of semantics for counterfactuals confront the true–true problem: when the antecedent and consequent of a counterfactual are both actually true, the counterfactual is automatically true. This problem presents a challenge to safety-based accounts of knowledge. In this paper, drawing on work by Angelika Kratzer, Alan Penczek, and Duncan Pritchard, we propose a revised understanding of semantics for counterfactuals utilizing machinery from generalized quantifier theory which enables safety theorists to meet the challenge (...) of the true–true problem. (shrink)

We construct a causal-modeling semantics for both indicative and counterfactual conditionals. As regards counterfactuals, we adopt the orthodox view that a counterfactual conditional is true in a causal model M just in case its consequent is true in the submodel M∗, generated by intervening in M, in which its antecedent is true. We supplement the orthodox semantics by introducing a new manipulation called extrapolation. We argue that an indicative conditional is true in a causal (...) model M just in case its con- sequent is true in certain submodels M∗, generated by extrapolating M, in which its antecedent is true. We show that the proposed semantics can account for some important minimal pairs nicely and naturally. We also prove a theorem showing under what conditions intervention and extrapolation will yield the same result, and thus explain how counterfactual and indicative conditionals would behave in a causal-modeling semantics. (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)

In this article, I propose a semantic account of temporally mismatched past subjunctive counterfactuals. The proposal consists of the following parts. First, I show that in cases of temporal mismatch, [past] cannot be interpreted inside the proposition where it occurs at surface structure. Instead, it must be interpreted as constraining the time argument of the accessibility relation. This has the effect of shifting the time of the evaluation of the conditional to some contextually salient past time. Second, I will (...) propose specific felicity conditions (presuppositions) for subjunctive conditionals and I will argue that there is a strict correspondence between the time of evaluation in the truth conditions of a conditional and the time relevant for the felicity conditions. In other words, if the time relevant for the accessibility relation has been shifted to the past, then the conditional's presupposition will make reference to a past context. On the other hand, if no past is constraining the time argument of the accessibility relation, the conditional's felicity will make reference to the current (main) context. Third, I will argue that the intuition that the antecedent of mismatched counterfactuals is not true is a scalar implicature arising from a competition not between assertions but between presuppositions. Finally, I will investigate the repercussions of my proposal for the general theory of modality. (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)

Are counterfactuals with true antecedents and consequents trivially true? The principle of Conjunction Conditionalization →) is highly controversial. Many philosophers view it as an attractive feature of Lewis’s semantics for counterfactuals that it can easily be modified to avoid this principle. However, Walters and Williams beg to differ. They argue that Conjunction Conditionalization is an indispensable ingredient of any Lewisian semantics, since CC is entailed by standard Lewisian theorems and a plausible semantic claim about irrelevant semifactuals. (...) If this is true, the entire tradition of revisionist counterfactual semantics is misguided, and so are many philosophical theories in which counterfactuals play a role. We argue, in defense of the revisionist tradition, that Walters and Williams’ ‘plausible semantic claim’ is in fact anything but plausible. It turns out to entail semantic principles far more controversial than Conjunction Conditionalization. (shrink)

In evaluating conditionals concerning what a person would have done in counterfactual circumstances, we suppose the counterfactual antecedent to be true, just as in what I loosely term the standard "Ramsey" procedure; but then we follow a different path--a simulative path--in evaluating the consequent. The simulative path imposes an implicit restriction on possible worlds, a procedural guarantee that the individual simulated is aware of or knows about the counterfactual condition. This difference makes clear the way in which reason (...) explanations are implicitly cognitive and psychological. (shrink)

According to david lewis, When the conditional excluded middle is accepted for would-Asserting counterfactuals, It becomes difficult or impossible to define their might-Asserting counterparts. But I provide a definition of "might" counterfactuals that does agree with cem: a "might" counterfactual is true iff its consequent is true at some antecedent-World within a set whose membership is determined by appeal to various categories of possibility.

The thesis that a temporal asymmetry of counterfactual dependence characterizes our world plays a central role in Lewis’s philosophy, as. among other things, it underpins one of Lewis most renowned theses—that causation can be analyzed in terms of counterfactual dependence. To maintain that a temporal asymmetry of counterfactual dependence characterizes our world, Lewis committed himself to two other theses. The first is that the closest possible worlds at which the antecedent of a counterfactual conditional is true is one (...) in which a small miracle occurs—i.e. one whose laws differ from the actual laws in a small spatiotemporal region. The second is that our world is characterized by a temporal asymmetry of miracles. In this paper, I will argue, first, that the latter thesis is either false or incompatible with the picture of the relations among temporal asymmetries endorsed by Lewis and, second, that former thesis conflicts with some of the intuitions which seem to guide us when engaging in counterfactual reasoning. If there is any fact of the matter as to which possible worlds in which the antecedent of a counterfactual conditional is true are closest to the actual world, these are not worlds at which a small miracle occurs. (shrink)

Granting that there could be true subjunctive conditionals of libertarian freedom (SCLs), I argue (roughly) that there could be such conditionals only in connection with individual "possible creatures" (in contrast to types). This implies that Molinism depends on the view that, prior to creation, God grasps possible creatures in their individuality. In making my case, I explore the notions of counterfactual implication (that relationship between antecedent and consequent of an SCL which consists in its truth) and counterfactual relevance (...) (that feature of an antecedent in virtue of which it counterfactually implies something or other). (shrink)

It is proposed that the recent controversy over "time-symmetric quantum counterfactuals" (TSQCs), based on the Aharonov-Bergmann-Lebowitz Rule for measurements of pre- and post-selected systems, can be clarified by taking TSQCs to be counterfactuals with a specific type of compound antecedent. In that case, inconsistency proofs such as that of Sharp and Shanks (1993) are not applicable, and the main issue becomes not whether such statements are true, but whether they are nontrivial. The latter question is addressed (...) and answered in the negative. Thus it is concluded that TSQCs, understood as counterfactuals with a compound antecedent, are true but only trivially so, and provide no new contingent information about specific quantum systems (except in special cases already identified in literature). (shrink)

I reply to Ahmed’s rejection (2011) of my argument (Walters 2009) that all counterfactuals with true antecedents and consequents are themselves true.

A counterpossible is a counterfactual whose antecedent is impossible. The vacuity thesis says all counterpossibles are true solely because their antecedents are impossible. Recently, some have rejected the vacuity thesis by citing purported non-vacuous counterpossibles in science. One limitation of this work, however, is that it is not grounded in experimental data. Do scientists actually reason non-vacuously about counterpossibles? If so, what is their basis for doing so? We presented biologists (N = 86) with two counterfactual formulations of (...) a well-known model in biology, the antecedents of which contain what many philosophers would characterize as a metaphysical impossibility. Participants consistently judged one counterfactual to be true, the other to be false, and they explained that they formed these judgments based on what they perceived to be the mathematical relationship between the antecedent and consequent. Moreover, we found no relationship between participants’ judgments about the (im)possibility of the antecedent and whether they judged a counterfactual to be true or false. These are the first experimental results on counterpossibles in science with which we are familiar. We present a modal semantics that can capture these judgments, and we deal with a host of potential objections that a defender of the vacuity thesis might make. (shrink)

One popular approach to the metaphysics of dispositional properties takes them to involve ascribing a conditional property, a property corresponding to a conditional statement. This chapter looks at some recent work on the semantics and logic of conditionals, followed by a consideration of Hypotheticalism, Nomism, Neo‐Humeism, and Powerism. It examines directly the question whether Hypotheticalism or Anti‐Hypotheticalism (categoricalism) is correct, and shows how to evaluate counterfactual conditionals. The evaluation of conditionals seems to turn on two sorts of facts about the (...) actual world: the laws of nature, and the true propositions that are co‐tenable with the conditional's antecedent. Strong Hypotheticalists hold that the truths of counterfactual conditionals are fundamental, and that truths about the laws of nature and of powers and dispositions are reducible to them. (shrink)

The traditional Lewis–Stalnaker semantics treats all counterfactuals with an impossible antecedent as trivially or vacuously true. Many have regarded this as a serious defect of the semantics. For intuitively, it seems, counterfactuals with impossible antecedents—counterpossibles—can be non-trivially true and non-trivially false. Whereas the counterpossible "If Hobbes had squared the circle, then the mathematical community at the time would have been surprised" seems true, "If Hobbes had squared the circle, then sick children in the mountains (...) of Afghanistan at the time would have been thrilled" seems false. Many have proposed to extend the Lewis–Stalnaker semantics with impossible worlds to make room for a non-trivial or non-vacuous treatment of counterpossibles. Roughly, on the extended Lewis–Stalnaker semantics, we evaluate a counterfactual of the form "If A had been true, then C would have been true" by going to closest world—whether possible or impossible—in which A is true and check whether C is also true in that world. If the answer is "yes", the counterfactual is true; otherwise it is false. Since there are impossible worlds in which the mathematically impossible happens, there are impossible worlds in which Hobbes manages to square the circle. And intuitively, in the closest such impossible worlds, sick children in the mountains of Afghanistan are not thrilled—they remain sick and unmoved by the mathematical developments in Europe. If so, the counterpossible "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would have been thrilled" comes out false, as desired. In this paper, I will critically investigate the extended Lewis–Stalnaker semantics for counterpossibles. I will argue that the standard version of the extended semantics, in which impossible worlds correspond to maximal, logically inconsistent entities, fails to give the correct semantic verdicts for many counterpossibles. In light of the negative arguments, I will then outline a new version of the extended Lewis–Stalnaker semantics that can avoid these problems. (shrink)

We present four classical theories of counterpossibles that combine modalities and counterfactuals. Two theories are anti-vacuist and forbid vacuously true counterfactuals, two are quasi-vacuist and allow counterfactuals to be vacuously true when their antecedent is not only impossible, but also inconceivable. The theories vary on how they restrict the interaction of modalities and counterfactuals. We provide a logical cartography with precise acceptable boundaries, illustrating to what extent nonvacuism about counterpossibles can be reconciled with (...) classical logic. (shrink)

According to the most popular theories, counterfactuals with impossible antecedents are vacuously true. Critiques of this view argue that contrary to this, we tend to consider only some of them true and others to be false. In his recent paper Timothy Williamson has ingeniously explained the motivations for the orthodox view and argued that although there are some heuristic reasons that may suggest the plausibility of the unorthodox view, they are fallible. The most important of Williamson’s arguments (...) is that the unorthodox interpretation is inconsistent with the heuristic assumption that supposedly motivates this very view. The aim of this paper is to consider Williamson’s critique and to support the unorthodox approach towards counterpossibles. In order to do so, we argue in favor of the modified version of the heuristic assumption. (shrink)

Conditional logics were originally developed for the purpose of modeling intuitively correct modes of reasoning involving conditional—especially counterfactual—expressions in natural language. While the debate over the logic of conditionals is as old as propositional logic, it was the development of worlds semantics for modal logic in the past century that catalyzed the rapid maturation of the field. Moreover, like modal logic, conditional logic has subsequently found a wide array of uses, from the traditional (e.g. counterfactuals) to the exotic (e.g. (...) conditional obligation). Despite the close connections between conditional and modal logic, both the technical development and philosophical exploitation of the latter has outstripped that of the former, with the result that noticeable lacunae exist in the literature on conditional logic. My dissertation addresses a number of these underdeveloped frontiers, producing new technical insights and philosophical applications. -/- I contribute to the solution of a problem posed by Priest of finding sound and complete labeled tableaux for systems of conditional logic from Lewis' V-family. To develop these tableaux, I draw on previous work on labeled tableaux for modal and conditional logic; errors and shortcomings in recent work on this problem are identified and corrected. While modal logic has by now been thoroughly studied in non-classical contexts, e.g. intuitionistic and relevant logic, the literature on conditional logic is still overwhelmingly classical. Another contribution of my dissertation is a thorough analysis of intuitionistic conditional logic, in which I utilize both algebraic and worlds semantics, and investigate how several novel embedding results might shed light on the philosophical interpretation of both intuitionistic logic and conditional logic extensions thereof. -/- My dissertation examines deontic and connexive conditional logic as well as the underappreciated history of connexive notions in the analysis of conditional obligation. The possibility of interpreting deontic modal logics in such systems (via embedding results) serves as an important theoretical guide. A philosophically motivated proscription on impossible obligations is shown to correspond to, and justify, certain (weak) connexive theses. Finally, I contribute to the intensifying debate over counterpossibles, counterfactuals with impossible antecedents, and take—in contrast to Lewis and Williamson—a non-vacuous line. Thus, in my view, a counterpossible like "If there had been a counterexample to the law of the excluded middle, Brouwer would not have been vindicated" is false, not (vacuously) true, although it has an impossible antecedent. I exploit impossible (non-normal) worlds—originally developed to model non-normal modal logics—to provide non-vacuous semantics for counterpossibles. I buttress the case for non-vacuous semantics by making recourse to both novel technical results and theoretical considerations. (shrink)

Counterpossibles are counterfactuals with necessarily false antecedents. The problem of counterpossibles is easiest to state within the "nearest possible world" framework for counterfactuals: on this approach, a counterfactual is true (roughly) when the consequent is true in the "nearest" possible world where the antecedent is true. Since counterpossibles have necessarily false antecedents, there is no possible world where the antecedent is true. On the approach favored by Lewis, Stalnaker, Williamson, and others, counterpossibles (...) are all trivially true. I introduce several arguments against the trivial approach. First, it is counter-intuitive to think that all counterpossibles are true. Second, if all counterpossibles were true, then we could not make sense of their use in logical, philosophical, or mathematical arguments. Making sense of the role of sentences like these requires that they not have vacuous truth conditions. The account of counterpossibles I ultimately favor is an extension of the "nearest possible world" semantics discussed above. The Lewis/Stalnaker account is supplemented with the addition of impossible worlds, and the nearness metric is extended to range over these impossible worlds as well as possible worlds. Thus, a counterfactual is true when its consequent is true in the nearest world where the antecedent is true; if the counterfactual's antecedent is impossible, then the nearest world in question will be an impossible world. Once the framework of impossible worlds and similarity is in place, we can put it to use in the analysis of other philosophical phenomena. I examine one proposal that makes use of a theory of counterpossibles to develop an analysis of the notion of metaphysical dependence. (shrink)

A counterpossible conditional is a counterfactual with an impossible antecedent. Common sense delivers the view that some such conditionals are true, and some are false. In recent publications, Timothy Williamson has defended the view that all are true. In this paper we defend the common sense view against Williamson’s objections.

I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as 'If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,' which is true, and 'If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,' which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counterfactuals, which would treat them as (...) uniformly true. What’s more, I argue that these counterpossibles don’t just appear in the periphery of relative computability theory but instead they play an ineliminable role in the development of the theory. Finally, I present and discuss a model theory for these counterfactuals that is a straightforward extension of the familiar comparative similarity models. (shrink)

Counterpossibles, counterfactuals conditional with impossible antecedents, are notoriously contested; while the standard view makes them trivially true, some authors argue that they can be non-trivially true. In this paper, I examine the use of counterfactuals in the context of games, and argue that there is a case to be made for their non-triviality in a restricted sense. In particular, I examine the case of retro problems in chess, where it can happen that one is tasked with (...) evaluating counterfactuals about illegal positions. If we understand illegality as a type of restricted impossibility, those counterfactuals are non-trivial counterpossibles. I suggest that their non-triviality stems from their role in practices of rule coordination and revision, and suggest that this model could be generalized to counterpossibles in different domains. I then compare the approach to the accounts of Vetter 2016 and Locke 2019. (shrink)

Since the publication of David Lewis’ Counterfactuals, the standard line on subjunctive conditionals with impossible antecedents (or counterpossibles) has been that they are vacuously true. That is, a conditional of the form ‘If p were the case, q would be the case’ is trivially true whenever the antecedent, p, is impossible. The primary justification is that Lewis’ semantics best approximates the English subjunctive conditional, and that a vacuous treatment of counterpossibles is a consequence of that very (...) elegant theory. Another justification derives from the classical lore than if an impossibility were true, then anything goes. In this paper we defend non-vacuism, the view that counterpossibles are sometimes non-vacuously true and sometimes non-vacuously false. We do so while retaining a Lewisian semantics, which is to say, the approach we favor does not require us to abandon classical logic or a similarity semantics. It does however require us to countenance impossible worlds. An impossible worlds treatment of counterpossibles is suggested (but not defended) by Lewis (Counterfactuals. Blackwell, Oxford, 1973), and developed by Nolan (Notre Dame J Formal Logic 38:325–527, 1997), Kment (Mind 115:261–310, 2006a: Philos Perspect 20:237–302, 2006b), and Vander Laan (In: Jackson F, Priest G (eds) Lewisian themes. Oxford University Press, Oxford, 2004). We follow this tradition, and develop an account of comparative similarity for impossible worlds. (shrink)

One well-known objection to the traditional Lewis-Stalnaker semantics of counterfactuals is that it delivers counterintuitive semantic verdicts for many counterpossibles (counterfactuals with necessarily false antecedents). To remedy this problem, several authors have proposed extending the set of possible worlds by impossible worlds at which necessary falsehoods may be true. Linguistic ersatz theorists often construe impossible worlds as maximal, inconsistent sets of sentences in some sufficiently expressive language. However, in a recent paper, Bjerring (2014) argues that the “extended” (...) Lewis-Stalnaker semantics delivers the wrong truth-values for many counterpossibles if impossible worlds are required to be maximal. To make room for non-maximal or partial impossible worlds, Bjerring considers two alternative world-ontologies: either (i) we construe impossible worlds as arbitrary (maximal or partial) inconsistent sets of sentences, or (ii) we construe them as (maximal or partial) inconsistent sets of sentences that are closed and consistent with respect to some non-classical logic. Bjerring raises an objection against (i), and suggests that we opt for (ii). In this paper, I argue, first, that Bjerring’s objection against (i) conflates two different conceptions of what it means for a logic to be true at a world. Second, I argue that (ii) imposes too strong constraints on what counts as an impossible world. I conclude that linguistic ersatzists should construe impossible worlds as arbitrary (maximal or partial) inconsistent sets of sentences. (shrink)

A recent group of social scientists have argued that counterfactual questions play an essential role in their disciplines, and that it is possible to have rigorous methods to investigate them. Unfortunately, there has been little (if any) interaction between these social scientists and the philosophers who have long held that rigorous counterfactual reasoning is possible. In this paper, I hope to encourage some fresh thinking on both sides by creating new connections between them. I describe what I term "problem of (...) selecting antecedent scenarios," and show that this is an essential challenge in real-life counterfactual reasoning. Then, I demonstrate that the major extant theories of counterfactuals (especially the Lewis/Stalnaker theory and Igal Kvart's rival account) are unable to solve this problem. I show that there are instances of real-life counterfactual reasoning in the social sciences that are counterexamples to both of these accounts. And finally, I develop a new theory of how to select antecedent scenarios that overcomes these difficulties, and so would be part of a more adequate theory of counterfactuals (and counterfactual reasoning). (shrink)

Standard accounts of counterfactuals with metaphysically impossible antecedents take them to by trivially true. But recent work shows that nontrivial countermetaphysicals are frequently appealed to in scientific modeling and are indispensable for a number of metaphysical projects. I focus on three recent discussions of counterpossible counterfactuals, which apply counterpossibles in both scientific and metaphysical modeling. I show that a sufficiently developed modal counterpart theory can provide a semantics for a wide range of counterpossibles without any inconsistent possibilities (...) or other forms of impossible worlds. But such a view faces problems: in order for the metaphysical views I discuss to bear weight, there must be a significant difference between the metaphysical possibilities and impossibilities. I will show how the counterpart-theoretic view delineates the possible from impossible, while still making room for the impossible. (shrink)

Counterpossibles are counterfactuals with an impossible antecedent. According to the orthodox view of counterfactuals, all counterpossibles are vacuously true. This is puzzling because some counterpossible statements seem to be false. The paper analyzes two approaches to explaining why certain counterpossibles, though perhaps true, may appear to be false. The first, which appeals to the Gricean mechanism of conversational implicatures, asserts that some counterpossibles appear to be false because their assertion carries with it a false conversational (...) implicature. However, I argue that, under a closer scrutiny, this approach collapses. I therefore turn to a second approach, proposed by Timothy Williamson. It appeals to a heuristic according to which speakers may regard a counterpossible to be false if they have previously accepted its opposite. Since the applicability of Williamson’s solution is limited, I suggest a more general account. Its underlining idea is that a counterpossible is rejected if the speaker cannot find what they regard as a universally true conditional function derivable from the counterpossible by substitutions and syntactic transformations. (shrink)

This article explores three ways in which physics may involve counterpossible reasoning. The first way arises when evaluating false theories: to say what the world would be like if the theory were true, we need to evaluate counterfactuals with physically impossible antecedents. The second way relates to the role of counterfactuals in characterizing causal structure: to say what causes what in physics, we need to make reference to physically impossible scenarios. The third way is novel: to model (...) metaphysical dependence in physics, we need to consider counterfactual consequences of metaphysical impossibilities. Physics accordingly bears substantial and surprising counterpossible commitments. (shrink)

There is at present a certain dispute about counterfactuals taking place. What is at issue is whether counterfactuals with necessarily false antecedents are all true. Some hold that such counterfactuals are vacuously true, appearances notwithstanding. Let us call such people vacuists. Others hold that some counterfactuals with necessarily false antecedents are true; some are false: it just depends on their contents. Let us call such people non-vacuists. As a notable representative of the vacuists, (...) I will take Tim Williamson. On the other side, I will take the position defended by Berto, French, Priest, and Ripley. I will argue (unsurprisingly) that the better choice is Non-Vacuism. That, however, is a subsidiary aim of this paper. The main point is to illustrate the method of theory-choice. (shrink)

A proposal by Baron, Colyvan, and Ripley to extend the counterfactual theory of explanation to include counterfactual reasoning about mathematical explanations of physical facts is discussed. Their suggestion is that the explanatory role of mathematics can best be captured counterfactually. This paper focuses on their example with a number-theoretic antecedent. Incorporating discussions on the structure and de re knowledge of numbers, it is argued that the approach leads to a change in the structure of numbers. As a result, the (...) counterfactual is not about the natural numbers anymore. Linking the antecedent and consequent of the counterfactual also becomes problematic. (shrink)