Semantics For Counterfactuals Research Articles

From Dispositions to Possible Worlds

AbstractDispositions (powers, potentialities) have become popular in metaphysics in recent years, and some of their proponents are advertising them as the best metaphysical grounds for modality. This project has a logical as well as an ontological side: dispositionalists offer modal and counterfactual semantics that make no use of possible worlds. I argue that, as a result of their counterfactual semantics, dispositionalists are in fact committed to entities that play the same theoretical role as possible worlds. Roughly, the claim is that certain counterfactuals (ones that concern 'very large' states) force the dispositionalist to posit world-sized states that play the theoretical role of worlds. As a result, dispositionalists can (and perhaps should) make use of the mainstream framework (Kripke frames and the Lewis–Stalnaker counterfactual semantics) even if they ground all modal facts in dispositions.

Ambifictional Counterfactuals

In this paper, I argue that David Lewis’s possible world semantics for counterfactual discourse and for fictional discourse are apparently inconsistent and in need of revision. The problem emerges for Lewis’s account once one considers how to evaluate ambifictional counterfactuals. Since this is likely not a concept familiar to most, and since it does not appear that the problem has been previously recognized in the critical literature, I will begin by rehearsing Lewis’s possible worlds semantics for counterfactuals and fiction. Then I will explicate the distinction between intrafictional, extrafictional, interfictional, and ambifictional propositions. Next, I will state what an ambifictional counterfactual proposition is, and explain why this kind of discourse confounds Lewis’s system. I will conclude, finally, with a brief discussion of how the Lewisian would be best advised to resolve the paradox.

Backtracking through interventions: An exogenous intervention model for counterfactual semantics

Causal models show promise as a foundation for the semantics of counterfactual sentences. However, current approaches face limitations compared to the alternative similarity theory: they only apply to a limited subset of counterfactuals and the connection to counterfactual logic is not straightforward. This article addresses these difficulties using exogenous interventions, where causal interventions change the values of exogenous variables rather than structural equations. This model accommodates judgments about backtracking counterfactuals, extends to logically complex counterfactuals, and validates familiar principles of counterfactual logic. This combines the interventionist intuitions of the causal approach with the logical advantages of the similarity approach.

What embedded counterfactuals tell us about the semantics of attitudes.

We discuss German examples where counterfactuals restricting an epistemic modal are embedded under glauben ‘believe’. Such sentences raise a puzzle for the analysis of counterfactuals, modals, and belief attributions within possible-worlds semantics. Their truth conditions suggest that the modal’s domain is determined exclusively by the subject’s belief state, but evaluating the counterfactual separately at each of the subject’s doxastic alternatives does not yield the correct quantificational domain: the domain ends up being determined by the facts of each particular world, which include propositions the subject does not believe. We therefore revise the semantics of counterfactuals: counterfactuals still rely on an ordering among worlds that can be derived from a premise set (Kratzer, Angelika. 1978. Semantik der Rede: Kontexttheorie – Modalwörter – Konditionalsätze (Monographien Linguistik und Kommunikationswissenschaft 38). Königstein: Scriptor, 2012 [1981]a. The notional category of modality. In Modals and conditionals (Oxford studies in theoretical linguistics 36), 27–69. Oxford: Oxford University Press), but rather than uniquely characterizing a world, this premise set can be compatible with multiple worlds. In belief contexts, the attitude subject’s belief state as a whole determines the relevant ordering. This, in turn, motivates a revision of the semantics of believe: following Yalcin’s work on epistemic modals (Yalcin, Seth. 2007. Epistemic modals. Mind 116. 983–1026), we submit that evaluation indices are complex, consisting of a world and an ordering among worlds. Counterfactuals are sensitive to the ordering component of an index. Attitude verbs shift both components, relativizing the ordering to the attitude subject.

Alternatives in Counterfactuals: What IsRightand What IsNot

AbstractClassical semantics for counterfactuals is based on a notion of minimal change: If ${\textsf {A}}$, would ${\textsf {C}}$ says that the worlds that make ${\textsf {A}}$ true and that are otherwise minimally different from the actual world are ${\textsf {C}}$-worlds. This semantics suffers from a well-known difficulty with disjunctive antecedents (see e.g. Alonso-Ovalle, 2009; Willer, 2018; Santorio, 2018, a.o.). In a recent study, Ciardelli, Zhang, and Champollion (Ciardelli et al., 2018b; henceforth, CZC) present new, related difficulties for the classical approach having to do with unpredicted differences between counterfactuals with De Morgan-equivalent antecedents, and related pattern of inferences. They propose a new semantics for counterfactuals, which builds on inquisitive semantics (see Ciardelli et al., 2018a) and gives up on minimal change. Building on this debate, we report on a series of experiments that investigate the role of overt negation in this data. Our results replicate CZC’s main effects, but they also indicate that those effects are linked to the presence of overt negation. We propose a novel account, based on three key assumptions: (i) the semantics for counterfactuals does involve a notion of minimal change, after all; (ii) the meanings of disjunction and negation are associated with alternatives, which interact with the meaning of counterfactuals; (iii) the alternatives generated by negation are partially determined by the question under discussion (QUD). We compare our account with other existing accounts, including CZC’s own proposal, as well as Schulz (2019) and Bar-Lev & Fox (2020) ones.

Choice-Driven Counterfactuals

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 (Belnap et al. 2001; Horty 2001), with the well-known logic of counterfactuals due to Stalnaker (1968) and Lewis (1973). 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 (Nous13(4), 455–476 1979) and the other called independence models motivated by well-known counterexamples to Lewis’s proposal Slote (Philos. Rev.87(1), 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.

Morgenbesser’s Coin

AbstractBefore a fair, indeterministic coin is tossed, Lucky, who is causally isolated from the coin-tossing mechanism, declines to bet on heads. The coin lands heads. The consensus is that the following counterfactual is true:(M:) If Lucky had bet heads, he would have won the bet.It is also widely believed that to rule (M) true, any plausible semantics for counterfactuals must invoke causal independence. But if that’s so, the hope of giving a reductive analysis of causation in terms of counterfactuals is undermined. Here I argue that there is compelling reason to question the assumption that (M) is true.

Language-based Decisions

In Savage's classic decision-theoretic framework, actions are formally defined as functions from states to outcomes. But where do the state space and outcome space come from? Expanding on recent work by Blume, Easley, and Halpern (BEH), we consider a language-based framework in which actions are identified with (conditional) descriptions in a simple underlying language, while states and outcomes (along with probabilities and utilities) are constructed as part of a representation theorem. Our work expands the role of language from that of BEH by using it not only for the conditions that determine which actions are taken, but also the effects. More precisely, we take the set of actions to be built from those of the form "do(phi)", for formulas phi in the underlying language. This presents a problem: how do we interpret the result of do(phi) when phi is underspecified (i.e., compatible with multiple states)? We answer this using tools familiar from the semantics of counterfactuals: roughly speaking, do(phi) maps each state to the "closest" phi-state. This notion of "closest" is also something we construct as part of the representation theorem; in effect, then, we prove that (under appropriate assumptions) the agent is acting as if each underspecified action is first made definite and then evaluated (i.e., by maximizing expected utility). Of course, actions in the real world are often not presented in a fully precise manner, yet agents reason about and form preferences among them all the same. Our work brings the abstract tools of decision theory into closer contact with such real-world scenarios.

What Killed Your Plant? Profligate Omissions and Weak Centering

This paper is on the problem of profligate omissions. The problem is that counterfactual definitions of causation identify as a cause anything that could have prevented an effect but that did not actually occur, which is a highly counterintuitive result. Many solutions of this problem appeal to normative, epistemic, pragmatic, or metaphysical considerations. These existing solutions are in some sense substantive. In contrast, this paper concentrates on the semantics of counterfactuals. I propose to replace Strong Centering with Weak Centering. This allows that the actual world is not the only world that is closest to the actual world. As a result, some counterfactuals that would otherwise have been true, turn out to be false. When these counterfactuals concern causation, fewer causal claims are true. In addition to describing steps towards solving the problem of profligate omissions, the proposal captures an abstraction that is shared by many of the existing solutions: depending on how the distance ordering underlying the Weak Centering condition is constructed and interpreted, some of these existing solutions can be recovered.

Counterfactual similarity, nomic indiscernibility, and the paradox of quidditism

ABSTRACT Aristotle is essentially human; that is, for all possible worlds metaphysically consistent with our own, if Aristotle exists, then he is human. This is a claim about the essential property of an object. The claim that objects have essential properties has been hotly disputed, but for present purposes, we can bracket that issue. In this essay, we are interested, rather, in the question of whether properties themselves have essential properties (or features) for their existence. We call those who suppose they do ‘property essentialists’; those who do not, ‘property anti-essentialists,’ or ‘quidditists.’ We offer two complementary arguments. Our total argument is under-girded by two assumptions: transworld identity theory and ‘received view’ counterfactual semantics, a la David Lewis. We then argue that, if one presumes that these are true, then one risks running headlong into paradox if one also accepts property anti-essentialism. That’s the first argument. By contrast, if one accepts these same assumptions in conjunction with property essentialism, then the paradox is avoided. This is the second argument. We take it that our arguments work to show that, between property essentialism and quidditism, the property essentialist is on better footing. Plausibly, properties themselves do have essential properties for their existence.

Calculus and counterpossibles in science

A mathematical model in science can be formulated as a counterfactual conditional, with the model’s assumptions in the antecedent and its predictions in the consequent. Interestingly, some of these models appear to have assumptions that are metaphysically impossible. Consider models in ecology that use differential equations to track the dynamics of some population of organisms. For the math to work, the model must assume that population size is a continuous quantity, despite that many organisms (e.g., rabbits) are necessarily discrete. This means our counterfactual representation of the model can have an impossible antecedent, giving us a counterpossible. Analogous counterpossibles arise in other sciences, as we’ll see. According to a prominent view in counterfactual semantics, the vacuity thesis, all counterpossibles are vacuously true, that is, true merely because their antecedents are necessarily false. But some counterpossible formulations of differential equation models in science are not all vacuously true—some are non-vacuously true, and some are false. I go on to show how an alternative semantics, one that employs impossible worlds, can deliver this judgment.

The non-maximality-solution to counterfactual scepticism

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.

Heim Sequences and Why Most Unqualified ‘Would’-Counterfactuals Are Not True

ABSTRACT The apparent consistency of Sobel sequences (example below) famously motivated David Lewis to defend a variably strict conditional semantics for counterfactuals. If Sophie had gone to the parade, she would have seen Pedro. If Sophie had gone to the parade and had been stuck behind someone tall, she would not have seen Pedro. But if the order of the counterfactuals in a Sobel sequence is reversed—in the example, if (b) is asserted prior to (a)—the second counterfactual asserted no longer rings true. This is the Heim sequence problem. That the order of assertion makes this difference is surprising on the variably strict account. Some argue that this is reason to reject the Lewis-Stalnaker semantics outright. Others argue that the problem motivates a contextualist rendering of counterfactuals. Still others maintain that the explanation for the phenomenon is merely pragmatic. I argue that none of these is right, and I defend a novel way to understand the phenomenon. My proposal avoids the problems faced by the alternative analyses and enjoys independent support. There is, however, a difficulty for my view: it entails that many ordinarily accepted counterfactuals are not true. I argue that this (apparent) cost is acceptable.

Relevance first: relocating similarity in counterfactual semantics

The last several decades of research on counterfactual conditionals in the fields of philosophy and linguistics have yielded a predominant paradigm according to which the notion of similarity plays the starring role. Roughly, a counterfactual of the form A > C (if A were the case, C would be the case) is true iff the closest A-worlds are all Cworlds, where the closeness of a world is a function of its similarity, in a certain sense, to the actual world. I argue that this is deeply misguided. In some cases we may only care about the closest A-worlds, but quite often we care about some broader variety of A-worlds varying in closeness. After presenting several problem cases for the similarity-based paradigm, some new and some known, I propose an alternative paradigm for the semantics of counterfactuals, which introduces the notion of Ascenarios, understood roughly as different ways of making A true. According to this view, A > C is true iff all the contextually relevant ways of making A true also make C true. I then more carefully spell out a working view that formalizes this idea with greater precision, and explore the consequences of that version of the view.

Counterfactuals, counteractuals, and free choice

In a recent paper, Pruss (Can J Philos 43:430–437, 2013) proves the validity of the rule beta-2 relative to Lewis’s semantics for counterfactuals, which is a significant step forward in the debate about the consequence argument. Yet, we believe there remain intuitive counter-examples to beta-2 formulated with the actuality operator and rigidified descriptions. We offer a novel and two-dimensional formulation of the Lewisian semantics for counterfactuals and prove the validity of a new transfer rule according to which a new version of the consequence argument can be formulated. This new transfer rule is immune to the counter-examples involving the actuality operator and rigidified descriptions. However, we show that counter-examples to this new rule can also be generated, demanding that the Lewisian semantics be generalized for higher dimensions where counter-examples can always be generated.

Précis of "Transformative Experience"

As we live our lives, we repeatedly make decisions that affect our future circumstances and shape the sort of person we will become. Some of these are major, life-changing decisions. In such cases, we stand at a personal crossroads and must choose our direction. If we make these sorts of life-changing decisions about our futures rationally, can we also make them authentically? In Transformative Experience I argue that, under the most natural and ordinary construal of decisions like this, we cannot. My argument draws on debates in philosophy of mind about how experience is necessary for us to have certain epistemic capacities and cognitive abilities. It also draws on debates about the intrinsic value of subjective color experience, and the importance of the first-personal perspective in understanding the self and its possibilities. I use familiar examples from these classic philosophical debates to raise new questions about experience, its value, and its role in prospectively assessing our first personal futures. Using formal tools drawn from decision theory, causal modeling, and cognitive science, I assess first personal decision making and self-construction in contexts of what I call “transformative decision-making”, a well-defined and—it turns out—very common choice situation in everyday life. In the Afterword, I discuss how the argument has formal applications in and substantive relevance to counterfactual semantics, formal epistemology, and the philosophy of statistics, social science, cognitive science and psychology.

Should Special Science Laws Be Written into the Semantics of Counterfactuals?

Abstract Adam Elga has presented an anti-thermodynamic process as a counterexample to Lewis’s default semantics for counterfactuals. The outstanding reaction of Jonathan Schaffer and Boris Kment is revisionary. It sacrifices Lewis’s aim of defining causation in terms of counterfactual dependence. Lewis himself suggested an alternative: «counter-entropic funnybusiness» should make for dissimilarity. But how is this alternative to be spelled out? I discuss a recent proposal: include special science laws, among them the laws of thermodynamics. Although the proposal fails, it serves to uncover the limits of Elga’s example.

The Neo-Molinist Square Stands Firm

In a previous issue of Philosophia Christi, Kirk MacGregor responded to an essay of mine in which I argued for a neo-Molinist account of open theism. The argument demonstrated how, given standard counterfactual semantics, one could derive an “open future square of opposition,” that is, a depiction of the logical relations that hold between future-tense statements from an open theistic standpoint. Conceding the validity of the argument, MacGregor nevertheless sought to deny its soundness by criticizing both its conclusion and the Stalnaker-Lewis semantics on which the argument was based. In this paper, I argue that MacGregor’s reasons for rejecting the open future square, as well as his Molinist alternative to the Stalnaker-Lewis semantics, are uncompelling.

Wierenga on theism and counterpossibles

Several theists, including Linda Zagzebski, have claimed that theism is somehow committed to nonvacuism about counterpossibles. Even though Zagzebski herself has rejected vacuism, she has offered an argument in favour of it, which Edward Wierenga has defended as providing strong support for vacuism that is independent of the orthodox semantics for counterfactuals, mainly developed by David Lewis and Robert Stalnaker. In this paper I show that argument to be sound only relative to the orthodox semantics, which entails vacuism, and give an example of a semantics for counterfactuals countenancing impossible worlds for which it fails.

Conjunction Conditionalization and Irrelevant Semifactuals

Are counterfactuals with true antecedents and consequents trivially true? The principle of Conjunction Conditionalization ((A˄C)→(A>C)) 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 (2013) 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.