Impossible Worlds

[Draft of October 2024] David Lewis acclimated us to talk of “nonactual concreta that exist,” regarding talking donkeys and the like. I shall argue that this was not for the best, and try to normalize a way of describing them as “actual concreta that do not exist.” The basis of this is a defense of the Meinongian thesis “there are objects of which it is true that there are no such objects,” re: fictitious and illusory objects. I first formulate the (...) problem of negative existentials in a novel way, and discuss why this new version is more forceful against anti-Meinongians. Additional data is also pressed against anti-Meinongians--e.g., the truth of ‘Pegasus is imaginary’, and a reading of ‘There actually are illusory objects’ where it comes out true. The Meinongian, in contrast, easily and uniformly explains the same data, by allowing the existence Pegasus, pink elephants, and the like. But contra Meinong, these cases suggest that the nonexistent objects are mind-dependent objects, and I clarify and defend this suggestion from several objections. The resulting Meinongianism is thus “conservative” in that it merely acknowledges the sense in which there are mind-dependent objects, imaginary and illusory objects being prime examples. Of special note, the “ideology” is conservative as well in that the typical Meinongian jargon of “nuclear” or “encoded” properties is paraphrased away. New suggestions about the ontology of abstracta, mere possibilia, and impossibilia are sketched in light of this. Comparisons are also made with Crane and McGinn, among others. (shrink)

The dogma that the propositional logic of metaphysical modality is S5 is rebutted in related installments (previously published and unpublished essays).

In this discussion note I reply to some criticisms that Marc Lange (2022) has directed at my Humean view of scientific laws (Bhogal, 2020) -- about whether Humean views can make sense of the apparent fact that laws are counterfactually invariant. The key idea of my response is that the Humean should think of their reduction of the laws to the Humean mosaic as closely related to other views where we reduce one domain to another but still allow that the (...) higher-level domain can be `autonomous' of the lower-level in some respects -- like, for example, the view that the special sciences reduce to physics but can still can work autonomously of physics. (shrink)

Humean accounts of chance have a problem with undermining futures: they have to accept that some series of events are physically possible and have a nonzero chance but are inconsistent with the chances being what they are. This contradicts basic platitudes about chances (such as those given by Bigelow et al. (1993) and Schaffer (2007)) and leads to inconsistency between plausible constraints on credences. We show how Humeans can avoid these contradictions by drawing on metaphysically impossible worlds that are, nevertheless, (...) scientifically possible. One major advantage of our approach is that one single move deals with these both problems, whereas previous Humean approaches to undermining (such as that given by Lewis (1994), Thau (1994), and Hall (1994)) have only addressed the connection between credence and chance. Furthermore, our approach connects more closely with the way we employ stochastic scientific theories. And it’s part of a unified solution to other challenges that the Humean faces. (shrink)

At first glance, impossible world semantics appear to be useful adaptations of normal modal logic. Proponents of impossible worlds argue, e.g., that in the context of metaphysical disagreement, impossible worlds would provide a key to modelling the respective dispute situation. The same philosophers also argue that we need impossible worlds to model what they consider to be the conceivability of logical impossibilities. With the help of Wittgenstein’s early philosophy, or, better said, with what I believe to be a visualisation of (...) his ideas on nesting models for possibility, I develop some thoughts on the likely shared weaknesses of such arguments for nonnormal world approaches. Said goes hand in hand with the supplementary proposal of rethinking our conventional nesting models for possibility. (shrink)

What is the connection between valid inference and true conditionals? Many conditional logics require that when A is a logical consequence of B, "if B then A" is true. Taking counterlogical conditionals seriously leads to systems that permit counterexamples to that general rule. However, this leaves those of us who endorse non-trivial accounts of counterpossible conditionals to explain what the connection between conditionals and consequence is. The explanation of the connection also answers a common line of objection to non-trivial counterpossibles, (...) which is based on a transition from valid arguments to the corresponding conditionals. It also contributes to the wider project of illuminating the connections between contexts of utterance, on the one hand, and the truth-conditions of conditionals uttered in those contexts, on the other. (shrink)

An alternative to the classical Stalnaker-Lewis account of subjunctive conditionals is outlined. A distinction is drawn between a basic notion of “wouldness” and a more full-bloodedly modal variant, each with its own logic. Previous philosophers have challenged the alleged vacuity of counterpossibles using logico-mathematically impossible worlds. Here the vacuity thesis as well as other orthodox alleged logical principles are challenged instead through consideration of a logico-mathematically possible world. The impossible-world theorist’s Strangeness of Impossibility Condition is also challenged using the same (...) logico-mathematically possible world. The dogma that the truth-condition of a subjunctive invokes the antecedent worlds sufficiently “closest” to (most like) the actual world is also challenged through consideration of the same logico-mathematically possible world. The dogma is a variation on Lewis’s counterpart theory, and is flawed in the same way. (shrink)

The problem of counterpossibles concerns the truth-values of counterfactuals with impossible antecedents. This paper approaches the issue from the perspective of truthmaker semantics (TMS). I argue that, despite its hyperintensional character, TMS ultimately assigns the same truth-value to all counterpossibles. Consequently, TMS fails to satisfy the unorthodoxy postulate, according to which some counterpossibles are true while others are false.

I address objections to impossible worlds (IWs) by Timothy Williamson and Kit Fine. Two species of IWs Mark Jago and I had in our Impossible Worlds book were FDE worlds (worlds used in the semantics of the nonclassical logic of First Degree Entailment) and open worlds (worlds not closed under any non-trivial logical consequence relation). Williamson attacks the idea that propositional contents are sets of open worlds; but we explicitly disavowed that very idea. He endorses uses of IWs we developed, (...) except he calls these ‘pseudo-worlds’. In Angellic Content (AC), Fine champions a truthmaker semantics and in Constructing the Impossible advocates its superiority over IWs. But his semantics also includes states that are IWs, as characterized in the literature: representations of absolute impossibilities. They are like Barwise and Perry’s situations – which is how FDE worlds have been interpreted for decades. A key difference between AC and FDE is that only the latter validates ‘absorption principles’ one may find unwelcome in a characterization of propositional content. But a more topic-sensitive FDE can make them fail. Williamson has also objected to the idea of giving truth(making) and falsity(making) conditions separately, as in both AC and FDE. But FDE can work with truth conditions only and the compatibility semantics for negation. AC can work the same way. (shrink)

One strategy sometimes employed in defense of realism about impossible fiction is the endorsement of the principle of poetic license. While the principle of poetic license has become the focus of much discussion on impossible fiction, I argue that the principle of poetic license is neither necessary nor sufficient for realism about impossible fiction. The principle can be strengthened so as to entail realism about impossible fiction, but I argue that the strengthened principle is empirically inadequate given the data provided (...) by fictionality puzzles. I then provide a different argument from existential generalization for realism about impossible fiction which does not rely on either variant of the principle of poetic license. I suggest that this position, which leaves open the possibility that certain sets of propositions could not be jointly true-in-fiction, accommodates the data provided by fictionality puzzles and is more theoretically attractive than an account that endorses either variant of the principle of poetic license. Following which, I defend realism about impossible fiction from error theories about impossible fiction. (shrink)

There has been a sharp increase in the use of impossible worlds as theoretical tools for solving difficult philosophical problems. Some philosophers, however, warn against their use. For example, Timothy Williamson argues that impossible worlds should not be used in an analysis of conditionals because they do not provide a compositional semantics. In this paper, we set out to resolve some of the potential problems associated with impossible worlds, thereby providing justification for their uses in a variety of contexts and (...) applications. Graham Priest provides two directives for an account of impossible worlds. We argue that Priest’s directives, and, thus, the traditional view on impossibility, overextend the class of impossible worlds. We argue that all worlds, possible or impossible, are describable and that nonsense cannot play a role in a proper description. So, putative worlds that include nonsense are not worlds at all, possible or impossible. The exclusion of nonsense sentences from worlds undermines Priest’s two directives, but by separating nonsense from impossibility, we can resolve many of the worries about the use of impossible worlds. (shrink)

We investigate how compositionality can be preserved when modeling semantic content within an impossible worlds framework based on linguistic ersatzism. After a critical assessment of an existing technique due to Francesco Berto and Mark Jago, we illustrate how to overcome its limitations. We introduce a general method for recovering compositionality across a broad range of alternative notions of content and synonymy, as induced by the syntactic characterizations of popular conceptivist logics. Finally, we discuss the advantages and limitations of the strategy, (...) and conclude with some further critical remarks on linguistic ersatzism. (shrink)

It is widely held that metaphysical modality is the broadest non-epistemic, alethic modality, and that /a posteriori/ modal essentialist truths, like that gold has atomic number 79, enjoy the necessity of the broadest alethic modality. One prominent argument for these conclusions--given by Cian Dorr, John Hawthorne, and Juhani Yli-Vakkuri--rests upon an extremely dubious premise: that certain pairs of properties—e.g., being gold and being made of atoms containing 79 protons—are one and the very same property. The two properties are seen to (...) be distinct on independent philosophical grounds. Metaphysical modality is in fact a restricted alethic modality. In particular, mathematical modality is broader than metaphysical modality. Arguably, the broadest alethic modality is logical modality, which is distinct from metaphysical modality. Even if it is metaphysically necessary that gold have atomic number 79, there is no logical/analytical inconsistency in the supposition that it does not. (shrink)

A new argument is offered which proceeds through epistemic possibility (for all S knows, p), cutting a trail from modality to Millianism, the controversial thesis that the semantic content of a proper name is simply its bearer. New definitions are provided for various epistemic modal notions. A surprising theorem about epistemic necessity is proved. A proposition p can be epistemically necessary for a knowing subject S even though p is /a posteriori/ and S does not know p. The identity relation (...) is well-behaved in metaphysically possible worlds but can go rogue in epistemically possible worlds. Whereas it can be epistemically possible that Lewis Carroll is not Charles Lutwidge Dodgson, this is not epistemically possible in the manner that anti-Millianism requires. (shrink)

Starting with considerations on why one would want hyperintensional theories of content, this thesis engages in an exploration of three main strands in contemporary hyperintensional semantics and metaphysics: impossible worlds semantics, subject matter theory and truthmaker semantics. Its central claim is that the best hyperintensional theories for various purposes use important insights from these three ways of doing semantics. Starting with a space of possible worlds and expanding it, as Berto and Jago (2019) do, to a space of ‘open’ impossible (...) worlds, we get too anarchic a space of worlds, however closing it under any logical consequence relation, like FDE, we idealize too much if our goal is to model realistic epistemic agents. Adding subject matters (Silva, 2024a) helps to find a happy middle ground. This leaves open the question of how to characterize subject matters, and here the notion of exact verification, I argue, helps in defining a new notion of what we may call `topical truthmaking' which in turn helps define the notion of a subject matter. Closing the circle, recently Berto and Jago (2023) have argued that truthmaker semantics and impossible worlds semantics are notational variants of one another, save for the former’s emphasis on exact verification. I myself argue for this equivalence (Silva, 2024c) by showing that the ontology presupposed by standard truthmaker semantics, as presented in (Fine, 2017a), is the same as the one employed by Berto and Jago (2019). Having developed the aforementioned theoretical background in the first part of the thesis, I then apply the hyperintensional framework in the second part. Namely, I do so to: epistemic logic; the demarcation of the logical vocabulary; and transfeminist philosophy. Longer proofs were saved for a formal appendix. (shrink)

Some philosophers advance the claim that the phenomena of logical omniscience and of the indiscernibility of metaphysical statements, which arise in (certain) interpretations of normal modal logic, provide strong reasons in favour of impossible world approaches. These two specific lines of argument will be presented and discussed in this paper. Contrary to the recent much-held view that the characteristics of these two phenomena provide us with strong reasons to adopt impossible world approaches, the view defended here is that no such (...) ‘knock-down arguments’ do emanate on those grounds. This is not to rule out that there cannot be any other good reasons for assuming impossible world semantics. However, the discussion of a further argument for impossible worlds will suggest that different attempts to argue for them likely present intertwined problems. (shrink)

Recently, Yudkowsky and Soares (2018) and Levinstein and Soares (2020) have developed a novel decision theory, Functional Decision Theory (FDT). They claim FDT outperforms both Evidential Decision Theory (EDT) and Causal Decision Theory (CDT). Yet FDT faces several challenges. First, it yields some very counterintuitive results (Schwarz 2018; MacAskill 2019). Second, it requires a theory of counterpossibles, for which even Yudkowsky and Soares (2018) and Levinstein and Soares (2020) admit we lack a “full” or “satisfactory” account. Here, I focus on (...) the latter problem of counterpossibles. My aim is to establish two claims. First, the problem of counterpossibles does not even arise without a fairly strong assumptionone that rarely applies to human agents, but may apply to artificial agents. And second, even given this assumption, the problem is solvable, though how best to solve it remains an open question. (shrink)

Real human agents, even when they are rational by everyday standards, sometimes assign different credences to objectively equivalent statements, such as ‘Orwell is a writer’ and ‘E.A. Blair is a writer’, or credences less than 1 to necessarily true statements, such as not-yet-proven theorems of arithmetic. Anna Mahtani calls this the phenomenon of ‘opacity’. Opaque credences seem probabilistically incoherent, which goes against a key modelling assumption of probability theory. I sketch a modelling strategy for capturing opaque credence assignments without abandoning (...) probabilistic coherence. I draw on ideas from judgement-aggregation theory, where we face similar challenges of defining the ‘objects of judgement’. (shrink)

Saul Kripke’s work on the semantics of non-normal modal logics introduced the idea of non-normal worlds, worlds where certain connectives behave differently from the way in which they behave in the worlds of normal modal logics. Such worlds may be thought of as impossible worlds, though Kripke did not, himself, talk of them in this way. Since Kripke’s invention, the notion of an impossible world has undergone much fruitful development and application. Impossible worlds may be of different kinds—or maybe different (...) degrees of impossibility; and these worlds have found application in many areas where hyperintensionality appears to play a significant role: intentional mental states, counterfactuals, meaning, property theory, to name but a few areas. But what, exactly, is an impossible world? How is it best to characterise the notion? To date, the notion is used more by example than by definition. In this paper I will investigate the question, and propose a general characterisation, suitable for all standard purposes and tastes. (shrink)

This book argues for the importance and commonness of reasonings concerning impossibilities. Its aim is twofold – descriptive and constructive. Since hypothetical reasoning about impossibilities calls for explanation, the book provides a comprehensive guide through popular semantic theories of conditionals. Each is examined from the perspective of the question of impossibilities and the logic and metaphysics surrounding them. This provides the ground for a further aim. In the final chapter, I endeavor to combine the best features of the existing theories (...) and explore the possibility of a novel hybrid account. (shrink)

Developments in truthmaker semantics for the most part stay clear of the metaphysical issue of what sort of entities serve as the truthmakers and falsitymakers for sentences. It is assumed that perhaps facts or states of affairs (Fine 2017a; Jago 2020), with these taken sometimes as concrete particulars (Hawke 2018) could serve for the job, but nonetheless that some such entities would do. In this paper I take a closer look at the issue of what entities could or could not (...) play the role of truthmakers and falsitymakers in standard truthmaker semantics (Fine 2016, 2017a, b; Fine and Jago 2019), based on desiderata imposed by metaphysical and semantic considerations. (shrink)

In this paper, I develop an algorithmic impossible-worlds model of belief and knowledge that provides a middle ground between models that entail that everyone is logically omniscient and those that are compatible with even the most egregious kinds of logical incompetence. In outline, the model entails that an agent believes (knows) φ just in case she can easily (and correctly) compute that φ is true and thus has the capacity to make her actions depend on whether φ. The model thereby (...) captures the standard view that belief and knowledge ground are constitutively connected to dispositions to act. As I explain, the model improves upon standard algorithmic models developed by Parikh, Halpern, Moses, Vardi, and Duc, among other ways, by integrating them into an impossible-worlds framework. The model also avoids some important disadvantages of recent candidate middle-ground models based on dynamic epistemic logic or step logic, and it can subsume their most important advantages. (shrink)

Possible worlds have revolutionised philosophy and some related fields. But, in recent years, tools based on possible worlds have been found to be limited in many respects. Impossible worlds have been introduced to overcome these limitations. This Element aims to raise and answer the neglected question of what is characteristically impossible about impossible worlds. The Element sheds new light on the nature of impossible worlds. It also aims to analyse the main features and utility of impossible worlds and examine how (...) impossible worlds can capture distinctions which are unavailable if we limit ourselves to possible world-based tools. (shrink)

Actual facts abound and actual propositions are true because there is a world, the actual world, that the propositions correctly describe. Possibilities abound as well. The actual world reveals what there is, but it is far from clear that it also reveals what there might be. Philosophers have been aware of this limitation and have introduced the notion of a possible world. Finally, impossibilities abound because it turned out that possibilities do not exhaust the modal space as a whole. Beside (...) the actual facts, and facts about the possible, there are facts about what is impossible. In order to explain this, philosophers have introduced the notion of an impossible world. -/- This article is about impossible worlds. First, there is a presentation of the motivations for postulating impossible worlds as a tool for analysing impossible phenomena. This apparatus seems to deliver great advances in modal logic and semantics, but at the same time it gives rise to metaphysical issues concerning the nature of impossible worlds. Discourse about impossible worlds is explained in Sections 2 and 3. Section 4 provides an overview of the theories in discussion in the academic literature, and Section 5 summarises the drawbacks of those theories. Section 6 takes a closer look at the logical structure of impossible worlds, and Section 7 discusses the connection between impossible worlds and hyperintensionality. (shrink)

In this paper we discuss how Causal Decision Theory should be modified to handle a class of problematic cases involving deterministic laws. Causal Decision Theory, as it stands, is problematically biased against your endorsing deterministic propositions (for example it tells you to deny Newtonian physics, regardless of how confident you are of its truth). Our response is that this is not a problem for Causal Decision Theory per se, but arises because of the standard method for assessing the truth of (...) certain counterfactuals. The truth of deterministic laws is `modally fragile' on the standard semantics for counterfactuals: if determinism is true and you were to do otherwise, the laws would be different. We provide two ways of avoiding this problem: 1) supplement the standard semantics for counterfactuals with impossible worlds, or 2) introduce rigid designators into the description of problematic decision situations. We argue that both of these approaches are well-motivated and can be readily incorporated into Lewisian Causal Decision Theory. (shrink)

A great deal has been written about 'would' counterfactuals of causal dependence. Comparatively little has been said regarding 'would' counterfactuals of ontological dependence. The standard Lewis-Stalnaker semantics is inadequate for handling such counterfactuals. That's because some of these counterfactuals are counterpossibles, and the standard Lewis-Stalnaker semantics trivializes for counterpossibles. Fortunately, there is a straightforward extension of the Lewis-Stalnaker semantics available that handles counterpossibles: simply take Lewis's closeness relation that orders possible worlds and unleash it across impossible worlds. To apply the (...) extended semantics, an account of the closeness relation for counterpossibles is needed. In this paper I offer a strategy for evaluating 'would' counterfactuals of ontological dependence that understands closeness between worlds in terms of the metaphysical concept of grounding. (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.

Some philosophers worry that if modal realism is true, you have no reason to prevent evils. For if you prevent an evil, you’ll have a counterpart somewhere that allows a similar evil. And if you refrain, your counterpart will end up preventing the relevant evil. Either way one evil is prevented and one is allowed. Your act makes no difference. I argue that this is mistaken. If modal realism is true, you are in a variant of Newcomb’s Problem. And if (...) Lewis’ view about Newcomb’s Problem is true, then your act does make a difference and you should prevent the evil. (shrink)

Book Review of Impossible Worlds, by Francesco Berto and Mark Jago. Oxford: Oxford University Press, 2019.

Epistemological accounts that make use of a safety condition on knowledge, historically, face serious problems regarding beliefs that are necessarily true. This is because necessary truths are true in all possible worlds, and so such beliefs can be safe even when the bases for the beliefs are epistemically problematic. The existence of such problematically safe beliefs would undermine a major motivation for the condition itself: the ability to evaluate how well a belief tracks the truth. This paper argues that incorporating (...) impossible worlds into the evaluation of beliefs solves this problem, but only if the relevant account of impossible worlds entails that many impossible worlds are incredibly similar to the actual world. Further, the paper argues that, as a result of including impossible worlds, some philosophical beliefs are unsafe, and many more are potentially unsafe. But, it argues, even if this is the case, we can still make philosophical progress. (shrink)

An overview of hyperintensionality is provided. Hyperintensional languages have expressions with meanings that are more fine-grained than necessary equivalence. That is, the expressions may necessarily co-apply and yet be distinct in meaning. Adequately accounting for theories cast in hyperintensional languages is important in the philosophy of language; the philosophy of mind; metaphysics; and elsewhere. This entry presents a number of areas in which hyperintensionality is important; a range of approaches to theorising about hyperintensional matters; and a range of debates that (...) attention to hyperintensional constructions has generated. (shrink)

A counterpossible is a counterfactual with an impossible antecedent. Counterpossibles present a puzzle for standard theories of counterfactuals, which predict that all counterpossibles are semantically vacuous. Moreover, counterpossibles play an important role in many debates within metaphysics and epistemology, including debates over grounding, causation, modality, mathematics, science, and even God. In this article, we will explore various positions on counterpossibles as well as their potential philosophical consequences.

Sentences about logic are often used to show that certain embedding expressions are hyperintensional. Yet it is not clear how to regiment “logic talk” in the object language so that it can be compositionally embedded under such expressions. In this paper, I develop a formal system called hyperlogic that is designed to do just that. I provide a hyperintensional semantics for hyperlogic that doesn’t appeal to logically impossible worlds, as traditionally understood, but instead uses a shiftable parameter that determines the (...) interpretation of the logical connectives. I argue this semantics compares favorably to the more common impossible worlds semantics, which faces difficulties interpreting propositionally quantified logic talk. (shrink)

Modal knowledge accounts that are based on standards possible-worlds semantics face well-known problems when it comes to knowledge of necessities. Beliefs in necessities are trivially sensitive and safe and, therefore, trivially constitute knowledge according to these accounts. In this paper, I will first argue that existing solutions to this necessity problem, which accept standard possible-worlds semantics, are unsatisfactory. In order to solve the necessity problem, I will utilize an unorthodox account of counterfactuals, as proposed by Nolan, on which we also (...) consider impossible worlds. Nolan’s account for counterpossibles delivers the intuitively correct result for sensitivity i.e. S’s belief is sensitive in intuitive cases of knowledge of necessities and insensitive in intuitive cases of knowledge failure. However, we acquire the same plausible result for safety only if we reject his strangeness of impossibility condition and accept the modal closeness of impossible worlds. In this case, the necessity problem can be analogously solved for sensitivity and safety. For some, such non-moderate accounts might come at too high a cost. In this respect, sensitivity is better off than safety when it comes to knowing necessities. (shrink)

Possible worlds have found many applications in contemporary philosophy: from theories of possibility and necessity, to accounts of conditionals, to theories of mental and linguistic content, to understanding supervenience relationships, to theories of properties and propositions, among many other applications. Almost as soon as possible worlds started to be used in formal theories in logic, philosophy of language, philosophy of mind, metaphysics, and elsewhere, theorists started to wonder whether impossible worlds should be postulated as well. In many applications, possible worlds (...) face limitations that can be dealt with through postulating impossible worlds as well. This chapter examines some of the uses of impossible worlds, and philosophical challenges theories of impossible worlds face. (shrink)

Abstract Impossible fictions have lessons to teach us about linguistic representation, about mental content and concepts, and about uses of conceivability in epistemology. An adequate theory of impossible fictions may require theories of meaning that can distinguish between different impossibilities; a theory of conceptual truth that allows us to make useful sense of a variety of conceptual falsehoods; and a theory of our understanding of necessity and possibility that permits impossibilities to be conceived. After discussing these questions, strategies for resisting (...) the picture of impossible fictions presented here and in Part I are discussed. Perhaps apparently impossible fictions describe possibilities after all; or perhaps impossible fictions are all trivial; or perhaps some apparently intelligible impossible fictions are unintelligible after all. (shrink)

Many explanations rely on identity facts. In this paper, I propose an account of how identity facts explain: roughly, the fact that A is identical to B explains another fact whenever that other fact depends, counterfactually, on A being identical to B. As I show, this account has many virtues. It avoids several problems facing accounts of explanatory identities, and when precisified using structural equations, it can be used to defend interventionist accounts of causation against an objection.

It is widely held that counterfactuals, unlike attitude ascriptions, preserve the referential transparency of their constituents, i.e., that counterfactuals validate the substitution of identicals when their constituents do. The only putative counterexamples in the literature come from counterpossibles, i.e., counterfactuals with impossible antecedents. Advocates of counterpossibilism, i.e., the view that counterpossibles are not all vacuous, argue that counterpossibles can generate referential opacity. But in order to explain why most substitution inferences into counterfactuals seem valid, counterpossibilists also often maintain that counterfactuals (...) with possible antecedents are transparency‐preserving. I argue that if counterpossibles can generate opacity, then so can ordinary counterfactuals with possible antecedents. Utilizing an analogy between counterfactuals and attitude ascriptions, I provide a counterpossibilist‐friendly explanation for the apparent validity of substitution inferences into counterfactuals. I conclude by suggesting that the debate over counterpossibles is closely tied to questions concerning the extent to which counterfactuals are more like attitude ascriptions and epistemic operators than previously recognized. (shrink)

In this paper, we argue that a distinction ought to be drawn between two ways in which a given world might be logically impossible. First, a world w might be impossible because the laws that hold at w are different from those that hold at some other world (say the actual world). Second, a world w might be impossible because the laws of logic that hold in some world (say the actual world) are violated at w. We develop a novel (...) way of modelling logical possibility that makes room for both kinds of logical impossibility. Doing so has interesting implications for the relationship between logical possibility and other kinds of possibility (for example, metaphysical possibility) and implications for the necessity or contingency of the laws of logic. (shrink)

We present a theory of truth in fiction that improves on Lewis's [1978] ‘Analysis 2’ in two ways. First, we expand Lewis's possible worlds apparatus by adding non-normal or impossible worlds. Second, we model truth in fiction as belief revision via ideas from dynamic epistemic logic. We explain the major objections raised against Lewis's original view and show that our theory overcomes them.

This chapter conceptualizes information in terms of ruling out scenarios. It discusses informative identity statements, which give rise to Frege’s puzzle, and the problem understanding how a valid logical inference can be informative. An analysis of informative logical inferences is given, on which the content of a valid deduction is often indeterminate. A consequence is that it is indeterminate exactly which logical inferences are informative. The chapter then analyses a rather different notion of content, concerning _what is said_ by a (...) speaker in making an utterance. (shrink)

Imagination seems to have a logic, albeit one which is hyperintensional and sensitive to context. This chapter offers a semantics of imagination, with operators expressing ‘imaginative acts’ of mental simulation. A number of conditions that could be imposed on the semantics are then discussed, in order to validate certain inferences. One important issue is how acts of imagination interact with disjunction: one can imagine some disjunction as obtaining without being imaginatively specific about which disjunction obtains. This chapter subsequently turns to (...) non-monotonicity: how _B_ may follow from imagining that _A_, but not from imagining that _A_ ∧ _C._ Finally, the _Principle of Imaginative Equivalents_ is discussed. (shrink)

_Vacuism_ is the view that all counterpossibles are trivially true. There are reasons to think it incorrect. An impossible worlds semantics for counterfactuals is offered, which makes room for non-trivial counterpossibles. One principle which pins down its application is the _Strangeness of Impossibility_ condition: for any given possible world, any impossible worlds is further away from it than any possible world is. A number of Williamson’s objections to the non-vacuist approach are discussed and it is argued that they can be (...) overcome. The question of whether counterfactuals in general should permit the substitution of rigidly coreferential terms is then raised. Having defended non-vacusim against Williamson’s objections, a range of arguments in its favour are considered. (shrink)

This chapter introduces normal propositional modal logics, then non-normal systems which invalidate the Necessitation rule (N). It shows how to model these logics using non-normal or impossible worlds, thought of as ‘logic violators’. This approach comes with non-uniform truth conditions: some operators are understood in one way at normal worlds, in another way at non-normal worlds. This may or may not be a problem. The specific case of non-adjunctive and non-prime worlds are then discussed, where conjunction and disjunction can behave (...) in unusual ways. (shrink)

This chapter asks whether hyperintensionality is a genuine phenomenon, or rather, a feature to be explained away. It then focuses on the epistemic case, considering arguments from Stalnaker and Lewis which attempt to explain away hyperintensionality. The argument for a genuinely hyperintensional notion of content is subsequently considered. Having made the case for genuine hyperintensionality, the chapter turns to the _granularity issue_: how fine-grained are impossible worlds? This is one of the most difficult issues any theory of hyperintensionality faces. The (...) focus then returns to the _compositionality objection_ and it is argued that some accounts of impossible worlds deliver a fully compositional theory of meaning. (shrink)

Relevant logics aim to avoid the ‘paradoxes’ of the material and strict conditionals. Their most natural semantics, the _Routley-Meyer semantics_, is given in terms of impossible worlds. By placing certain further conditions on those worlds, we can obtain stronger relevant logics. One of the main philosophical issues surrounding the general approach concerns how to interpret the Routley-Meyer ternary relation on worlds and the Routley star. The information-theoretic interpretation has proved popular but, it is argued, it faces philosophical issues. An alternative (...) interpretation takes its cue from ways of thinking about conditionality in general. The three options are considered, but issues are found with each of them. A final option is the truthmaker interpretation of relevant logics, which is promising but under-developed. (shrink)

Possible worlds are ways things might have been. They find applications in analysing possibility and necessity; propositions; knowledge and belief; information; and indicative and counterfactual conditionals. But possible worlds semantics faces the issue of hyperintensionality, generated by concepts that require distinctions between logical or necessary equivalents. The problems of distinguishing equivalent propositions, of logical omniscience, of information overload, of irrelevant conditionals, and of counterpossible conditionals, are all instances of the general issue. Adding impossible worlds promises to help with these puzzles. (...) But can we genuinely think about the impossible? It is argued that we can. (shrink)

This chapter begins with the problem of what counts as true in a given fiction, beyond what’s explicitly given in that fiction. It then considers the problem of inconsistent fictions, which are naturally handled using impossible worlds. An account of truth in fiction is presented, which develops one of Lewis’s analyses into an approach which can handle inconsistent fictions with ease. The chapter then turns to the second main topic: how we should think about fictional entities. Realism and fictionalism about (...) fictional characters are contrasted. A third option is then considered, which takes the Meinongian line that fictional characters are non-existent objects. Several versions of this idea and their various issues are discussed. (shrink)

Impossible Worlds focuses on an exciting new theory in philosophy, with applications in metaphysics, logic, and the theory of meaning. Its central topic is: how do we meaningfully talk and reason about situations which, unbeknownst to us, are impossible? This issue emerges as a central problem in contemporary philosophical accounts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition. The book is written bytwo of the leading philosophers in the area and contains original research of relevance to professional philosophers (...) and logicians working in metaphysics, philosophy of language, formal logic, and adjacentareas. (shrink)

Ersatz possible worlds can be understood as maximal states of affairs; maximal properties; recombinations of actual bits of reality; as maps; or as entities built from propositions or sentences. The question was: can these approaches be extended to include impossible worlds? The states of affairs approach can, with some modification, accommodate impossible worlds. The property approach too can, with some modification, be extended to impossible worlds. It is argued that the extended approach is best viewed as a form of linguistic (...) ersatzism. The combinatorial faces the question: what _are_ recombinations, metaphysically speaking? This approach collapses into one of the others. Map ersatzism does not seem general enough to accommodate all the impossibilities. The most promising approach is linguistic ersatzism. The chapter discusses an issue all ersatz accounts face: the problem of _aliens_. (shrink)