Impossible Worlds

[Draft substantially revised, September 2021] 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 Thomasson, Crane, and McGinn, among others. (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)

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)

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.

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, 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. In this paper, we’ll argue 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, we’ll argue that, as a result of including impossible worlds, some philosophical beliefs are unsafe, and many more are potentially unsafe. But, we argue, even if this is the case, we can still make philosophical progress. (shrink)

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.

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)

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)

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)

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)

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)

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.

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)

Sentences about logic are often used to show that certain embedding expressions, including attitude verbs, conditionals, and epistemic modals, are hyperintensional. Yet it not clear how to regiment “logic talk” in the object language so that it can be compositionally embedded under such expressions. This paper does two things. First, it argues against a standard account of logic talk, viz., the impossible worlds semantics. It is shown that this semantics does not easily extend to a language with propositional quantifiers, which (...) are necessary for regimenting some logic talk. Second, it develops an alternative framework based on logical expressivism, which explains logic talk using shifting conventions. When combined with the standard S5π+ semantics for propositional quantifiers, this framework results in a well-behaved system that does not face the problems of the impossible worlds semantics. It can also be naturally extended with hybrid operators to regiment a broader range of logic talk, e.g., claims about what laws hold according to other logics. The resulting system, called hyperlogic, is therefore a better framework for modeling logic talk than previous accounts. (shrink)

Nina Emery and Christopher Hill proposed a pragmatic approach toward the debate about counterpossibles—i.e., counterfactuals with impossible antecedents. The core of this approach is to move the burden of the problem from the notion of truth value into the notion of assertion. This is meant to explain our pre-theoretical intuitions about counterpossibles while claiming that each and every counterpossible is vacuously true. The aim of this paper is to indicate a problematic aspect of this view.

Fictionalists maintain that possible worlds, numbers or composite objects exist only according to theories which are useful but false. Hale, Divers and Woodward have provided arguments which threaten to show that fictionalists must be prepared to regard the theories in question as contingently, rather than necessarily, false. If warranted, this conclusion would significantly limit the appeal of the fictionalist strategy rendering it unavailable to anyone antecedently convinced that mathematics and metaphysics concern non-contingent matters. I try to show that their arguments (...) can be resisted by developing and defending a strategy suggested by Rosen, Nolan and Dorr, according to which the fiction-operator is to be analysed in terms of a counterfactual that admits of non-trival truth-values even when the antecedent is impossible. (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.

Galen Strawson’s Basic Argument is that because self-creation is required to be truly morally responsible and self-creation is impossible, it is impossible to be truly morally responsible for anything. I contend that the Basic Argument is unpersuasive and unsound. First, I argue that the moral luck debate shows that the self-creation requirement appears to be contradicted and supported by various parts of our commonsense ideas about moral responsibility, and that this ambivalence undermines the only reason that Strawson gives for the (...) self-creation requirement. Second, I argue that the self-creation requirement is so demanding that either it is an implausible requirement for a species of true moral responsibility that we take ourselves to have or it is a plausible requirement of a species of true moral responsibility that we have never taken ourselves to have. Third, I explain that Strawson overgeneralizes from instances of constitutive luck that obviously undermine moral responsibility to all kinds of constitutive luck. (shrink)

What does it mean for the laws of logic to fail? My task in this paper is to answer this question. I use the resources that Routley/Sylvan developed with his collaborators for the semantics of relevant logics to explain a world where the laws of logic fail. I claim that the non-normal worlds that Routley/Sylvan introduced are exactly such worlds. To disambiguate different kinds of impossible worlds, I call such worlds logically impossible worlds. At a logically impossible world, the laws (...) of logic fail. In this paper, I provide a definition of logically impossible worlds. I then show that there is nothing strange about admitting such worlds. (shrink)

I want to model a finite, fallible cognitive agent who imagines that p in the sense of mentally representing a scenario—a configuration of objects and properties—correctly described by p. I propose to capture imagination, so understood, via variably strict world quantifiers, in a modal framework including both possible and so-called impossible worlds. The latter secure lack of classical logical closure for the relevant mental states, while the variability of strictness captures how the agent imports information from actuality in the imagined (...) non-actual scenarios. Imagination turns out to be highly hyperintensional, but not logically anarchic. Section 1 sets the stage and impossible worlds are quickly introduced in Sect. 2. Section 3 proposes to model imagination via variably strict world quantifiers. Section 4 introduces the formal semantics. Section 5 argues that imagination has a minimal mereological structure validating some logical inferences. Section 6 deals with how imagination under-determines the represented contents. Section 7 proposes additional constraints on the semantics, validating further inferences. Section 8 describes some welcome invalidities. Section 9 examines the effects of importing false beliefs into the imagined scenarios. Finally, Sect. 10 hints at possible developments of the theory in the direction of two-dimensional semantics. (shrink)

Possible-worlds accounts of mental or linguistic content are often criticized for being too coarse-grained. To make room for more fine-grained distinctions among contents, several authors have recently proposed extending the space of possible worlds by "impossible worlds". We argue that this strategy comes with serious costs: we would effectively have to abandon most of the features that make the possible-worlds framework attractive. More generally, we argue that while there are intuitive and theoretical considerations against overly coarse-grained notions of content, the (...) same kinds of considerations also prohibit an overly fine-grained individuation of content. An adequate notion of content, it seems, should have intermediate granularity. However, it is hard to construe a notion of content that meets these demands. Any notion of content, we suggest, must be either implausibly coarse-grained or implausibly fine-grained (or both). (shrink)

In this critical notice of Kment's _Modality and Explanatory Reasoning_, we focus on Kment’s arguments for impossible worlds and on a key part of his discussion of the interactions between modality and explanation – the analogy that he draws between scientific and metaphysical explanation.

Co-hyperintensionality, or hyperintensional equivalence, is a relation holding between two or more contents that can be substituted in a hyperintensional context salva veritate. I argue that two strategies used to provide criteria for co-hyperintensionality fail. I argue that there is no generalized notion of co-hyperintensionality that meets plausible desiderata, by showing that the opposite thesis leads to falsity. As a conclusion, I suggest to take co-hyperintensionality as a primitive and I provide a general criterion of co-hyperintensionality whose content depends on (...) each hyperintensional notion we aim to formalize. (shrink)

What are contents? The answer provided by the possible worlds approach is that contents are sets of possible worlds. This approach incurs serious problems and to solve them Jago suggests, in The Impossible, to get rid of the ‘possible’ bit and allowing some impossible worlds to be part of the game. In this note, I briefly consider the metaphysics behind Jago’s account and then focus on whether Jago is right in thinking that his worlds and his worlds only can do (...) the explanatory work he posits them for. (shrink)

Modal realism is an ontological position made familiar by David Lewis, according to which there exist possible worlds other than the actual world that we inhabit. It is hard to uphold modal realism, and indeed modal realism has only a few advocates. However, as most contemporary metaphysicians agree, this does not mean that it is easy to refute modal realism. In this paper, I argue against modal realism from a metaontological point of view. First, I provide a precise formulation of (...) modal realism based on Lewis’ discussion of modal realism. Second, I argue that modal realism is undermined unless it incorporates a view of metaontology known as ontological realism. Third, I point out that if modal realism incorporates ontological realism, it comes into conflict with its own formulation. (shrink)

Traditional conventionalism about modality claims that a proposition is necessarily true iff it is true by convention. In the wake of the widespread repudiation of truth-byconvention, traditional conventionalism has fallen out of favour. However, a family of theories of modality have arisen that, whilst abandoning truth-by-convention, retain the spirit of traditional conventionalism. These ‘neo-conventionalist’ theories surpass their forebears and don’t fall victim to the criticisms inherited through truth-by-convention. However, not all criticisms levelled at traditional conventionalism target truth-by-convention. Any conventional theory (...) of modality must face the contingency problem. This claims that the contingency of our linguistic conventions jeopardises the necessity of the necessities they determine. I present the contingency problem as relevant to both the traditional conventionalist and the neo-conventionalist. I examine a response from Einheuser that builds upon a response from Wright. I show that the Einheuser response does more to accommodate the conventionalist’s modal beliefs, but that it does not fully satisfy some further conditions that ought to be laid upon such a response. I then suggest how the response can be revised so as to satisfy these conditions. The resulting model of conventionalism is compatible with the validity of S4, and suitably in the spirit of conventionalism. (shrink)

A standing challenge in the theory of counterfactuals is to solve the “deviation problem”. Consider ordinary counterfactuals involving an antecedent concerning a difference from the actual course of events at a particular time, and a consequent concerning, at least in part, what happens at a later time. In the possible worlds framework, the problem is often put in terms of which are the relevant antecedent worlds. Desiderata for the solution include that the relevant antecedent worlds be governed by the actual (...) laws of nature with no miracles; that the past in those worlds before the antecedent time matches the actual past; that the account is compatible with determinism, and that many of our ordinary counterfactual judgments are correct, and would be correct even given determinism. Many theorists have compromised on one or more of these desiderata, but this paper presents an account employing impossible worlds that satisfies them all. (shrink)

Externalism holds that the content of our utterances and thoughts are determined partly by the environment. Here, I offer an argument which suggests that externalism is incompatible with a natural view about ontological commitment--namely, the Quinean view that such commitments are fixed by the range of the variables in your theory. The idea in brief is that if Oscar mistakenly believes that water = XYZ, the externalist ontologically commits Oscar to two waterish kinds, whereas the Quinean commits him to one (...) such kind (albeit a metaphysically impossible kind). The penultimate section addresses a variety of objections to the argument. (shrink)

Subtraction arguments support the view that there might have been nothing. The best-developed SA to date, due to David Efird and Tom Stoneham, is claimed by its authors to entail that there are worlds in which there are space-time points but no concrete objects: Efird and Stoneham hold that space-time points are not concrete and that a world made up from them alone contains nothing concrete. In this paper it is argued that whole space-times are concrete and subtractable, so that (...) a subtraction argument commits us to a bolder conclusion: namely, that there are worlds in which there is no space-time. This result has far-reaching consequences: it supports the view that there might have been no time; and constrains accounts of possible worlds. In the course of developing this revised subtraction argument, I counter suggestions that SAs are question-begging. (shrink)

This paper gives a framework for understanding causal counterpossibles, counterfactuals imbued with causal content whose antecedents appeal to metaphysically impossible worlds. Such statements are generated by omissive causal claims that appeal to metaphysically impossible events, such as “If the mathematician had not failed to prove that 2+2=5, the math textbooks would not have remained intact.” After providing an account of impossible omissions, the paper argues for three claims: (i) impossible omissions play a causal role in the actual world, (ii) causal (...) counterpossibles have broad applications in philosophy, and (iii) the truth of causal counterpossibles provides evidence for the nonvacuity of counterpossibles more generally. (shrink)

I defend the view that it is not impossible to see the impossible. I provide two examples in which one sees the impossible and defend these examples from potential objections. Theories of depiction should make room for impossible depictions.

Modal Meinongianism is a form of Meinongianism whose main supporters are Graham Priest and Francesco Berto. The main idea of modal Meinongianism is to restrict the logical deviance of Meinongian non-existent objects to impossible worlds and thus prevent it from “contaminating” the actual world: the round square is round and not round, but not in the actual world, only in an impossible world. In the actual world, supposedly, no contradiction is true. I will show that Priest’s semantics, as originally formulated (...) in Towards Non-being, tell us something different. According to certain models, there are true contradictions in the actual world. Berto and Priest have noticed this unexpected consequence and have suggested a solution, but I will show that their solution is highly questionable. In the last section of this paper, I will introduce a new and simpler version of modal Meinongianism that avoids the problem. (shrink)

Guy Kahane asks an axiological question: what value would (or does) God’s existence bestow on the world? Supposing God’s existence is a matter of necessity, this axiological question faces a problem because answering it will require assessing the truth-value of counterpossibles. I argue that Kahane, Paul Moser, and Richard Davis and Paul Franks fail in their attempts to render the axiological question substantive. I then offer my own solution by bringing work in cognitive psychology and philosophy of mind to bear (...) on the possibility of assessing counterpossibles. I argue that humans can engage in counterpossible reasoning by “accepting” or “supposing” that the antecedent is true and “screening out” those beliefs that would result in contradictions when combined in inferences with the acceptance or supposition. These screened out propositions are not treated as false, but are ignored. I offer a three-valued logic for counterpossible reasoning. I conclude by outlining some implications for the axiological question. (shrink)

Curry's paradox for "if.. then.." concerns the paradoxical features of sentences of the form "If this very sentence is true, then 2+2=5". Standard inference principles lead us to the conclusion that such conditionals have true consequents: so, for example, 2+2=5 after all. There has been a lot of technical work done on formal options for blocking Curry paradoxes while only compromising a little on the various central principles of logic and meaning that are under threat. -/- Once we have a (...) sense of the technical options, though, a philosophical choice remains. When dealing with puzzles in the logic of conditionals, a natural place to turn is independently motivated semantic theories of the behaviour of "if... then...". This paper argues that the closest-worlds approach outlined in Nolan 1997 offers a philosophically satisfying reason to deny conditional proof and so block the paradoxical Curry reasoning, and can give the verdict that standard Curry conditionals are false, along with related "contraction conditionals". (shrink)

A principle endorsed by many theories of objective chance, and practically forced on us by the standard interpretation of the Kolmogorov semantics for chance, is the principle that when a proposition P has a chance, any proposition Q that is necessarily equivalent to P will have the same chance as P. Call this principle SUB (for the substitution of necessary equivalents into chance ascriptions). I will present some problems for a theory of chance, and will argue that the best way (...) to resolve these problems is to reject SUB, and similar principles e.g. for the chances of outcomes or the chances of events. Objective chance, it turns out, carves things more finely than necessary equivalence does. (shrink)

The article looks at the structure of impossible worlds, and their deployment in the analysis of some intentional notions. In particular, it is argued that one can, in fact, conceive anything, whether or not it is impossible. Thus a semantics of conceivability requires impossible worlds.

The aim of this paper is to show why the theories of impossible worlds do not fully solve the problem of counterpossibles, but merely shift it. Moreover, by making a distinction between two types of languages, we will show that some expectations about proper theory of counterfactuals might be too great.

The subject of this paper is the notion of similarity between the actual and impossible worlds. Many believe that this notion is governed by two rules. Ac-cording to the first rule, every non-trivial world is more similar to the actual world than the trivial world is. The second rule states that every possible world is more similar to the actual world than any impossible world is. The aim of this paper is to challenge both of these rules. We argue that (...) acceptance of the first rule leads to the claim that the rule ex contradictione sequitur quodlibet is invalid in classical logic. The second rule does not recognize the fact that objects might be similar to one an-other due to various features. (shrink)

The topic of this special issue of Synthese is hyperintensionality. This introduction offers a brief survey of the very notion of hyperintensionality followed by a summary of each of the papers in this collection. The papers are foundational studies of hyperintensionality accompanied by ample philosophical applications.Hyperintensionality concerns the individuation of non-extensional entities such as propositions and properties, relations-in-intension and individual roles, as well as, for instance, proofs and judgments and computational procedures, in case these do not reduce to any of (...) the former. Hyperintensional individuation is frequently also referred to as ‘fine-grained’ or sometimes simply ‘intensional’ individuation, when ‘intensional’ is not understood in the specific sense of possible-world semantics or in the pejorative sense of flouting various logical rules of extensional logic. A principle of individuation qualifies as hyperintensional as soon as it is finer than necessary .. (shrink)

The pressure to individuate propositions more finely than intensionally—that is, hyper-intensionally—has two distinct sources. One source is the philosophy of mind: one can believe a proposition without believing an intensionally equivalent proposition. The second source is metaphysics: there are intensionally equivalent propositions, such that one proposition is true in virtue of the other but not vice versa. I focus on what our theory of propositions should look like when it's guided by metaphysical concerns about what is true in virtue of (...) what. In this paper I articulate and defend a metaphysical theory of the individuation of propositions, according to which two propositions are identical just in case they occupy the same nodes in a network of invirtuation relations. Invirtuation is here taken to be a primitive relation of metaphysical explanation exemplified by propositions that, in conjunction with truth, defines the notion of true in virtue of. After formulating the theory, I compare it with a view.. (shrink)