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 impossibleworlds. 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 impossibleworlds 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)
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 impossibleworlds. 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 impossibleworlds. 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)
We present a theory of truth in fiction that improves on Lewis's  ‘Analysis 2’ in two ways. First, we expand Lewis's possible worlds apparatus by adding non-normal or impossibleworlds. 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.
Impossibleworlds are representations of impossible things and impossible happenings. They earn their keep in a semantic or metaphysical theory if they do the right theoretical work for us. As it happens, a worlds-based account provides the best philosophical story about semantic content, knowledge and belief states, cognitive significance and cognitive information, and informative deductive reasoning. A worlds-based story may also provide the best semantics for counterfactuals. But to function well, all these accounts need (...) use of impossible and as well as possible worlds. So what are impossibleworlds? Graham Priest claims that any of the usual stories about possible worlds can be told about impossibleworlds, too. But far from it. I'll argue that impossibleworlds cannot be genuine worlds, of the kind proposed by Lewis, McDaniel or Yagisawa. Nor can they be ersatz worlds on the model proposed by Melia or Sider. Constructing impossibleworlds, it turns out, requires novel metaphysical resources. (shrink)
Accounts of propositions as sets of possible worlds have been criticized for conflating distinct impossible propositions. In response to this problem, some have proposed to introduce impossibleworlds to represent distinct impossibilities, endorsing the thesis that impossibleworlds must be of the same kind; this has been called the parity thesis. I show that this thesis faces problems, and propose a hybrid account which rejects it: possible worlds are taken as concrete Lewisian (...) class='Hi'>worlds, and impossibilities are represented as set-theoretic constructions out of them. This hybrid account (1) distinguishes many intuitively distinct impossible propositions; (2) identifies impossible propositions with extensional constructions; (3) avoids resorting to primitive modality, at least so far as Lewisian modal realism does. (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 impossibleworlds, I call such worlds logically impossibleworlds. (...) At a logically impossible world, the laws of logic fail. In this paper, I provide a definition of logically impossibleworlds. I then show that there is nothing strange about admitting such worlds. (shrink)
In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossibleworlds where the truths of logic can be false. As we shall see, if we admit impossibleworlds where “anything goes” in modal space, it is easy to model (...) extremely non-ideal agents that are incapable of performing even the most elementary logical deductions. A much harder, and considerably less investigated challenge is to ensure that the resulting modal space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out subtly impossibleworlds that verify complex logical falsehoods, they are nevertheless able to rule out blatantly impossibleworlds that verify obvious logical falsehoods. To model moderately ideal agents, I argue, the job is to construct a modal space that contains only possible and non-trivially impossibleworlds where it is not the case that “anything goes”. But I prove that it is impossible to develop an impossible-world framework that can do this job and that satisfies certain standard conditions. Effectively, I show that attempts to model moderately ideal agents in a world-involving framework collapse to modeling either logical omniscient agents, or extremely non-ideal agents. (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 impossibleworlds that satisfies them all. (shrink)
Several theorists have been attracted to the idea that in order to account for counterpossibles, i.e. counterfactuals with impossible antecedents, we must appeal to impossibleworlds. However, few have attempted to provide a detailed impossibleworlds account of counterpossibles. Berit Brogaard and Joe Salerno’s ‘Remarks on Counterpossibles’ is one of the few attempts to fill in this theoretical gap. In this article, I critically examine their account. I prove a number of unanticipated implications of their (...) account that end up implying a counterintuitive result. I then examine a suggested revision and point out a surprising implication of the revision. (shrink)
In this paper, I argue for a particular conception of impossibleworlds. Possible worlds, as traditionally understood, can be used in the analysis of propositions, the content of belief, the truth of counterfactuals, and so on. Yet possible worlds are not capable of differentiating propositions that are necessarily equivalent, making sense of the beliefs of agents who are not ideally rational, or giving truth values to counterfactuals with necessarily false antecedents. The addition of impossible (...) class='Hi'>worlds addresses these issues. The kinds of impossibleworlds capable of performing this task are not mysterious sui generis entities, but sets of structured propositions that are themselves constructed out of possible worlds and relations. I also respond to a worry that these impossibleworlds are unable to represent claims about the shape of modal space itself. (shrink)
Lewisian Genuine Realism about possible worlds is often deemed unable to accommodate impossibleworlds and reap the benefits that these bestow to rival theories. This thesis explores two alternative extensions of GR into the terrain of impossibleworlds. It is divided in six chapters. Chapter I outlines Lewis’ theory, the motivations for impossibleworlds, and the central problem that such worlds present for GR: How can GR even understand the notion of an (...)impossible world, given Lewis’ reductive theoretical framework? Since the desideratum is to incorporate impossibleworlds into GR without compromising Lewis’ reductive analysis of modality, Chapter II defends that analysis against objections. The rest of the thesis is devoted to incorporating impossibleworlds into GR. Chapter III explores GR-friendly impossibleworlds in the form of set-theoretic constructions out of genuine possibilia. Then, Chapters IV-VI venture into concrete impossibleworlds. Chapter IV addresses Lewis’ objection against such worlds, to the effect that contradictions true at impossibleworlds amount to true contradictions tout court. I argue that even if so, the relevant contradictions are only ever about the non-actual, and that Lewis’ argument relies on a premise that cannot be nonquestion- beggingly upheld in the face of genuine impossibleworlds in any case. Chapter V proposes that Lewis’ reductive analysis can be preserved, even in the face of genuine impossibilia, if we differentiate the impossible from the possible by means of accessibility relations, understood non-modally in terms of similarity. Finally, Chapter VI counters objections to the effect that there are certain impossibilities, formulated in Lewis’ theoretical language, which genuine impossibilia should, but cannot, represent. I conclude that Genuine Realism is still very much in the running when the discussion turns to impossibleworlds. (shrink)
We need to understand the impossible. Francesco Berto and Mark Jago start by considering what the concepts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition have in common. They are all concepts which divide the world up more finely than logic does. Logically equivalent sentences may carry different meanings and information and may differ in how they're believed. Fictions can be inconsistent yet meaningful. We can suppose impossible things without collapsing into total incoherence. Yet for the (...) leading philosophical theories of meaning, these phenomena are an unfathomable mystery. To understand these concepts, we need a metaphysical, logical, and conceptual grasp of situations that could not possibly exist: ImpossibleWorlds. This book discusses the metaphysics of impossibleworlds and applies the concept to a range of central topics and open issues in logic, semantics, and philosophy. It considers problems in the logic of knowledge, the meaning of alternative logics, models of imagination and mental simulation, the theory of information, truth in fiction, the meaning of conditional statements, and reasoning about the impossible. In all these cases, impossibleworlds have an essential role to play. (shrink)
Theories of content are at the centre of philosophical semantics. The most successful general theory of content takes contents to be sets of possible worlds. But such contents are very coarse-grained, for they cannot distinguish between logically equivalent contents. They draw intensional but not hyperintensional distinctions. This is often remedied by including impossible as well as possible worlds in the theory of content. Yet it is often claimed that impossibleworlds are metaphysically obscure; and it (...) is sometimes claimed that their use results in a trivial theory of content. In this paper, I set out the need for impossibleworlds in a theory of content; I briefly sketch a metaphysical account of their nature; I argue that worlds in general must be very fine-grained entities; and, finally, I argue that the resulting conception of impossibleworlds is not a trivial one. (shrink)
The best arguments for possible worlds as states of affairs furnish us with equally good arguments for impossibleworlds of the same sort. I argue for a theory of impossibleworlds on which the impossibleworlds correspond to maximal inconsistent classes of propositions. Three objections are rejected. In the final part of the paper, I present a menu of impossibleworlds and explore some of their interesting formal properties.
In this critical notice of Kment's _Modality and Explanatory Reasoning_, we focus on Kment’s arguments for impossibleworlds 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.
One response to the problem of logical omniscience in standard possible worlds models of belief is to extend the space of worlds so as to include impossibleworlds. It is natural to think that essentially the same strategy can be applied to probabilistic models of partial belief, for which parallel problems also arise. In this paper, I note a difficulty with the inclusion of impossibleworlds into probabilistic models. Under weak assumptions about the space (...) of worlds, most of the propositions which can be constructed from possible and impossibleworlds are in an important sense inexpressible; leaving the probabilistic model committed to saying that agents in general have at least as many attitudes towards inexpressible propositions as they do towards expressible propositions. If it is reasonable to think that our attitudes are generally expressible, then a model with such commitments looks problematic. (shrink)
David Lewis famously dismisses genuine impossibleworlds on the basis that a contradiction bound within the scope of his modifier ‘at w’ amounts to a contradiction tout court—an unacceptable consequence. Motivated by the rising demand for impossibleworlds in philosophical theorising, this paper examines whether anything coherent can be said about an extension of Lewis’ theory of genuine, concrete possible worlds into genuine, concrete impossibleworlds. Lewis’ reasoning reveals two ways to carve out (...) conceptual space for the genuinely impossible. The first is to abandon Lewis’ classical translation schema for negation, on the basis that it begs the question against incomplete and inconsistent worlds. I argue that, whilst this option incurs some loss in the semantics, it preserves the core spirit of Lewis’ metaphysics. The alternative is to bite the bullet, abandon classical logic and embrace true contradictions. The key challenge with this strategy is that the resulting theory seems committed to a particularly strong kind of dialethism—one that even dialethists would be reluctant to accept. I motivate such a dialethic account of genuine impossibilia using Lewis’ own methodology and defend it against triviality objections. I close with a few comments on why impossibleworlds should not be reduced to set theoretic constructs out of possible worlds. (shrink)
One well-known objection to the traditional Lewis-Stalnaker semantics of counterfactuals is that it delivers counterintuitive semantic verdicts for many counterpossibles (counterfactuals with necessarily false antecedents). To remedy this problem, several authors have proposed extending the set of possible worlds by impossibleworlds at which necessary falsehoods may be true. Linguistic ersatz theorists often construe impossibleworlds as maximal, inconsistent sets of sentences in some sufficiently expressive language. However, in a recent paper, Bjerring (2014) argues that (...) the “extended” Lewis-Stalnaker semantics delivers the wrong truth-values for many counterpossibles if impossibleworlds are required to be maximal. To make room for non-maximal or partial impossibleworlds, Bjerring considers two alternative world-ontologies: either (i) we construe impossibleworlds as arbitrary (maximal or partial) inconsistent sets of sentences, or (ii) we construe them as (maximal or partial) inconsistent sets of sentences that are closed and consistent with respect to some non-classical logic. Bjerring raises an objection against (i), and suggests that we opt for (ii). In this paper, I argue, first, that Bjerring’s objection against (i) conflates two different conceptions of what it means for a logic to be true at a world. Second, I argue that (ii) imposes too strong constraints on what counts as an impossible world. I conclude that linguistic ersatzists should construe impossibleworlds as arbitrary (maximal or partial) inconsistent sets of sentences. (shrink)
The paper deals with such a modification of genuine modal realism as to accommodate impossibleworlds into its ontology. First of all, the theory of modal realism is presented. Next, several motivations for the acceptance of impossibleworlds are adduced. Further, Lewis’s argument against impossibleworlds is presented. It is argued that the argument can be weakened by rejection of one of its premises. Finally, two objections against the proposal are countered. Although my strategy (...) accounts for the Opinion concerning the impossible, it allegedly violates another Opinion which conceives the reality classical. It seems, however, that there is no no-question-begging reason to think that reality is classical. How can we know, after all, which logic describes reality? Without a definite answer to the question, the incredibility objection then simply collapses into a statement of a possibilist dogma. (shrink)
It is a venerable slogan due to David Hume, and inherited by the empiricist tradition, that the impossible cannot be believed, or even conceived. In Positivismus und Realismus, Moritz Schlick claimed that, while the merely practically impossible is still conceivable, the logically impossible, such as an explicit inconsistency, is simply unthinkable. -/- An opposite philosophical tradition, however, maintains that inconsistencies and logical impossibilities are thinkable, and sometimes believable, too. In the Science of Logic, Hegel already complained against (...) “one of the fundamental prejudices of logic as hitherto understood”, namely that “the contradictory cannot be imagined or thought” (Hegel 1931: 430). Our representational capabilities are not limited to the possible, for we appear to be able to imagine and describe also impossibilities — perhaps without being aware that they are impossible. -/- Such impossibilities and inconsistencies are what this entry is about... (shrink)
The theory of possible worlds has permeated analytic philosophy in recent decades, and its best versions have a consequence which has gone largely unnoticed: in addition to the panoply of possible worlds, there are a great many impossibleworlds. A uniform ontological method alone should bring the friends of possible worlds to adopt impossibleworlds, I argue, but the theory's applications also provide strong incentives. In particular, the theory facilitates an account of counterfactuals (...) which avoids several of the implausible results of David Lewis's account, and it paves the way for the analogues of Kripkean semantics for epistemic and relevant logics. On the theories of possible worlds as abstract objects, worlds bear a strong resemblance to propositions. I contend that if there are distinct necessarily false propositions, then there are likewise distinct impossibleworlds. However, one who regards possible worlds as concrete objects must not recognize impossibleworlds, in part because concrete worlds cannot misrepresent certain features of reality, as some impossibleworlds must. Accordingly, I defend and develop a theory of impossibleworlds as maximal impossible states of affairs. Impossibleworlds perform admirably in the analysis of counterfactuals with impossible antecedents. I argue that, contrary to standard accounts, not all counterpossibles are trivially true, and I develop a Lewis-style semantics which allows this result. The point is crucial, since many views presuppose that some counterpossibles are substantive philosophical truths. Finally, I show that impossibleworlds hold great promise for doxastic and relevant logics. Epistemic logic needs a domain of propositions which is not closed under strict implication to avoid the problem of logical omniscience, and relevant logic needs such a domain to avoid the famous paradoxes of implication. In sum, impossible world theory promises natural, elegant solutions to philosophical problems in numerous areas where possible worlds alone flounder. These solutions come to most possible world theorists at no cost, since the existence of impossibleworlds is entailed by theses they already hold. (shrink)
Reasoning about situations we take to be impossible is useful for a variety of theoretical purposes. Furthermore, using a device of impossibleworlds when reasoning about the impossible is useful in the same sorts of ways that the device of possible worlds is useful when reasoning about the possible. This paper discusses some of the uses of impossibleworlds and argues that commitment to them can and should be had without great metaphysical or (...) logical cost. The paper then provides an account of reasoning with impossibleworlds, by treating such reasoning as reasoning employing counterpossible conditionals, and provides a semantics for the proposed treatment. (shrink)
Philosophers have found postulating possible worlds to be very useful in a number of areas, including philosophy of language and mind, logic, and metaphysics. Impossibleworlds are a natural extension to this use of possible worlds, and can help resolve a number of difficulties thrown up by possible‐worlds frameworks.
A theory of ersatz impossibleworlds is developed to deal with the problem of counterpossible conditionals. Using only tools standardly in the toolbox of possible worlds theorists, it is shown that we can construct a model for counterpossibles. This model is a natural extension of Lewis's semantics for counterfactuals, but instead of using classical logic as its base, it uses the logic LP.
The appeal to possible worlds in the semantics of modal logic and the philosophical defense of possible worlds as an essential element of ontology have led philosophers and logicians to introduce other kinds of `worlds' in order to study various philosophical and logical phenomena. The literature contains discussions of `non-normal worlds', `non-classical worlds', `non-standard worlds', and `impossibleworlds'. These atypical worlds have been used in the following ways: (1) to interpret unusual (...) modal logics, (2) to distinguish logically equivalent propositions, (3) to solve the problems associated with propositional attitude contexts, intentional contexts, and counterfactuals with impossible antecedents, and (4) to interpret systems of relevant and paraconsistent logic. However, those who have attempted to develop a genuine metaphysical theory of such atypical worlds tend to move too quickly from philosophical characterizations to formal semantics. (shrink)
The intuitive notion behind the usual semantics of most systems of modal logic is that of ?possible worlds?. Loosely speaking, an expression is necessary if and only if it holds in all possible worlds; it is possible if and only if it holds in some possible world. Of course, contradictory expressions turn out to hold in no possible worlds, and logically true expressions turn out to hold in every possible world. A method is presented for transforming standard (...) modal systems into systems of modal logic for impossibleworlds. To each possible world there corresponds an impossible world such that an expression holds in the impossible world if and only if it does not hold in the possible world. One can then talk about such worlds quite consistently, and there seems to be no logical reason for excluding them from consideration. (shrink)
Among the many possible approaches to dealing with logical omniscience, I consider here awareness and impossibleworlds structures. The former approach, pioneered by Fagin and Halpern, distinguishes between implicit and explicit knowledge, and avoids logical omniscience with respect to explicit knowledge. The latter, developed by Rantala and by Hintikka, allows for the existence of logically impossibleworlds to which the agents are taken to have access; since such worlds need not behave consistently, the agents’ knowledge (...) is fallible relative to logical omniscience. The two approaches are known to be equally expressive in propositional systems interpreted over Kripke semantics. In this paper I show that the two approaches are equally expressive in propositional systems interpreted over Montague-Scott (neighborhood) semantics. Furthermore, I provide predicate systems of both awareness and impossibleworlds structures interpreted on neighborhood semantics and prove the two systems to be equally expressive. (shrink)
This paper gives a framework for understanding causal counterpossibles, counterfactuals imbued with causal content whose antecedents appeal to metaphysically impossibleworlds. 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)
￼Mark Jago presents an original philosophical account of meaningful thought: in particular, how it is meaningful to think about things that are impossible. We think about impossible things all the time. We can think about alchemists trying to turn base metal to gold, and about unfortunate mathematicians trying to square the circle. We may ponder whether God exists; and philosophers frequently debate whether properties, numbers, sets, moral and aesthetic qualities, and qualia exist. In many philosophical or mathematical debates, (...) when one side of the argument gets things wrong, it necessarily gets them wrong. As we consider both sides of one of these philosophical arguments, we will at some point think about something that’s impossible. Yet most philosophical accounts of meaning and content hold that we can’t meaningfully think or reason about the impossible. -/- In The Impossible, Jago argues that we often gain new information, new beliefs, and, sometimes, fresh knowledge through logic, mathematics, and philosophy. That is why logic, mathematics, and philosophy are useful. We therefore require accounts of knowledge and belief, of information and content, and of meaning which allow space for the impossible. Jago’s aim in this book is to provide such accounts. He gives a detailed analysis of the concept of hyperintensionality, whereby logically equivalent contents may be distinct, and develops a theory in terms of possible and impossibleworlds. Along the way, he provides a theory of what those worlds are and how they feature in our analysis of normative epistemic concepts: knowledge, belief, information, and content. (shrink)
You and I can differ in what we say, or believe, even though the things we say, or believe, are logically equivalent. Discussing what is said, or believed, requires notions of content which are finer-grained than sets of (metaphysically or logically) possible worlds. In this paper, I develop the approach to fine-grained content in terms of a space of possible and impossibleworlds. I give a method for constructing ersatz worlds based on theory of substantial facts. (...) I show how this theory overcomes an objection to actualist constructions of ersatz worlds and argue that it naturally gives rise to useful notions of fine-grained content. (shrink)
World semantics for relevant logics include so-called non-normal or impossibleworlds providing model-theoretic counterexamples to such irrelevant entailments as (A ∧ ¬A) → B, A → (B∨¬B), or A → (B → B). Some well-known views interpret non-normal worlds as information states. If so, they can plausibly model our ability of conceiving or representing logical impossibilities. The phenomenon is explored by combining a formal setting with philosophical discussion. I take Priest’s basic relevant logic N4 and extend it, (...) on the syntactic side, with a representation operator, (R), and on the semantic side, with particularly anarchic non-normal worlds. This combination easily invalidates unwelcome “logical omniscience” in- ferences of standard epistemic logic, such as belief-consistency and closure under entailment. Some open questions are then raised on the best strategies to regiment (R) in order to express more vertebrate kinds of conceivability. (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 impossibleworlds 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)
The paper investigates the system of 'Imaginary Logic' created by the Russian logician N.A. Vasil'ev (1880-1940), considered by some to be a forerunner of paraconsistent or intuitionistic logics. It is shown how he constructs a logic without the law of contradiction redefining the concept of negation. Vasil'ev singles out two levels of logic, an external one which is absolute and one depending on commitments in relation to cognizable objects which is not absolute. His reconstruction of the syllogism shows the viability (...) of his system and indicates how, indeed, he may be called an initiator of nonclassical logics. (shrink)
Since the publication of David Lewis’ Counterfactuals, the standard line on subjunctive conditionals with impossible antecedents (or counterpossibles) has been that they are vacuously true. That is, a conditional of the form ‘If p were the case, q would be the case’ is trivially true whenever the antecedent, p, is impossible. The primary justification is that Lewis’ semantics best approximates the English subjunctive conditional, and that a vacuous treatment of counterpossibles is a consequence of that very elegant theory. (...) Another justification derives from the classical lore than if an impossibility were true, then anything goes. In this paper we defend non-vacuism, the view that counterpossibles are sometimes non-vacuously true and sometimes non-vacuously false. We do so while retaining a Lewisian semantics, which is to say, the approach we favor does not require us to abandon classical logic or a similarity semantics. It does however require us to countenance impossibleworlds. An impossibleworlds treatment of counterpossibles is suggested (but not defended) by Lewis (Counterfactuals. Blackwell, Oxford, 1973), and developed by Nolan (Notre Dame J Formal Logic 38:325–527, 1997), Kment (Mind 115:261–310, 2006a: Philos Perspect 20:237–302, 2006b), and Vander Laan (In: Jackson F, Priest G (eds) Lewisian themes. Oxford University Press, Oxford, 2004). We follow this tradition, and develop an account of comparative similarity for impossibleworlds. (shrink)
This chapter provides an introduction to possible worlds semantics in both logic and the philosophy of language, including a discussion of some of the advantages and challenges for possible worlds semantics.
Several recent arguments purport to show that omnipotence is incompatible with the possession of various necessary properties. These arguments appeal to one of two plausible but false principles about the nature of power: that if it is metaphysically impossible for a being to actualize a state of affairs, then that being does not have the power to actualize that state of affairs, or that if it is impossible given some contingent facts about the world that a being actualize (...) a state of affairs, then that being does not have the power to actualize that state of affairs. I pose several problems for both principles, thereby undermining the plausibility of these arguments. I then consider the implications of rejecting these principles for related principles in the free will debate. These implications suggest important differences between having the power to bring about a state of affairs, having a choice about whether it obtains, and being able to bring it about. (shrink)
Several themes of David Lewis's theory of counterfactuals, especially their sensitivity to context, pave the way for a viable theory of non-trivial counterpossibles. If Lewis was successful in defending his account against the early objections, a semantics of counterpossibles can be defended from similar objections in the same way. The resulting theory will be extended to address 'might' counterfactuals and questions about the relative "nearness" of impossibleworlds.
Jonathan Schaffer argues against a necessary connection between properties and laws. He takes this to be a question of what possible worlds we ought to countenance in our best theories of modality, counterfactuals, etc. In doing so, he unfairly rigs the game in favor of contingentism. I argue that the necessitarian can resist Schaffer’s conclusion while accepting his key premise that our best theories of modality, counterfactuals, etc. require a very wide range of things called ‘possible worlds’. However, (...) the necessitarian can and should insist that, in many cases, these worlds are not metaphysically possible. I will further argue that, having taken such a stance, the necessitarian has additional resources to respond to Schaffer’s other arguments against the view. (shrink)
The traditional Lewis–Stalnaker semantics treats all counterfactuals with an impossible antecedent as trivially or vacuously true. Many have regarded this as a serious defect of the semantics. For intuitively, it seems, counterfactuals with impossible antecedents—counterpossibles—can be non-trivially true and non-trivially false. Whereas the counterpossible "If Hobbes had squared the circle, then the mathematical community at the time would have been surprised" seems true, "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the (...) time would have been thrilled" seems false. Many have proposed to extend the Lewis–Stalnaker semantics with impossibleworlds to make room for a non-trivial or non-vacuous treatment of counterpossibles. Roughly, on the extended Lewis–Stalnaker semantics, we evaluate a counterfactual of the form "If A had been true, then C would have been true" by going to closest world—whether possible or impossible—in which A is true and check whether C is also true in that world. If the answer is "yes", the counterfactual is true; otherwise it is false. Since there are impossibleworlds in which the mathematically impossible happens, there are impossibleworlds in which Hobbes manages to square the circle. And intuitively, in the closest such impossibleworlds, sick children in the mountains of Afghanistan are not thrilled—they remain sick and unmoved by the mathematical developments in Europe. If so, the counterpossible "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would have been thrilled" comes out false, as desired. In this paper, I will critically investigate the extended Lewis–Stalnaker semantics for counterpossibles. I will argue that the standard version of the extended semantics, in which impossibleworlds correspond to maximal, logically inconsistent entities, fails to give the correct semantic verdicts for many counterpossibles. In light of the negative arguments, I will then outline a new version of the extended Lewis–Stalnaker semantics that can avoid these problems. (shrink)