David Lewis holds that a single possible world can provide more than one way things could be. But what are possible worlds good for if they come apart from ways things could be? We can make sense of this if we go in for a metaphysical understanding of what the world is. The world does not include everything that is the case—only the genuine facts. Understood this way, Lewis's “cheap haecceitism” amounts to a kind of metaphysical anti-haecceitism: (...) it says there aren't any genuine facts about individuals over and above their qualitative roles. (shrink)

Metaphysically possible worlds have many uses. Epistemically possible worlds promise to be similarly useful, especially in connection with propositions and propositional attitudes. However, I argue that there is a serious threat to the natural accounts of epistemically possible worlds, from a version of Russell’s paradox. I contrast this threat with David Kaplan’s problem for metaphysical possible world semantics: Kaplan’s problem can be straightforwardly rebutted, the problems I raise cannot. I argue that although there (...) may be coherent accounts of epistemically possible worlds with fruitful applications, any such an account must fundamentally compromise the basic idea behind epistemic possibility. (shrink)

In this chapter, I survey what I call Lewisian approaches to modality: approaches that analyze modality in terms of concrete possible worlds and their parts. I take the following four theses to be characteristic of Lewisian approaches to modality. (1) There is no primitive modality. (2) There exists a plurality of concrete possible worlds. (3) Actuality is an indexical concept. (4) Modality de re is to be analyzed in terms of counterparts, not transworld identity. After an (...) introductory section in which I motivate analyzing modality in terms of possible worlds, I devote one section to each of these four theses. For each thesis, I take Lewis’s interpretation and defense as my starting point. I then consider and endorse alternative ways of accepting the thesis, some of which disagree substantially with Lewis’s interpretation or defense. There is more than one way to be a Lewisian about modality. (shrink)

The puzzle of petitionary prayer: if we ask for the best thing, God was already going to do it, and if we ask for something that's not the best, God's not going to grant our request. In this paper, we give a new solution to the puzzle.

Among the most remarkable developments in metaphysics since the 1950’s is the explosion of philosophical interest in possible worlds. This paper proposes an explanation of what possible worlds are, and argues that this proposal, the interpreted models conception, should be attractive to anyone who thinks that modal facts are primitive, and so not to be explained in terms of some non-modal notion of “possible world.” I articulate three constraints on any acceptable primitivist explanation of the (...) nature of possible worlds, and show that the interpreted models conception meets the three constraints. (shrink)

This paper surveys recent "new actualist" approaches to modality that do without possible worlds and locate modality squarely in the actual world. New actualist theories include essentialism and dispositionalism about modality, each of which can come in different varieties. The commonalities and differences between these views, as well as their shared motivations, are layed out.

In this paper I explore the relationship between the idea of possible worlds and the notion of the beauty of God. I argue that there is a clear contradiction between the idea that God is utterly and completely beautiful on the one hand and the notion that He contains within himself all possible worlds on the other. Since some of the possible worlds residing in the mind of the deity are ugly, their presence seems (...) to compromise God's complete and utter beauty. (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.

In this paper I argue that there is a difficulty for Fine's exact semantics for counterfactuals. The difficulty undermines Fine's reasons for preferring exact semantics to possible worlds semantics.

The main objective of the paper is to give initial answers to three important questions. Why did Leibniz visit Spinoza? Why did his preparation for this meeting include a modification of the ontological proof of God? What is the philosophical result of the meeting and what do possible worlds have to do with it? In order to provide answers, three closely related manuscripts by Leibniz from November 1676 have been compared and the slow conceptual change of his philosophical (...) apparatus has been analyzed. The last of these manuscripts was presented and read in front of Spinoza. Around that time Leibniz abandoned the idea of plurality of worlds (cf. Tschirnhaus) and instead proposed the idea of possible worlds, thus introducing possibility into the (onto/theo)logical structure itself in order to avoid the “precipice” of Spinoza’s necessity. What is interesting, however, is how exactly this conceptual change occurred at the end of 1676 and what its philosophical and methodological implications are. (shrink)

The Brock-Rosen problem has been one of the most thoroughly discussed objections to the modal fictionalism bruited in Gideon Rosen’s ‘Modal Fictionalism’. But there is a more fundamental problem with modal fictionalism, at least as it is normally explained: the position does not resolve the tension that motivated it. I argue that if we pay attention to a neglected aspect of modal fictionalism, we will see how to resolve this tension—and we will also find a persuasive reply to the Brock-Rosen (...) objection. Finally, I discuss an alternative reading of Rosen, and argue that this position is also able to fend off the Brock-Rosen objection. (shrink)

The standard view of clauses embedded under attitude verbs or modal predicates is that they act as terms standing for propositions, a view that faces a range of philosophical and linguistic difficulties. Recently an alternative has been explored according to which embedded clauses act semantically as predicates of content-bearing objects. This paper argues that this approach faces serious problems when it is based on possible worlds-semantics. It outlines a development of the approach in terms of truthmaker theory instead.

Despite the notions of possible worlds and substances are very important subjects of contemporary metaphysics, there are relatively few attempts to combine these in a united framework. This paper considers the metaphysical model of the origins and the evolution of possible worlds that occurs from an interaction between substances. I involve Leibniz’s doctrine of the striving possibles that every possibility of substance has its own essence and tendency towards existence. It is supposed that the activities of (...) substances are constantly aimed at using this tendency in all possible ways. Only the consistent and stable interactions between the substances give birth to stable objects in one of many worlds. Thus activity of substances changes from the possible modality of being to the actual modality of being in form of existence of the worlds. I divide substance’s possibility into two aspects—dynamic (possible or virtual history) and static (possible or potential mutual state). Thanks to the summation of virtual histories, in the possible modality of being, the maximal number of virtual histories is combined into the actual history in the actual modality. (shrink)

A common argument for atheism runs as follows: God would not create a world worse than other worlds he could have created instead. However, if God exists, he could have created a better world than this one. Therefore, God does not exist. In this paper I challenge the second premise of this argument. I argue that if God exists, our world will continue without end, with God continuing to create value-bearers, and sustaining and perfecting the value-bearers he has already (...) created. Given this, if God exists, our world—considered on the whole—is infinitely valuable. I further contend that this theistic picture makes our world's value unsurpassable. In support of this contention, I consider proposals for how infinitely valuable worlds might be improved upon, focusing on two main ways—adding value-bearers and increasing the value in present value-bearers. I argue that neither of these can improve our world. Depending on how each method is understood, either it would not improve our world, or our world is unsurpassable with respect to it. I conclude by considering the implications of my argument for the problem of evil more generally conceived. (shrink)

Leibniz said that the universe, if God-created, would exist at a unique, conjoint, physical maximum: Of all possible worlds, it would be richest in phenomena, but its richness would arise from the simplest physical laws and initial conditions. Using concepts of ‘‘variety’’ and algorithmic informational complexity, Leibniz’ claim can be reframed as a testable theory. This theory predicts that the laws and conditions of the actual universe should be simpler, and the universe richer in phenomena, than the presence (...) of observers would require. Tegmark has shown that inhabitants of an infinite multiverse would likely observe simple laws and conditions, but also phenomenal richness just great enough to explain their existence. Empirical observations fit the claim of divine choice better than the claim of an infinite multiverse. The future of the universe, including its future information-processing capacity, is predicted to be endless. -/- . (shrink)

The standard view about counterfactuals is that a counterfactual (A > C) is true if and only if the A-worlds most similar to the actual world @ are C-worlds. I argue that the worlds conception of counterfactuals is wrong. I assume that counterfactuals have non-trivial truth-values under physical determinism. I show that the possible-worlds approach cannot explain many embeddings of the form (P > (Q > R)), which intuitively are perfectly assertable, and which must be (...) true if the contingent falsity of (Q > R) is to be explained. If (P > (Q > R)) has a backtracking reading then the contingent facts that (Q > R) needs to be true in the closest P-worlds are absent. If (P > (Q > R)) has a forwardtracking reading, then the laws required by (Q > R) to be true in the closest P-worlds will be absent, because they are violated in those worlds. Solutions like lossy laws or denial of embedding won't work. The only approach to counterfactuals that explains the embedding is a pragmatic metalinguistic approach in which the whole idea that counterfactuals are about a modal reality, be it abstract or concrete, is given up. (shrink)

The paper is a polemic with Richard Swinburne. According to him, both the possible worlds -- the ’world with God’ and the ’world without God’ -- contain moral properties. The ’world with God’, however, is morally "richer" because the existence of God entails some additional obligations; God may affect moral "facts" through creating some nonmoral facts; God may formulate some additional commands. I think that these differences lead to a greater difference in understanding morality: in the ’world without (...) God’ morality is at most a consequence of some contingent nonmoral states of affairs; whereas in the ’world with God’ it is the correlate and intended "work" of a perfect personal being. (shrink)

In his early lecture note Versuch einiger Betrachtungen über den Optimismus (1759) a young supporter of metaphysical optimism called Immanuel Kant tested the Leibnizian optimism by posing some counter-arguments against it only to falsify them. His counter-arguments were very inventive and they feature often in modern scholarship on Leibniz. In this paper I will present Kant’s main arguments and evaluate them. I will argue that Kant’s understanding on Leibnizian optimism is little misguided and for this reason his own positive counter-argument (...) despite its ingeniousness is problematic. His second solution to the problem is comparable to the doctrine of metaphysical optimism, but fails also for the same reason as the first one. -/- . (shrink)

The concept of the best of all possible worlds is widely considered to be incoherent on the grounds that, for any world that might be termed the best, there is always another that is better. I note that underlying this argument is a conviction that the goodness of a world is determined by a single kind of good, the most plausible candidates for which are not maximizable. Against this I suggest that several goods may have to combine to (...) determine the goodness of a world, and because of logical conflicts between them, the goods can be optimized to give a genuine best of all possible worlds. (shrink)

The subject of zombies is one of the most discussed and controversial topics of philosophy of mind. In this paper I will first examine the main argument of zombies, providing a summary of the current discussion. Then I will introduce a thought experiment, an epistemic window on a metaphysical scenario. By the thought experiment I will argue that zombies are logically impossible. Further I will discuss another recent epistemic window. Finally I will provide some other logical consideration to prove that (...) intentionality is not reducible to the cognitive functional aspects of the mind and that, moreover, the subjective recognition of semantic contents is necessary in order to consider as sensical the verbal behavior of a zombie. (shrink)

Are transcendental phenomenology and possible worlds semantics, two seemingly disparate, perhaps even incompatible philosophical traditions, actually complementary? Have two well-known representatives of each tradition, J.N. Mohanty and J. Hintikka, misinterpreted the other's philosophical "program" in such a way that they did not recognize the complementarity? Charles Harvey 1 has recently argued that the answer to both questions is "yes." Here I intend to argue that the answer to the first is unclear, whereas the answer to the second is (...) "no." Mohanty (at least) rightly cites fundamental differences between transcendental phenomenology and possible worlds semantics. (shrink)

Dualism about possible worlds says that merely possible worlds aren’t concrete objects, but the actual world is concrete. This view seems to be the natural one for ersatzers about merely possible worlds to take; yet one is hard-pressed to find any defenders of it in contemporary modal metaphysics. The main reason is that Dualism struggles with the issue of how merely possible worlds could have been actual. I explain that there are two (...) different Dualist strategies that can be taken to address the problem. Furthermore, one or other of these strategies should be plausible to anyone who accepts both Existentialism—which tells us that the existence of singular propositions depends on what they directly refer to—and Serious Actualism—which tells us that things must exist in order to instantiate properties. Though it has long been ignored, Dualism is a live option. (shrink)

In his "Two concepts of possible worlds", Peter Van Inwagen explores two kinds of views about the nature of possible worlds : abstractionism and concretism. The latter is the view defended by David Lewis who claims that possible worlds are concrete spatio-temporal universes, very much like our own, causally and spatio-temporally disconnected from each other. The former is the view of the majority who claims that possible worlds are some kind of abstract (...) objects – such as propositions, properties, states of affairs, or sets of numbers. In this paper, I will develop this view in an 'extreme abstractionist' way, appealing to a 'modal bundle theory', and I will try to show that it is preferable to the standard abstractionist ones. Finally, I will compare this kind of abstractionism to concretism, only to find that the difference between the two is minimal. (shrink)

Pietroski (1993) offers a semantics for belief sentences that is supposed to address the problem of equivalence. This paper argues that his proposal fails to solve the problem.

This thesis is an argument for the view that there are problems for Modal Reductionism, the thesis that modality can satisfactorily be defined in non-modal terms. -/- I proceed via a case study of David Lewis’s theory of concrete possible worlds. This theory is commonly regarded as the best and most influential candidate reductive theory of modality. Based on a detailed examination of its ontology, analysis and justification, I conclude that it does badly with respect to the following (...) four minimal conditions on a satisfactory reductive theory of modality: that it be (a) genuinely reductive, (b) materially adequate, (c) conceptually adequate and (d) that its justification provides good reason to think it true. -/- These problems for Lewis’s theory are not, I suggest, due to his idiosyncratic conception of possible worlds as concrete entities. Rather, because Lewis’s theory can be seen to represent an important class of structurally similar reductive theories of modality, the problems for Lewis’s theory generalise to problems for these other theories. This suggests that Modal Reductionism is unpromising. In the light of this, the alternative approach to understanding modality, Modal Primitivism, appears more attractive. (shrink)

McCall (1984) offered a semantics of counterfactual conditionals based on “real possible worlds” that avoids using the vague notion of similarity between possible worlds. I will propose an interpretation of McCall’s counterfactuals in a formal framework based on Baltag-Moss-Solecki events and protocols. Moreover, I will argue that using this interpretation one can avoid an objection raised by Otte (1987).

In this paper, I shall consider the challenge that Quine posed in 1947 to the advocates of quantified modal logic to provide an explanation, or interpretation, of modal notions that is intuitively clear, allows “quantifying in”, and does not presuppose, mysterious, intensional entities. The modal concepts that Quine and his contemporaries, e.g. Carnap and Ruth Barcan Marcus, were primarily concerned with in the 1940’s were the notions of (broadly) logical, or analytical, necessity and possibility, rather than the metaphysical modalities that (...) have since become popular, largely due to the influence of Kripke. In the 1950’s modal logicians responded to Quine’s challenge by providing quantified modal logic with model-theoretic semantics of various types. In doing so they also, explicitly or implicitly addressed Quine’s interpretation problem. Here I shall consider the approaches developed by Carnap in the late 1940’s, and by Kanger, Hintikka, Montague, and Kripke in the 1950’s, and discuss to what extent these approaches were successful in meeting Quine’s doubts about the intelligibility of quantified modal logic. (shrink)

Suppose the members of a group (e.g., committee, jury, expert panel) each form a judgment on which worlds in a given set are possible, subject to the constraint that at least one world is possible but not all are. The group seeks to aggregate these individual judgments into a collective judgment, subject to the same constraint. I show that no judgment aggregation rule can solve this problem in accordance with three conditions: “unanimity,” “independence” and “non-dictatorship,” Although the (...) result is a variant of an existing theorem on “group identification” (Kasher and Rubinstein, Logique et Analyse 160:385–395, 1997), the aggregation of judgments on which worlds are possible (or permissible, desirable, etc.) appears not to have been studied yet. The result challenges us to take a stance on which of its conditions to relax. (shrink)

This paper contains an argument to the effect that possible worlds semantics renders semantic knowledge impossible, no matter what ontological interpretation is given to possible worlds. The essential contention made is that possible worlds semantic knowledge is unsafe and this is shown by a parallel with the preface paradox.

My main purpose in this article is to present an argument for the idea that necessity qua truth in all possible worlds, without other qualifications, leads us to contradiction. If we do not want to accept the contradiction, we will face a dilemma: or accepting that everything we take as contingent is in fact necessary, or accepting that we cannot translate some sentences – at least the indexed to worlds sentences – to the possible worlds (...) vocabulary. We have an intuition – and we develop an argument for it – that if “P”, evaluated in w*, is a contingent truth, so it cannot be the case that “P in w*” is a necessary truth. Generally, the argument tries to show that “P”, evaluated in w*, and “P in w*” are made true by the same contingent fact. If we suppose that “P in w*” is necessary, we would have to suppose that the fact that makes it true is also necessary, which would be contradictory with the fact that makes “P” true in w*, if we accept that what makes “P” in w* and “P in w*” true is the same fact. I attain such an aim by presenting an argument that is divided in two parts, one to imply the contradiction and the other to show that there is no relevant difference between the indicated sentences, by showing how the dilemma arises, and by answering some possible objections. This is an important objective because the possible worlds vocabulary is the default vocabulary to treat the modalities of necessity and possibility. And if it is flawed, it is important that we identify the flaw and fix it – which is exactly what we intend to do at the end of this article, by suggesting some qualification at the necessity notion, that the necessity is the native truth in all possible worlds. And this would save the possible worlds vocabulary from the presented objection. (shrink)

Leibniz’s claim that this is the best of all possible worlds has been subject to numerous criticisms, both from his contemporaries and ours. In this paper I investigate a cluster of such criticisms based on the existence, abundance or character of worldly evil. As several Leibniz-inspired versions of optimism have been advanced in recent years, the aim of my investigation is to assess not just how Leibniz’s brand of optimism fares against these criticisms, but also whether optimism as (...) a philosophy has the resources to meet these challenges. I show that none of the criticisms considered has sufficient force to pose a threat to Leibniz’s version of optimism or to one modelled on it. (shrink)

Impossible worlds 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 impossible worlds? Graham Priest claims that any of the usual stories about possible worlds can be told about impossible worlds, too. But far from it. I'll argue that impossible worlds 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 impossible worlds, it turns out, requires novel metaphysical resources. (shrink)

The best arguments for possible worlds as states of affairs furnish us with equally good arguments for impossible worlds of the same sort. I argue for a theory of impossible worlds on which the impossible worlds correspond to maximal inconsistent classes of propositions. Three objections are rejected. In the final part of the paper, I present a menu of impossible worlds and explore some of their interesting formal properties.

The first of three lectures on nominal and modal discourse reference across languages (IMS, Stuttgart, 2000).

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.

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 impossible worlds to represent distinct impossibilities, endorsing the thesis that impossible worlds 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 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)

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)

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)

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 impossible worlds. 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 impossible worlds into probabilistic models. Under weak assumptions about the space of (...) worlds, most of the propositions which can be constructed from possible and impossible worlds 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)

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 impossible worlds. 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)

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 impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds 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 impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out blatantly impossible worlds 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 impossible worlds 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)

Lewisian Genuine Realism about possible worlds is often deemed unable to accommodate impossible worlds and reap the benefits that these bestow to rival theories. This thesis explores two alternative extensions of GR into the terrain of impossible worlds. It is divided in six chapters. Chapter I outlines Lewis’ theory, the motivations for impossible worlds, 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 impossible worlds 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 impossible worlds into GR. Chapter III explores GR-friendly impossible worlds in the form of set-theoretic constructions out of genuine possibilia. Then, Chapters IV-VI venture into concrete impossible worlds. Chapter IV addresses Lewis’ objection against such worlds, to the effect that contradictions true at impossible worlds 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 impossible worlds 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 impossible worlds. (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)

The development of possible worlds semantics for modal claims has led to a more general application of that theory as a complete semantics for various formal and natural languages, and this view is widely held to be an adequate (philosophical) interpretation of the model theory for such languages. We argue here that this view generates a self-referential inconsistency that indicates either the falsity or the incompleteness of PWS.

“There are no gaps in logical space,” David Lewis writes, giving voice to sentiment shared by many philosophers. But different natural ways of trying to make this sentiment precise turn out to conflict with one another. One is a *pattern* idea: “Any pattern of instantiation is metaphysically possible.” Another is a *cut and paste* idea: “For any objects in any worlds, there exists a world that contains any number of duplicates of all of those objects.” We use resources (...) from model theory to show the inconsistency of certain packages of combinatorial principles and the consistency of others. (shrink)