_Possible Worlds_ presents the first up-to-date and comprehensive examination of one of the most important topics in metaphysics. John Divers considers the prevalent philosophical positions, including realism, antirealism and the work of important writers on possible worlds such as David Lewis, evaluating them in detail.

The most commonly heard proposals for reducing possible worlds to language succumb to a simple cardinality argument: it can be shown that there are more possible worlds than there are linguistic entities provided by the proposal. In this paper, I show how the standard proposals can be generalized in a natural way so as to make better use of the resources available to them, and thereby circumvent the cardinality argument. Once it is seen just what the (...) limitations are on these more general proposals, it can be clearly seen where the real difficulty lies with any attempt to reduce possible worlds to language. Roughly, the difficulty is this: no actual language could have the descriptive resources needed to represent all the ways things might have been. I conclude by arguing that this same difficulty spells doom for any nominalist or conceptualist proposal for reducing possible worlds. (shrink)

As part of an ongoing study of causal models in the history of science, a counterfactual scenario in the history of modern astronomy is explored with the aid of computer simulations. After the definition of “linking advance”, a possible world involving technological antecedence is described, branching out in 1510, in which the telescope is invented 70 years before its actual construction, at the time in which Fracastoro actually built the first prototelescope. By using the principle of the closest (...) class='Hi'>possible world, we estimate that in this scenario the discovery of the elliptical orbit of Mars would by anticipated by only 28 years. The second part of the paper involves an estimate of the probability of the previous scenario, guided by the principle that the actual world is the mean and using computer simulations to create possible worlds in which the time spans between advances is varied according to a gamma distribution function. Taking into account the importance of the use of the diaphragm for the invention of the telescope, the probability that the telescope were built by 1538 for a branching time at 1510 is found to be smaller than 1%. The work shows that one of the important features of computational simulations in philosophy of science is to serve as a consistency check for the intuitions and speculations of the philosopher. (shrink)

In the logic of theory change, the standard model is AGM, proposed by Alchourrón et al. (J Symb Log 50:510–530, 1985 ). This paper focuses on the extension of AGM that accounts for contractions of a theory by a set of sentences instead of only by a single sentence. Hansson (Theoria 55:114–132, 1989 ), Fuhrmann and Hansson (J Logic Lang Inf 3:39–74, 1994 ) generalized Partial Meet Contraction to the case of contractions by (possibly non-singleton) sets of sentences. In this (...) paper we present the possible worlds semantics for partial meet multiple contractions. (shrink)

Providing a possible worlds semantics for a logic involves choosing a class of possible worlds models, and setting up a truth definition connecting formulas of the logic with statements about these models. This scheme is so flexible that a danger arises: perhaps, any (reasonable) logic whatsoever can be modelled in this way. Thus, the enterprise would lose its essential tension. Fortunately, it may be shown that the so-called incompleteness-examples from modal logic resist possible worlds (...) modelling, even in the above wider sense. More systematically, we investigate the interplay of truth definitions and model conditions, proving a preservation theorem characterizing those types of truth definition which generate the minimal modal logic. (shrink)

This paper is about possible worlds semantics for propositional attitude sentences. In particular I shall focus on belief reports in English such as "Lusina believes that tofu is nutritious." It is well-known that possible worlds semantics for such reports suffers from the so-called _problem of equivalence_ . In this paper I shall examine some attempts to deal with this problem and argue that they are unsatisfactory.

The canonical version of possible worlds semantics for story prefixes is due to David Lewis. This paper reassesses Lewis's theory and draws attention to some novel problems for his account.

The numerous difficulties facing the traditional Humean regularity approach to the problem of causation have been discussed in the literature at great length. In view of the current interest in possible worlds semantics, it is not surprising that the only serious alternative treatment of causation presently available, the counterfactual approach, has been explored recently as a means of circumventing the apparently unresolvable difficulties facing regularity causal theories. It is the purpose of this paper to suggest that such a (...) strategy holds little promise. Specifically, I will argue that, in addition to giving rise to problems directly analogous to those facing regularity accounts, the counterfactual approach fails in principle to reflect important properties of causal relations as we understand them intuitively. David Lewis's possible worlds account, the most comprehensive counterfactual theory to date, is further criticized for implicit problems with natural lawhood even more serious than those typically raised for regularity accounts, for additional inadequacies in its analysis of causal relations, and for its failure to satisfy basic empiricist epistemological standards. (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)

If □ is conceived as an operator, i.e., an expression that gives applied to a formula another formula, the expressive power of the language is severely restricted when compared to a language where □ is conceived as a predicate, i.e., an expression that yields a formula if it is applied to a term. This consideration favours the predicate approach. The predicate view, however, is threatened mainly by two problems: Some obvious predicate systems are inconsistent, and possible-worlds semantics for (...) predicates of sentences has not been developed very far. By introducing possible-worlds semantics for the language of arithmetic plus the unary predicate □, we tackle both problems. Given a frame (W, R) consisting of a set W of worlds and a binary relation R on W, we investigate whether we can interpret □ at every world in such a way that □ $\ulcorner A \ulcorner$ holds at a world ᵆ ∊ W if and only if A holds at every world $\upsilon$ ∊ W such that ᵆR $\upsilon$ . The arithmetical vocabulary is interpreted by the standard model at every world. Several 'paradoxes' (like Montague's Theorem, Gödel's Second Incompleteness Theorem, McGee's Theorem on the ω-inconsistency of certain truth theories, etc.) show that many frames, e.g., reflexive frames, do not allow for such an interpretation. We present sufficient and necessary conditions for the existence of a suitable interpretation of □ at any world. Sound and complete semi-formal systems, corresponding to the modal systems K and K4, for the class of all possible-worlds models for predicates and all transitive possible-worlds models are presented. We apply our account also to nonstandard models of arithmetic and other languages than the language of arithmetic. (shrink)

The role of possible worlds in philosophy is hard to overestimate. Nevertheless, their nature and existence is very controversial. This is particularly serious, since their standard applications depend on there being sufficiently many of them. The paper develops an account of possible worlds on which it is particularly easy to believe in their existence: an account of possible worlds as pleonastic entities. Pleonastic entities are entities whose existence can be validly inferred from statements that (...) neither refer to nor quantify over them as a matter of conceptual necessity. Definitions are proposed that ensure that this is the case for possible worlds. (shrink)

We show that, given standard assumptions about classical dynamical systems, Lewis' conception of possible worlds is incompatible with classical physics in that it would imply that all dynamical systems were integrable.

This article includes a basic overview of possible world semantics and a relatively comprehensive overview of three central philosophical conceptions of possible worlds: Concretism (represented chiefly by Lewis), Abstractionism (represented chiefly by Plantinga), and Combinatorialism (represented chiefly by Armstrong).

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)

Over a longer period than I sometimes care to contemplate I have worked on possible-worlds semantics. The earliest work was in modal logic, to which I keep returning, but a sabbatical in 1970 took me to UCLA, there to discover the work of Richard Montague in applying possible-worlds semantics to natural lan guage. My own version of this appeared in Cresswell (1973) and was followed up in a number of articles, most of which were collected in (...) Cresswell (1985b). A central problem for possible worlds semantics is how to accommodate propositional attitudes. This problem was addressed in Cresswell (1985a), and the three books mentioned so far represent a reasonably complete picture of my positive views on formal semantics. I have regarded the presentation of a positive view as more important than the criticism of alternatives, although the works referred to do contain many passages in which I have tried to defend my own views against those of others. But such criticism is important in that a crucial element in establishing the content of a theory is that we be able to evaluate it in relation to its com petitors. It is for that reason that I have collected in this volume a number of articles in which I attempt to defend the positive semantical picture I favour against objections and competing theories. (shrink)

“The Craft of Formal Logic” is Arthur Prior’s unpublished textbook, written in 1950–51, in which he developed a theory of modality as quantification over possible worlds-like objects. This theory predates most of the prominent pioneering texts in possible worlds semantics and anticipates the significance of its basic concept in modal logic. Prior explicitly defines modal operators as quantifiers of ‘entities’ with modal character. Although he talks about these ‘entities’ only informally, and hesitates how to name them, (...) using alternately the phrases ‘possible states of affairs’, ‘chances’, ‘cases’ or ‘peculiar objects’, he is nevertheless very clear that they should be the fundamental concept of any theory of modality as a form of quantity. Without the assumption that modal operators quantify over such modal objects, the modal system will be incapable of distinguishing an actually true proposition from a necessarily true one. Due to the fact that Prior never made any direct reference to this theory in his subsequently published papers, it remained largely unknown. The comparison of “The Craft” with some of his papers on tense logic suggests that this early theory of modality underlies his later work on temporality. (shrink)

David Lewis' modal counterpart theory falls prey to the famous Saul Kripke's objection, and this is mostly due to his 'static' ontology (divergence) of possible worlds. This paper examines a genuinely realist but different, branching ontology of possible worlds and a new definition of the counterpart relation, which attempts to provide us with a better account of de re modality, and to meet satisfactorily Kripke's claim, while being also ontologically more 'parsimonious'.

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)

Most compatibilists have sought to defend their view by means of an analysis of the concept of ‘can’ in terms of subjunctive conditionals. Keith Lehrer opposes this analysis; he nevertheless embraces compatibilism. In a recent paper he has proposed a novel analysis of the concept of ‘can’ within the framework of possible-world semantics. The paper has provoked considerable discussion. In it Lehrer claims that he demonstrates the truth of compatibilism. Others have claimed that this is not so, but at (...) least one commentator has asserted that Lehrer's analysis strongly supports compatibilism. In this section I shall give a brief exposition of relevant portions of Lehrer's account of ‘can’ and then in the next section I shall seek to show that it fails to render compatibilism any more plausible than incompatibilism. Indeed, I shall seek to show that, if one of Lehrer's primitive concepts is understood as it seems it should be understood, then there would seem to be good reason to believe that his analysis supports not compatibilism but incompatibilism. (shrink)

Conditional structures lie at the heart of the sciences, humanities, and everyday reasoning. It is hence not surprising that conditional logics – logics specifically designed to account for natural language conditionals – are an active and interdisciplinary area. The present book gives a formal and a philosophical account of indicative and counterfactual conditionals in terms of Chellas-Segerberg semantics. For that purpose a range of topics are discussed such as Bennett’s arguments against truth value based semantics for indicative conditionals.

It is difficult to wander far in contemporary metaphysics without bumping into talk of possible worlds. And, reference to possible worlds is not confined to metaphysics. It can be found in contemporary epistemology and ethics, and has even made its way into linguistics and decision theory. What are those possible worlds, the entities to which theorists in these disciplines all appeal? Some have hoped that a theory of possible worlds can be used (...) to reduce modality to non-modal terms. This paper sets reductive theories aside, and articulates and applies a framework for evaluating non-reductive theories of possible worlds. I argue that, if we abjure reduction, we should aim for a theory of possible worlds that is user-friendly. I then outline four leading contemporary theories and consider objections to each. My conclusions are negative: every theory we discuss fails to be user-friendly in some significant respect. (shrink)

... 112 ROBERT STALNAKER example Alvin Plantinga and Robert Adams) define possible worlds in terms of states of affairs or propositions ; others (for example Max Cresswell) use a strategy quite similar to that of situation semantics, defining possible worlds as constructs out of ..

The question as to whether some objects are possible worlds that have an initial segment in common, i.e. so that their fusion is a temporal tree whose branches are possible worlds, arises both for those who hold that our universe has the structure of a temporal tree and for those who hold that what there is includes concrete universes of every possible variety. The notion of “possible world” employed in the question is seen to (...) be the notion of an object of a kind such that objects of that kind play a certain theoretical role. Lewis’s discussion of the question is thereby clarified but is nevertheless inadequate; his negative answer is correct but even from his combinatorialist viewpoint the rationale he provides for this answer is misguided. I explain why the combinatorialist advocate of concrete plenitude should hold that no object is a tree of possible worlds. Then I explain that for a different reason the nomic essentialist advocate of concrete plenitude should hold this much too. (shrink)

Those who object to David Lewis' modal realism express qualms about philosophical respectability of the Lewisian notion of a possible world and its correlate notion of an inhabitant of a possible world. The resulting impression is that these two notions either stand together or fall together. I argue that the Lewisian notion of a possible world is otiose even for a good Lewisian modal realist, and that one can carry out a good Lewisian semantics for modal discourse (...) without Lewisian possible worls. I do so by generalizing Lewis' own idea that restrictions on quantification come and go with the pragmatic wind and relativizing possible worlds as shifting domains of discourse. I then suggest a way to soften the infamous incredulous stare. (shrink)

When we watch movies, or are tricked by a trompe-l'oeil painting, we seem to be visually representing possible worlds; often non-actual possible worlds. This suggests that we really can visually represent possible worlds. The suggested claim is refined and developed here into a theory of visual experience that holds that all visual experiences, both veridical and non-veridical, represent possible worlds, many of which are non-actual.

A very common twofold view in contemporary philosophy is that classical logic is the correct view of logical consequence and that possibility conforms to classical logic in the sense that ‘possible worlds’ — whatever else they may be — are closed under classical logic. These two views are assumed in this paper. My aim in this paper is to show that a very natural ‘paraconsistent’ consequence relation is involved in the given view of possible worlds and (...) logical consequence. (shrink)

In a recent article Mark Ian Thomas Robson argues that there is a clear contradiction between the view that possible worlds are a part of God's nature and the theologically pivotal, but philosophically neglected, claim that God is perfectly beautiful. In this article I show that Robson's argument depends on several key assumptions that he fails to justify and as such that there is reason to doubt the soundness of his argument. I also demonstrate that if Robson's argument (...) were sound then this would be a problem for all classical theists and not just those who hold the possible worlds view. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Possible Worlds in the Tahâfut al-tahâfut:Averroes on Plenitude and PossibilityTaneli Kukkonen1.It has become customary to credit John Duns Scotus with having first systematically laid out the basis for treating the modal terms as referring to synchronic alternative states of affairs. This has been viewed as constituting a genuine shift in modal paradigms, as no former model had included the idea of genuine synchronic alternative possibilities. Historians of (...) modal logic and contemporary logicians alike have found it interesting that certain key features of Duns Scotus's theory and subsequent late medieval work markedly resemble the so-called possible worlds semantics approach of modern modal theory.1Duns Scotus' innovations were not completely without precedent. Several key elements in Scotus' theory were foreshadowed by twelfth-century developments. Perhaps somewhat amusingly, one of the most important forerunners to the Latin discussion was one in whose context the expression "possible worlds" would have made sense in a very special way.2 This is the medieval Arabic debate on the eternity of the world and its modal status. In this paper I propose to take stock of the positions the Arabs reached, and to do so by way of [End Page 329] consulting one of the documents central to the debate, the Tahâfut al-tahâfut or the "Incoherence of the Incoherence," by Abû al-Walîd Ibn Rushd (the Latin "Averroes," 1126-1198). In the first part I examine Averroes' exposition of the received Aristotelian tradition; in the second I assess the revisions to modal theory suggested by al-Ghazâlî (1058-1111), in the latter's comprehensive critique of philosophical doctrine. Though the two inquiries are obviously complementary, they can be accomplished independently of each other.It will be seen that Averroes' and his formidable adversary's views on the interpretation of the modal concepts differ quite fundamentally. What makes the ensuing debate, often fraught with misunderstandings and misrepresentation, so engaging is that both parties, in spite of their differences, refer to a common Aristotelian backdrop in questions of terminology and mode of argumentation. Both Averroes and al-Ghazâlî are well-placed to present a considered and balanced account of what they take to be crucial in the issues involved. It is on account of this that the complex interplay between the old and the new comes to the fore with exceptional force and clarity in the Tahâfut debates.2.The Tahâfut al-tahâfut, first published in 1180, is a philosophical rejoinder to an attack on philosophy, Abû Hâmid al-Ghazâlî's Tahâfut al-falâsifa or "The Incoherence of the Philosophers" (1095). In that celebrated work al-Ghazâlî had claimed to expose certain philosophical doctrines as not only contrary to orthodox Muslim belief, but also internally incoherent.3 Averroes' reply in turn was written in order "to show the different degrees of assent and conviction attained by the assertions in The Incoherence of the Philosophers, and to prove that the greater part has not reached the degree of evidence and of truth."4 The work is thus of a doubly dialectical nature. Whereas al-Ghazâlî tries to show the philosophers' reasoning to be defective, Averroes has to show both that al-Ghazâlî is likewise lacking in intellectual rigor and that philosophy, properly understood, is innocent of the charges leveled at it. If the Islamic philosophers (al-Fârâbî and, above all, Avicenna) have in fact erred, this is only to the extent that they have misrepresented correct Aristotelian doctrine. [End Page 330]Averroes' presentation is appropriately delicate considering the complexity of the task at hand. Averroes quotes al-Ghazâlî exclusively in full, lengthy passages, with the result of incorporating almost all of the Tahâfut al-falâsifa in his own work. In so doing he gives us an adequate and comparably fair representation of al-Ghazâlî's views. Averroes then goes on to discuss what al-Ghazâlî says both in the philosophers' name and in his own, and points out their respective deviations from Aristotelian doctrine. The text thus comes laid out in three successive layers, with Averroes' own... (shrink)

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)

God is traditionally taken to be a perfect being, and the creator and sustainer of all that is. So, if theism is true, what sort of world should we expect? To answer this question, we need an account of the array of possible worlds from which God is said to choose. It seems that either there is (a) exactly one best possible world; or (b) more than one unsurpassable world; or (c) an infinite hierarchy of increasingly better (...) worlds. Influential arguments for atheism have been advanced on each hierarchy, and these jointly comprise a daunting trilemma for theism. In this paper, I argue that if theism is true, we should expect the actual world to be a multiverse comprised of all and only those universes which are worthy of creation and sustenance. I further argue that this multiverse is the unique best of all possible worlds. Finally, I explain how his unconventional view bears on the trilemma for theism. (shrink)

The goal of theodicy is to show how God could create our world with all its evil. This paper argues that the theodicist can achieve her goal only if she gives up one of these three propositions: (1) evil does not exist in heaven; (2) heaven is better than the present world; (3) heaven is a possible world. Second, it is argued that the theodicist can reject (3) without giving up her belief that heaven exists, so that (3) is (...) her best alternative. (shrink)

In the paper we will study the notions of possible-worlds semantics, fiction, and creativity. The intention is to show how the notion of possible-worlds semantics allows us to generate a fresh interpretation of the notions of fiction and creativity. To do this, we have to consider the philosophy of logic. Possible-worlds semantics can be used in interpreting modal notions. The intention is to interpret the notions of fiction and creativity as modal notions. However, the (...) analysis shows that the notions of fiction and creativity are multimodal notions. (shrink)

Alvin Plantinga’s solution to J. L. Mackie’s logical problem of evil invokes possible-worlds metaphysics. There are reasons for thinking that the solution is, at least, problematic. Difficulties emerge in the attempts to answer four related questions. (1) Can God’s necessary existence, understood in terms of possible-world metaphysics, make God’s actual existence impossible to explain? (2) Can an omniscient being with knowledge of the contents of every possible world (a being endowed with “middle knowledge”) prove ignorant of (...) the consequences of his creative acts? (3) Can an immoral action performed by an agent suffering from “transworld depravity” also be free in the libertarian sense? (4) Does the possible-worlds interpretation of libertarian freedom generate a vicious infinite regress? Special focus is on the possibility, advanced by Plantinga, that there are possible worlds that even an omnipotent being cannot create. Plantinga’s views are contrasted with those of Thomas Aquinas. (shrink)

I outline a neo-Fregean strategy in the debate on the existence of possible worlds. The criterion of identity and the criterion of application are formulated. Special attention is paid to the fact that speakers do not possess proper names for worlds. A broadly Quinean solution is proposed in response to this difficulty.

This article explores four crucial problems regarding wu 無 (nothingness or nonexistence), a central concept in Chinese philosophy: (1) What is wu, and how does it relate to you 有 (somethingness or existence)? (2) Does ‘you arise from wu’ (you sheng yu wu 有生於無), and if so, how does this ‘arising’ occur? (3) Which takes precedence in Chinese philosophy, wu or you? (4) Does pursuing wu risk leading to nihilism? Drawing on Saul Kripke’s interpretation of possible worlds, I (...) propose that wu represents a realm of potential possibilities. I align with Kripke’s view that possible worlds lack actual existence but are anchored in the actual world. This view clarifies the seemingly paradoxical nature of Chinese philosophy: it is rooted in the mundane world while embracing a transcendental wu. Moreover, it helps avoid the nihilism that might arise from interpreting wu as a groundless void. (shrink)

Possible-worlds talk obscures, rather than clarifies, the debate about haecceitism. In this paper I distinguish haecceitism and anti-haecceitism from other doctrines that sometimes go under those names. Then I defend the claim that there are no non-tendentious definitions of ‘haecceitism’ and ‘anti-haecceitism’ using possible-worlds talk. That is, any definition of ‘haecceitism’ using possible-worlds talk depends, for its correctness, on a substantive theory of the nature of possible worlds. This explains why using (...) class='Hi'>possible-worlds talk when discussing haecceitism causes confusion: if the parties to the discussion presuppose different theories of the nature of possible worlds, then they will mean different things by ‘haecceitism’. (shrink)

The sensitivity account of knowledge is a modal epistemology, according to which S knows that p only if S's belief in p is sensitive in the sense that S would not believe that p if p were false. There are different ways to state the sensitivity condition by means of a possible worlds heuristic. The sensitivity account is thus rendered into different versions. This paper examines cases of knowledge and cases of luckily true beliefs (e.g., the Gettier cases) (...) and argues that no version of the sensitivity account accommodates all cases. Therefore, the account is unsuccessful as an account of knowledge. (shrink)

A prominent contemporary anti-skeptical strategy, most famously articulated by Keith DeRose, aims to cage the skeptic′s doubts by contextualizing subjunctive conditional accounts of knowledge through a conversational rule of sensitivity. This strategy, I argue, courts charges of circularity by selectively invoking heavy counterfactual machinery. The reason: such invocation threatens to utilize a metric for modal comparison that is implicitly informed by judgments of epistemic sameness. This gives us reason to fear that said modal metric is selectively cherry-picked in advance to (...) support the very anti-skeptical conclusion for which the contextualist longs. (shrink)

I rest this unusual claim on the ground of a metaphysics that is at odds with the metaphysical viewpoint implied in the theories of possible worlds. I suggest a different and, I think, superior way of conceiving the world, experience, and what we mean by possibility.

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.

Formalized physical theories are not, as a rule, stated in intensional languages. Yet in talking about them we often treat them as if they were. We say for instance: 'Consider what would happen if instead of p's being true q were. In such a case r would be likely.' If we say this sort of thing, p, q and r appear to stand for the meanings of sentences of the theory, but meanings in some intensional sense. Now it is very (...) easy to extend the syntax of the formal theory by adding all sorts of intensional operators, e.g. a modal operator; and it is possible to extend the semantics by adding a set of possible worlds and evaluating the modal formulae in the usual way. But this procedure is open to the criticism that we are extending the theory by adding something which is not already there. In particular the criticism will be that the possible worlds required by the semantics seem to have no connection with the intended interpretations of the original physical theory. The aim of this paper is to shew how a set of possible worlds is already implicit in the intended interpretations of a formally presented physical theory and that these interpretations induce, in a comparatively direct way, an intensional semantics which corresponds to the original one. (shrink)

This paper is predicated on the idea that some modal operators are better understood as quantificational expressions over worlds that determine not only first-order facts but modal facts also. In what follows, we will present a framework in which these two types of facts are brought closer together. Structural features will be located in the worlds themselves. This result will be achieved by decomposing worlds into parts, where some of these parts will have “modal import” in the (...) sense that they will determine structure on other worldly parts. The main upshot of this will be a clearer grasp of the interaction between modal notions. (shrink)

A possible worlds treatment of the normal alethic modalities was, after classical model theory, logic’s most significant semantic achievement in the century just past.[1] Kripke’s groundbreaking paper appeared in 1959 and, in the scant few succeeding years, its principal analytical tool, possible worlds, was adapted to serve a range of quite different-seeming purposes – from nonnormal logics,[2] to epistemic and doxastic logics[3], deontic[4] and temporal logics[5] and, not much later, the logic of counterfactual conditionals.[6] In short (...) order, possible worlds acquired a twofold reputation which has steadily enlarged to the present day. They were celebrated for both their mathematical power and their sheer versatility. This sets the stage for what I want to do here. I wish to explore the extent to which the supposed versatility of a possible worlds semantics is justified. In so doing, I shall confine my attention to its role in (1) logics of counterfactual conditionals, and (2) logics of belief. The question I pose is, why and on what grounds should we think that the device of possible worlds turns the semantic trick for these logics? My answer is that they do not turn the trick for them. Whereupon a further question presses for attention. If possible worlds semantics don’t work there, why does virtually everyone think that they do? Answering this second question is risky. Who am I to say why virtually everyone thinks that the possible worlds approach is more successful than I do? Who has vouchsafed me these powers? I shall try to mitigate the riskiness of my answer by contextualizing the evaluation of this approach in the following ways. First, the triumph of possible worlds occurred in the midst of a powerful general trend in logical theory, especially, in the past 60 years. In that period, logical theory became aggressively and widely pluralistic. Second, the versatility – the sheer ubiquity – of possible worlds as a tool of semantic and philosophical analysis, gives to possible worlds a kind of hegemonic standing.. (shrink)

If a possible-worlds semantic theory for modal logics is pure, then the assertion of the theory, taken at face-value, can bring no commitment to the existence of a plurality of possible worlds (genuine or ersatz). But if we consider an applied theory (an application of the pure theory) in which the elements of the models are required to be possible worlds, then assertion of such a theory, taken at face-value, does appear to bring commitment (...) to the existence of a plurality of possible worlds. Or at least that is so if the applied theory is adequate. For an applied possible-worlds semantic theory that is constrained to contain only one-world models is bound to deliver results on validity, soundness and completeness that are apt to seem disastrous. I attempt to steer a course between commitment to the existence of a plurality of possible worlds and commitment to such a disastrous applied possible-worlds semantics by noting, and developing, the position of one who asserts such a theory at face-value but who remains agnostic about the existence of other (non-actualized) possible worlds. Thus, a novel interpretation of applied possible-worlds semantics is offered on which we may lay claim to whatever benefits such a theory offers while avoiding realism about (other) possible worlds. Thereby, the contention that applied possible-worlds semantics gives us reason to be realists about possible worlds is (further) undermined. (shrink)